From 89815d0bc2451c0fd932a4bd34459d85de13199b Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 12 Jun 2023 13:35:51 +0200 Subject: [PATCH 01/48] Paper draft for JOSS --- paper/paper.bib | 343 ++++++++++++++++++++++++++++++++++++++++++++++++ paper/paper.md | 74 +++++++++++ 2 files changed, 417 insertions(+) create mode 100644 paper/paper.bib create mode 100644 paper/paper.md diff --git a/paper/paper.bib b/paper/paper.bib new file mode 100644 index 00000000..0e07ccef --- /dev/null +++ b/paper/paper.bib @@ -0,0 +1,343 @@ +@article{Togo2018, + author = {Atsushi Togo and Isao Tanaka}, + eid = {arXiv:1808.01590}, + eprint = {1808.01590}, + eprintclass = {cond-mat.mtrl-sci}, + eprinttype = {arXiv}, + journaltitle = {arXiv e-prints}, + pages = {arXiv:1808.01590}, + title = {Spglib: a software library for crystal symmetry search}, + year = {2018}, +} + +@article{Knoop2020, + title = {Anharmonicity measure for materials}, + author = {Knoop, Florian and Purcell, Thomas A. R. and Scheffler, Matthias and Carbogno, Christian}, + journal = {Phys. Rev. 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W. +and Nardelli, Marco Buongiorno +and Mingo, Natalio +and Sanvito, Stefano +and Levy, Ohad}, +title={The high-throughput highway to computational materials design}, +journal={Nature Materials}, +year={2013}, +volume={12}, +number={3}, +pages={191-201}, +issn={1476-4660}, +doi={10.1038/nmat3568}, +url={https://doi.org/10.1038/nmat3568} +} + +@article{Parlinski1997, +author = {Parlinski, K. and Li, Z. and Kawazoe, Y.}, +doi = {10.1103/PhysRevLett.78.4063}, +journal = {Phys. Rev. Lett.}, +number = {21}, +pages = {4063--4066}, +title = {{First-Principles Determination of the Soft Mode in Cubic ZrO2}}, +volume = {78}, +year = {1997} +} + +@article{Carbogno2016, +author = {Carbogno, Christian and Ramprasad, Rampi and Scheffler, Matthias}, +doi = {10.1103/PhysRevLett.118.175901}, +issn = {0031-9007}, +journal = {Phys. Rev. Lett.}, +number = {175901}, +pages = {1--5}, +title = {{Ab initio Green-Kubo Approach for the Thermal Conductivity of Solids}}, +volume = {118}, +year = {2017} +} + +@article{Eriksson2019, +author = {Eriksson, Fredrik and Fransson, Erik and Erhart, Paul}, +doi = {10.1002/adts.201800184}, +journal = {Adv. Theor. Simul.}, +number = {5}, +pages = {1800184}, +title = {{The Hiphive Package for the Extraction of High‐Order Force Constants by Machine Learning}}, +volume = {2}, +year = {2019} +} + +@article{Tian2019, +abstract = {Modern first-principles calculations predict that the thermal conductivity of boron arsenide is second only to that of diamond, the best thermal conductor, which may be of benefit for waste heat management in electronic devices. With the optimization of single-crystal growth methods, large-size and high-quality boron arsenide single crystals have been grown and thermal conductivity measurements have verified the related predictions. Benefiting from the increased size and improved qualities, additional properties have been characterized. Important factors related to boron arsenide, remaining challenges, and the future outlook are addressed in this minireview.}, +author = {Tian, Fei and Ren, Zhifeng}, +doi = {10.1002/anie.201812112}, +issn = {15213773}, +journal = {Angewandte Chemie - International Edition}, +keywords = {III–V compounds,boron arsenide,crystal growth,semiconductors,thermal conductivity}, +month = {apr}, +number = {18}, +pages = {5824--5831}, +pmid = {30523650}, +publisher = {Wiley-VCH Verlag}, +title = {{High Thermal Conductivity in Boron Arsenide: From Prediction to Reality}}, +url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201812112}, +volume = {58}, +year = {2019} +} + + +@article{Salzillo2016, +abstract = {Raman microscopy in the lattice phonon region coupled with X-ray diffraction have been used to study the polymorphism in crystals and microcrystals of the organic semiconductor 9,10-diphenylanthracene (DPA) obtained by various methods. While solution grown specimens all display the well-known monoclinic structure widely reported in the literature, by varying the growth conditions two more polymorphs have been obtained, either from the melt or by sublimation. By injecting water as a nonsolvent in a DPA solution, one of the two new polymorphs was predominantly obtained in the shape of microribbons. Lattice energy calculations allow us to assess the relative thermodynamic stability of the polymorphs and verify that the energies of the different phases are very sensitive to the details of the molecular geometry adopted in the solid state. The mobility channels of DPA polymorphs are shortly investigated.}, +author = {Salzillo, Tommaso and {Della Valle}, Raffaele Guido and Venuti, Elisabetta and Brillante, Aldo and Siegrist, Theo and Masino, Matteo and Mezzadri, Francesco and Girlando, Alberto}, +doi = {10.1021/acs.jpcc.5b11115}, +file = {:home/purcell/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Salzillo et al. - 2016 - Two New Polymorphs of the Organic Semiconductor 9,10-Diphenylanthracene Raman and X-ray Analysis.pdf:pdf}, +issn = {19327455}, +journal = {Journal of Physical Chemistry C}, +number = {3}, +pages = {1831--1840}, +publisher = {UTC}, +title = {{Two new polymorphs of the organic semiconductor 9,10-diphenylanthracene: Raman and X-ray analysis}}, +url = {https://pubs.acs.org/sharingguidelines}, +volume = {120}, +year = {2016} +} + +@article{Snyder2008, +abstract = {Thermoelectric materials, which can generate electricity from waste heat or be used as solid-state Peltier coolers, could play an important role in a global sustainable energy solution. Such a development is contingent on identifying materials with higher thermoelectric efficiency than available at present, which is a challenge owing to the conflicting combination of material traits that are required. Nevertheless, because of modern synthesis and characterization techniques, particularly for nanoscale materials, a new era of complex thermoelectric materials is approaching. We review recent advances in the field, highlighting the strategies used to improve the thermopower and reduce the thermal conductivity.}, +author = {Snyder, G. Jeffrey and Toberer, Eric S.}, +doi = {10.1038/nmat2090}, +issn = {14761122}, +journal = {Nature Materials}, +keywords = {Biomaterials,Condensed Matter Physics,Materials Science,Nanotechnology,Optical and Electronic Materials,general}, +month = {feb}, +number = {2}, +pages = {105--114}, +pmid = {18219332}, +publisher = {Nature Publishing Group}, +title = {{Complex thermoelectric materials}}, +url = {www.nature.com/naturematerials}, +volume = {7}, +year = {2008} +} + +@article{Evans2008, +author = {Evans, AG and Clarke, DR and Levi, CG}, +title = {{The influence of oxides on the performance of advanced gas turbines}}, +journal = {J. Eur. Ceram. Soc.}, +year = {2008}, +volume = {28}, +number = {7}, +pages = {1405--1419}, +doi = {10.1016/j.jeurceramsoc.2007.12.023} +} + +@article{West2006, +author = {West, D. and Estreicher, S. K.}, +doi = {10.1103/PhysRevLett.96.115504}, +journal = {Phys. Rev. Lett.}, +number = {11}, +pages = {22--25}, +pmid = {16605840}, +title = {{First-principles calculations of vibrational lifetimes and decay channels: Hydrogen-related modes in Si}}, +volume = {96}, +year = {2006} +} + +@article{Turney2009, +author = {Turney, JE and Landry, ES and McGaughey, AJH and Amon, CH}, +title = {{Predicting phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations}}, +journal = {Phys. Rev. B}, +year = {2009}, +volume = {79}, +number = {6}, +pages = {64301}, +doi = {10.1103/physrevb.79.064301} + +} + +@article{Gonze2020, + Author = "Gonze, Xavier and Amadon, Bernard and Antonius, Gabriel and Arnardi, Frédéric and Baguet, Lucas and Beuken, Jean-Michel and Bieder, Jordan and Bottin, François and Bouchet, Johann and Bousquet, Eric and Brouwer, Nils and Bruneval, Fabien and Brunin, Guillaume and Cavignac, Théo and Charraud, Jean-Baptiste and Chen, Wei and Côté, Michel and Cottenier, Stefaan and Denier, Jules and Geneste, Grégory and Ghosez, Philippe and Giantomassi, Matteo and Gillet, Yannick and Gingras, Olivier and Hamann, Donald R. and Hautier, Geoffroy and He, Xu and Helbig, Nicole and Holzwarth, Natalie and Jia, Yongchao and Jollet, François and Lafargue-Dit-Hauret, William and Lejaeghere, Kurt and Marques, Miguel A. L. and Martin, Alexandre and Martins, Cyril and Miranda, Henrique P. C. and Naccarato, Francesco and Persson, Kristin and Petretto, Guido and Planes, Valentin and Pouillon, Yann and Prokhorenko, Sergei and Ricci, Fabio and Rignanese, Gian-Marco and Romero, Aldo H. and Schmitt, Michael Marcus and Torrent, Marc and van Setten, Michiel J. and Troeye, Benoit Van and Verstraete, Matthieu J. and Zérah, Gilles and Zwanziger, Josef W.", + Journal = "Comput. Phys. Commun.", + Pages = "107042", + Title = "The Abinit project: Impact, environment and recent developments", + Volume = "248", + Year = "2020", + url = "https://doi.org/10.1016/j.cpc.2019.107042" +} + +@article{Draxl2018, + doi = {10.1557/mrs.2018.208}, + url = {https://doi.org/10.1557/mrs.2018.208}, + year = {2018}, + month = sep, + publisher = {Cambridge University Press ({CUP})}, + volume = {43}, + number = {9}, + pages = {676--682}, + author = {Claudia Draxl and Matthias Scheffler}, + title = {{NOMAD}: The {FAIR} concept for big data-driven materials science}, + journal = {{MRS} Bulletin} +} + +@misc{AiiDA, +Author = {Sebastiaan. P. Huber and Spyros Zoupanos and Martin Uhrin and Leopold Talirz and Leonid Kahle and Rico Häuselmann and Dominik Gresch and Tiziano Müller and Aliaksandr V. Yakutovich and Casper W. Andersen and Francisco F. Ramirez and Carl S. Adorf and Fernando Gargiulo and Snehal Kumbhar and Elsa Passaro and Conrad Johnston and Andrius Merkys and Andrea Cepellotti and Nicolas Mounet and Nicola Marzari and Boris Kozinsky and Giovanni Pizzi}, +Title = {AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance}, +Year = {2020}, +Eprint = {arXiv:2003.12476}, +doi = {10.1038/s41597-020-00638-4}, +} + diff --git a/paper/paper.md b/paper/paper.md new file mode 100644 index 00000000..051e734b --- /dev/null +++ b/paper/paper.md @@ -0,0 +1,74 @@ +--- +title: "TDEP: Temperature Dependent Effective Potenials" +tags: + - Fortran + - Physics + - Phonons + - Temperature + - Anharmonicity + - Neutron spectroscopy +authors: + - name: Florian Knoop + orcid: 0000-0002-7132-039X + affiliation: 1 + - name: Igor Abrikosov + orcid: 0000-0001-7551-4717 + affiliation: 1 + - name: Sergei Simak + orcid: 0000-0002-1320-389X + affiliation: 1 + - name: Olle Hellman + orcid: 0000-0002-3453-2975 + affiliation: 2 +affiliations: + - name: Linköping University, Linköping, Sweden + index: 1 + - name: Weizmann Institute of Science, Rehovot, Israel + index: 2 +date: August 2023 +bibliography: paper.bib +--- + +# Introduction + +Many properties of materials are influenced by temperature, i.e., the vibrational motion of nuclei. + +expand + + +# Statement of need +- TDEP contains the reference implementation for the method of the same name +- Clean and rigorous implementation of physical symmetries and invariances +- Fast implementation in Fortran +- code-agnostic input/output files that are very simple to provide +- spectral response code + +# Features + +- `crystal_structure_info`: Symmetry analysis (seekpath?) + +- `generate_structure`: generate supercells for materials simulations (algorithm to find cubic-as-possible cells of target size) + +- `extract_forceconstants`: force constants fit obeying physical invariances for finite differences or effective force constants + +- `canonical_configuration`: harmonic Monte Carlo samples generator for classical and quantum distributions of nuclei + +- `phonon_dispersion_relations`: Calculate phonon dispersion relations and related harmonic thermodynamic properties + +- `thermal_conductivity`: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of anharmonicity + +- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts + + + +# Summary + +list + +cite examples where TDEP has been used + +# Acknowledgements +- SeRC +- VR grants + +# References From b9baecba91f08ec540aa464707e10181bdf000d3 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Wed, 13 Sep 2023 17:55:48 +0200 Subject: [PATCH 02/48] paper | Intro --- paper/paper.md | 16 +++++++++++++--- 1 file changed, 13 insertions(+), 3 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 051e734b..9acbadc5 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -31,12 +31,19 @@ bibliography: paper.bib # Introduction -Many properties of materials are influenced by temperature, i.e., the vibrational motion of nuclei. +Properties of materials change with temperature, i.e., the vibrational motion of electrons and nuclei. In a static thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. -expand +In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtain temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics [cite Tuckerman]. + +The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. Based on this starting point, _anharmonic_ contributions are included by extending the harmonic reference Hamiltonian with terms that are cubic, quartic, and possibly higher-order in the displacements. These terms can be included via established perturbative techniques. However, as the complexity of the perturbative expansion grows very quickly with system size and perturbation order, this approach is limited to low-order corrections including the third, sometimes fourth order in practice. It follows that the lattice dynamics approach is _not_ formally exact, and a perfect quantitative agreement with experimental observables is not possible in principle. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can give _very good_ quantitative results, while providing _excellent_ qualitative microscopic insight into the physical mechanisms that drive certain phenomena as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made when describing the nuclear dynamics, but the _precision_ can be excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. + +The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve these lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. # Statement of need +The lattice dynamics model Hamiltonians can be constructed in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum positions, or in a temperature-dependent way by constructing _effective_ model Hamiltonians, which furthermore can be done _self-consistently_. A detailed conceptual comparison is given in Ref. [Castellano2023]. The motivation for TDEP derives from being able to describe systems at conditions where the Taylor expansion approach is invalid because the average atomic positions do _not_ coincide with minima of the potential energy. + +- - TDEP contains the reference implementation for the method of the same name - Clean and rigorous implementation of physical symmetries and invariances - Fast implementation in Fortran @@ -59,7 +66,10 @@ expand - `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts - + +## Overview of results + +- # Summary From 20cc4ab573eb082e6a225cef0425bc2d80a114e3 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 14 Sep 2023 15:21:17 +0200 Subject: [PATCH 03/48] paper | finish intro, add statement of need and summary --- paper/paper.md | 43 +++++++++++++++++++++++-------------------- 1 file changed, 23 insertions(+), 20 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 9acbadc5..6c7a7a1a 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -37,45 +37,48 @@ In _ab initio_ materials modeling, the electronic temperature contribution is st The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. Based on this starting point, _anharmonic_ contributions are included by extending the harmonic reference Hamiltonian with terms that are cubic, quartic, and possibly higher-order in the displacements. These terms can be included via established perturbative techniques. However, as the complexity of the perturbative expansion grows very quickly with system size and perturbation order, this approach is limited to low-order corrections including the third, sometimes fourth order in practice. It follows that the lattice dynamics approach is _not_ formally exact, and a perfect quantitative agreement with experimental observables is not possible in principle. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can give _very good_ quantitative results, while providing _excellent_ qualitative microscopic insight into the physical mechanisms that drive certain phenomena as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made when describing the nuclear dynamics, but the _precision_ can be excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. -The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve these lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. +The parameters in the lattice dynamics Hamiltonian, typically called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum positions, and idea that is more than a century old and traces back to Born and von Karman [CITE], or in a temperature-dependent way by constructing _effective_, renormalized model Hamiltonians in situation where the quadratic term in the Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [CITE deBoear1984], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [CITE ]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [CITE Klein1972]. + +The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve effective lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. # Statement of need -The lattice dynamics model Hamiltonians can be constructed in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum positions, or in a temperature-dependent way by constructing _effective_ model Hamiltonians, which furthermore can be done _self-consistently_. A detailed conceptual comparison is given in Ref. [Castellano2023]. The motivation for TDEP derives from being able to describe systems at conditions where the Taylor expansion approach is invalid because the average atomic positions do _not_ coincide with minima of the potential energy. +As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments evolve around finding practical ways of implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [CITE SCAILD/qSCAILD, SCHA/SSCHA, SCP/Alamode]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [cite Levy1984, Dove1986]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [cite Hellman2011, 2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [Shulumba2017, Benshalom2022]. + +While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants, typically third or third and fourth order [CITE Cowley, Hellman2013, ...]. These can be used to get better approximations to the free energy [CITE Wallace], describe thermal transport [CITE Broido, Romero], and linewidth broadening in spectroscopic experiments [CITE neutrons + Raman]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [CITE Castellano]. + +To extract force constants from thermal snapshots efficiently, TDEP employs the spacegroup symmetry of a given system to rigorously reduce the free parameters in the model to an irreducible set _before_ fitting the model parameters. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [cite Hellman2013b]. Furthermore, additional lattice dynamics sum rules such as acoustic (translational) and rotational invariances, as well the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [CITE BornHuang]. While TDEP was probably the first approach to exploit all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [CITE hiphive, Ponce]. -- -- TDEP contains the reference implementation for the method of the same name -- Clean and rigorous implementation of physical symmetries and invariances -- Fast implementation in Fortran -- code-agnostic input/output files that are very simple to provide -- spectral response code +TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both extracting force constants, as well as analyzing (effective) harmonic phonons and explicit anharmonic properties such as thermal transport and the full phonon spectral function across the Brillouin zone, from which spectroscopic properties can be obtained. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [CITE Benshalom]. -# Features +Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good supercell sizes, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. -- `crystal_structure_info`: Symmetry analysis (seekpath?) +Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, or self-documented HDF5 files for heavy data. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for higher-order force constants. -- `generate_structure`: generate supercells for materials simulations (algorithm to find cubic-as-possible cells of target size) +A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [CITE Ask], as well as processing and further analysis of TDEP output files is available as well [CITE tdeptools]. -- `extract_forceconstants`: force constants fit obeying physical invariances for finite differences or effective force constants +## Features -- `canonical_configuration`: harmonic Monte Carlo samples generator for classical and quantum distributions of nuclei +Here we list the most important codes that are shipped with the TDEP code and explain their purpose. Are more detailed explanation of all features can be found in the online documentation. -- `phonon_dispersion_relations`: Calculate phonon dispersion relations and related harmonic thermodynamic properties +- `extract_forceconstants`: Obtain force constants up to fourths order from a set of snapshots with positions and forces. -- `thermal_conductivity`: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of anharmonicity +- `phonon_dispersion_relations`: Calculate phonon dispersion relations and related harmonic thermodynamic properties from the second-order force constants. + +- `thermal_conductivity`: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of third-order anharmonicity. +- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone. +- `canonical_configuration`: Create supercells with thermal displacements from the force constants via Monte Carlo sampling from a classical and quantum canonical distribution. +- `generate_structure`: Generate supercells of target size that are as cubic as possible to maximize the largest possible real-space cutoff for the force constants. -- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts ## Overview of results -- +- some results? # Summary -list - -cite examples where TDEP has been used +The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name, which we have described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to a more in-depth discussion of the theory is given in the introduction. # Acknowledgements - SeRC From 23cca05d8b1d7af60fe626d6e30e0d2b3a13e6bb Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 14 Sep 2023 15:24:37 +0200 Subject: [PATCH 04/48] paper | add github action --- .github/workflows/draft-pdf.yml | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) create mode 100644 .github/workflows/draft-pdf.yml diff --git a/.github/workflows/draft-pdf.yml b/.github/workflows/draft-pdf.yml new file mode 100644 index 00000000..f85b711e --- /dev/null +++ b/.github/workflows/draft-pdf.yml @@ -0,0 +1,23 @@ +on: [push] + +jobs: + paper: + runs-on: ubuntu-latest + name: Paper Draft + steps: + - name: Checkout + uses: actions/checkout@v3 + - name: Build draft PDF + uses: openjournals/openjournals-draft-action@master + with: + journal: joss + # This should be the path to the paper within your repo. + paper-path: paper/paper.md + - name: Upload + uses: actions/upload-artifact@v1 + with: + name: paper + # This is the output path where Pandoc will write the compiled + # PDF. Note, this should be the same directory as the input + # paper.md + path: paper/paper.pdf From d56ca20e0aa68cf7f8f6a46904f3b728ffc2ae6b Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 14 Sep 2023 16:07:37 +0200 Subject: [PATCH 05/48] paper | minor update --- paper/paper.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 6c7a7a1a..5d109b09 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -35,25 +35,25 @@ Properties of materials change with temperature, i.e., the vibrational motion of In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtain temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics [cite Tuckerman]. -The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. Based on this starting point, _anharmonic_ contributions are included by extending the harmonic reference Hamiltonian with terms that are cubic, quartic, and possibly higher-order in the displacements. These terms can be included via established perturbative techniques. However, as the complexity of the perturbative expansion grows very quickly with system size and perturbation order, this approach is limited to low-order corrections including the third, sometimes fourth order in practice. It follows that the lattice dynamics approach is _not_ formally exact, and a perfect quantitative agreement with experimental observables is not possible in principle. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can give _very good_ quantitative results, while providing _excellent_ qualitative microscopic insight into the physical mechanisms that drive certain phenomena as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made when describing the nuclear dynamics, but the _precision_ can be excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. +The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. Based on this starting point, _anharmonic_ contributions are included by extending the harmonic reference Hamiltonian with terms that are cubic, quartic, and possibly higher-order in the displacements. These terms can be included via established perturbative techniques. However, as the complexity of the perturbative expansion grows very quickly with system size and perturbation order, this approach is limited to low-order corrections including the third, sometimes fourth order in practice. It follows that the lattice dynamics approach is _not_ formally exact, and a perfect quantitative agreement with experimental observables is not possible in principle. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can provide _excellent_ qualitative microscopic insight into the physical mechanisms that drive certain phenomena, and often even very good quantitative results, as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made when describing the nuclear dynamics, but the _precision_ can be excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. -The parameters in the lattice dynamics Hamiltonian, typically called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum positions, and idea that is more than a century old and traces back to Born and von Karman [CITE], or in a temperature-dependent way by constructing _effective_, renormalized model Hamiltonians in situation where the quadratic term in the Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [CITE deBoear1984], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [CITE ]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [CITE Klein1972]. - -The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve effective lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. +The parameters in the lattice dynamics Hamiltonian, typically called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [CITE]. Alternatively, temperature-dependent _effective_, renormalized model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [CITE deBoer1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [CITE Born, Hooton]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [CITE Klein1972]. # Statement of need +The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve temperature-dependent, effective lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. + As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments evolve around finding practical ways of implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [CITE SCAILD/qSCAILD, SCHA/SSCHA, SCP/Alamode]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [cite Levy1984, Dove1986]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [cite Hellman2011, 2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [Shulumba2017, Benshalom2022]. -While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants, typically third or third and fourth order [CITE Cowley, Hellman2013, ...]. These can be used to get better approximations to the free energy [CITE Wallace], describe thermal transport [CITE Broido, Romero], and linewidth broadening in spectroscopic experiments [CITE neutrons + Raman]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [CITE Castellano]. +While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants up to fourth order [CITE Cowley, Hellman2013, Feng2016 ...]. These can be used to get better approximations to the free energy [CITE Wallace], describe thermal transport [CITE Broido, Romero], and linewidth broadening in spectroscopic experiments [CITE neutrons + Raman]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [CITE Castellano]. To extract force constants from thermal snapshots efficiently, TDEP employs the spacegroup symmetry of a given system to rigorously reduce the free parameters in the model to an irreducible set _before_ fitting the model parameters. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [cite Hellman2013b]. Furthermore, additional lattice dynamics sum rules such as acoustic (translational) and rotational invariances, as well the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [CITE BornHuang]. While TDEP was probably the first approach to exploit all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [CITE hiphive, Ponce]. -TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both extracting force constants, as well as analyzing (effective) harmonic phonons and explicit anharmonic properties such as thermal transport and the full phonon spectral function across the Brillouin zone, from which spectroscopic properties can be obtained. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [CITE Benshalom]. +TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both extracting force constants, as well as analyzing (effective) harmonic phonons and explicit anharmonic properties such as thermal transport and the full phonon spectral function across the Brillouin zone, from which spectroscopic properties can be obtained. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [CITE Benshalom]. We highlight some applications and results below. Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good supercell sizes, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. -Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, or self-documented HDF5 files for heavy data. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for higher-order force constants. +Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readbale formats like csv, or self-documented HDF5 files for larger datasets. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for higher-order force constants. A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [CITE Ask], as well as processing and further analysis of TDEP output files is available as well [CITE tdeptools]. From 584ba979ed677b0dbb3b34d2c2dd39f753ace381 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 14 Sep 2023 16:48:00 +0200 Subject: [PATCH 06/48] paper | shorten --- paper/paper.md | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 5d109b09..3ee2c4f0 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -35,9 +35,9 @@ Properties of materials change with temperature, i.e., the vibrational motion of In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtain temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics [cite Tuckerman]. -The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. Based on this starting point, _anharmonic_ contributions are included by extending the harmonic reference Hamiltonian with terms that are cubic, quartic, and possibly higher-order in the displacements. These terms can be included via established perturbative techniques. However, as the complexity of the perturbative expansion grows very quickly with system size and perturbation order, this approach is limited to low-order corrections including the third, sometimes fourth order in practice. It follows that the lattice dynamics approach is _not_ formally exact, and a perfect quantitative agreement with experimental observables is not possible in principle. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can provide _excellent_ qualitative microscopic insight into the physical mechanisms that drive certain phenomena, and often even very good quantitative results, as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made when describing the nuclear dynamics, but the _precision_ can be excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. +The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions that are cubic or sometimes quartic in the displacements can be included via established perturbative techniques. Higher-order contributions are elusive in practice because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can provide _excellent_ qualitative microscopic insight into the physical mechanisms that drive certain phenomena, and often even very good quantitative results, as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made, but the _precision_ can be excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. -The parameters in the lattice dynamics Hamiltonian, typically called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [CITE]. Alternatively, temperature-dependent _effective_, renormalized model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [CITE deBoer1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [CITE Born, Hooton]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [CITE Klein1972]. +The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [CITE]. Alternatively, temperature-dependent _effective_, renormalized model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [CITE deBoer1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [CITE Born, Hooton]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [CITE Klein1972]. # Statement of need @@ -51,11 +51,9 @@ To extract force constants from thermal snapshots efficiently, TDEP employs the TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both extracting force constants, as well as analyzing (effective) harmonic phonons and explicit anharmonic properties such as thermal transport and the full phonon spectral function across the Brillouin zone, from which spectroscopic properties can be obtained. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [CITE Benshalom]. We highlight some applications and results below. -Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good supercell sizes, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. - Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readbale formats like csv, or self-documented HDF5 files for larger datasets. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for higher-order force constants. -A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [CITE Ask], as well as processing and further analysis of TDEP output files is available as well [CITE tdeptools]. +Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good simulation cells, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. ## Features @@ -70,6 +68,7 @@ Here we list the most important codes that are shipped with the TDEP code and ex - `canonical_configuration`: Create supercells with thermal displacements from the force constants via Monte Carlo sampling from a classical and quantum canonical distribution. - `generate_structure`: Generate supercells of target size that are as cubic as possible to maximize the largest possible real-space cutoff for the force constants. +A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [CITE Ask], as well as processing and further analysis of TDEP output files is available as well [CITE tdeptools]. ## Overview of results @@ -78,7 +77,7 @@ Here we list the most important codes that are shipped with the TDEP code and ex # Summary -The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name, which we have described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to a more in-depth discussion of the theory is given in the introduction. +The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name as described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to a more in-depth discussion of the theory is given in the introduction. # Acknowledgements - SeRC From b3409f061052528a609e70ad8ae7b977a498f1b3 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 14 Sep 2023 16:59:18 +0200 Subject: [PATCH 07/48] paper | update --- paper/paper.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 3ee2c4f0..5f74600c 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -35,7 +35,7 @@ Properties of materials change with temperature, i.e., the vibrational motion of In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtain temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics [cite Tuckerman]. -The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions that are cubic or sometimes quartic in the displacements can be included via established perturbative techniques. Higher-order contributions are elusive in practice because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can provide _excellent_ qualitative microscopic insight into the physical mechanisms that drive certain phenomena, and often even very good quantitative results, as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made, but the _precision_ can be excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. +The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can provide _excellent_ qualitative microscopic insight into physical phenomena, and often even very good quantitative results, as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made, but the _precision_ is excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [CITE]. Alternatively, temperature-dependent _effective_, renormalized model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [CITE deBoer1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [CITE Born, Hooton]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [CITE Klein1972]. @@ -43,13 +43,13 @@ The parameters in the lattice dynamics Hamiltonian, called _force constants_, ca # Statement of need The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve temperature-dependent, effective lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. -As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments evolve around finding practical ways of implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [CITE SCAILD/qSCAILD, SCHA/SSCHA, SCP/Alamode]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [cite Levy1984, Dove1986]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [cite Hellman2011, 2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [Shulumba2017, Benshalom2022]. +As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [CITE SCAILD/qSCAILD, SCHA/SSCHA, SCP/Alamode]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [cite Levy1984, Dove1986]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [cite Hellman2011, 2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [Shulumba2017, Benshalom2022]. While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants up to fourth order [CITE Cowley, Hellman2013, Feng2016 ...]. These can be used to get better approximations to the free energy [CITE Wallace], describe thermal transport [CITE Broido, Romero], and linewidth broadening in spectroscopic experiments [CITE neutrons + Raman]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [CITE Castellano]. To extract force constants from thermal snapshots efficiently, TDEP employs the spacegroup symmetry of a given system to rigorously reduce the free parameters in the model to an irreducible set _before_ fitting the model parameters. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [cite Hellman2013b]. Furthermore, additional lattice dynamics sum rules such as acoustic (translational) and rotational invariances, as well the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [CITE BornHuang]. While TDEP was probably the first approach to exploit all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [CITE hiphive, Ponce]. -TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both extracting force constants, as well as analyzing (effective) harmonic phonons and explicit anharmonic properties such as thermal transport and the full phonon spectral function across the Brillouin zone, from which spectroscopic properties can be obtained. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [CITE Benshalom]. We highlight some applications and results below. +TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both extracting force constants, as well as analyzing (effective) harmonic phonons and explicit anharmonic properties such as thermal transport and the full phonon spectral function across the Brillouin zone, from which spectroscopic properties can be obtained. This allows simulations even for complex bulk materials with reduced symmetry in practice. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [CITE Benshalom]. We highlight some applications and results below. Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readbale formats like csv, or self-documented HDF5 files for larger datasets. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for higher-order force constants. From 2eecd668aef466c4ee4f58fe934a45bf6122e3ac Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Fri, 15 Sep 2023 11:15:14 +0200 Subject: [PATCH 08/48] paper | update affiliations --- paper/paper.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 5f74600c..671481a6 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -11,6 +11,9 @@ authors: - name: Florian Knoop orcid: 0000-0002-7132-039X affiliation: 1 + - name: Aloïs Castellano + orcid: 0000-0002-8783-490X + affiliation: 3 - name: Igor Abrikosov orcid: 0000-0001-7551-4717 affiliation: 1 @@ -21,10 +24,12 @@ authors: orcid: 0000-0002-3453-2975 affiliation: 2 affiliations: - - name: Linköping University, Linköping, Sweden + - name: Theoretical Physics Division, Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden index: 1 - name: Weizmann Institute of Science, Rehovot, Israel index: 2 + - name: Nanomat group, QMAT center, CESAM research unit and European Theoretical Spectroscopy Facility, Université de Liège, allée du 6 août, 19, B-4000 Liège, Belgium + index: 3 date: August 2023 bibliography: paper.bib --- From 5fabe61bd2487b6fd2061f3f9caa13c017795b3a Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Fri, 15 Sep 2023 13:35:13 +0200 Subject: [PATCH 09/48] paper | add Jose and Matthieu --- paper/paper.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/paper/paper.md b/paper/paper.md index 671481a6..2b756ea9 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -14,6 +14,10 @@ authors: - name: Aloïs Castellano orcid: 0000-0002-8783-490X affiliation: 3 + - name: J. P. Alvarinhas Batista + affiliation: 3 + - name: Matthieu J. Verstraete + affiliation: 3 - name: Igor Abrikosov orcid: 0000-0001-7551-4717 affiliation: 1 From c0c6091c147eda8bddd7614b70024bd9886f4222 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Fri, 15 Sep 2023 13:40:31 +0200 Subject: [PATCH 10/48] paper | update authors --- paper/paper.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/paper/paper.md b/paper/paper.md index 2b756ea9..21657594 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -11,12 +11,16 @@ authors: - name: Florian Knoop orcid: 0000-0002-7132-039X affiliation: 1 + - name: Nina Shulumba + orcid: 0000-0002-2374-7487 - name: Aloïs Castellano orcid: 0000-0002-8783-490X affiliation: 3 - name: J. P. Alvarinhas Batista + orcid: 0000-0002-3314-249X affiliation: 3 - name: Matthieu J. Verstraete + orcid: 0000-0001-6921-5163 affiliation: 3 - name: Igor Abrikosov orcid: 0000-0001-7551-4717 From 2122a04c072b30f3634bd2bf35e96fda2843c3bf Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Fri, 15 Sep 2023 13:45:56 +0200 Subject: [PATCH 11/48] paper | add Johan --- paper/paper.md | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/paper/paper.md b/paper/paper.md index 21657594..53730797 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -22,6 +22,9 @@ authors: - name: Matthieu J. Verstraete orcid: 0000-0001-6921-5163 affiliation: 3 + - name: Johan Klarbring + orcid: 0000-0002-6223-5812 + affiliation: 1, 4 - name: Igor Abrikosov orcid: 0000-0001-7551-4717 affiliation: 1 @@ -38,6 +41,8 @@ affiliations: index: 2 - name: Nanomat group, QMAT center, CESAM research unit and European Theoretical Spectroscopy Facility, Université de Liège, allée du 6 août, 19, B-4000 Liège, Belgium index: 3 + - name: Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, UK + index: 4 date: August 2023 bibliography: paper.bib --- From 08dd1e25db0938c6e59c2a65ced75c80ba144d83 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 18 Sep 2023 16:16:39 +0200 Subject: [PATCH 12/48] paper | add David + Dennis --- paper/paper.md | 13 ++++++++++++- 1 file changed, 12 insertions(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 53730797..3783197c 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -13,6 +13,7 @@ authors: affiliation: 1 - name: Nina Shulumba orcid: 0000-0002-2374-7487 + affiliation: 1 - name: Aloïs Castellano orcid: 0000-0002-8783-490X affiliation: 3 @@ -22,6 +23,12 @@ authors: - name: Matthieu J. Verstraete orcid: 0000-0001-6921-5163 affiliation: 3 + - name: David Broido + orcid: 0000-0003-0182-4450 + affiliation: 5 + - name: Dennis S. Kim + orcid: 0000-0002-5707-2609 + affiliation: 6 - name: Johan Klarbring orcid: 0000-0002-6223-5812 affiliation: 1, 4 @@ -43,13 +50,17 @@ affiliations: index: 3 - name: Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, UK index: 4 + - name: Department of Physics, Boston College, Chestnut Hill, MA 02467, USA + index: 5 + - name: College of Letters and Science, Department of Chemistry and Biochemistry, University of California, Los Angeles (UCLA), California 90025, USA + index: 6 date: August 2023 bibliography: paper.bib --- # Introduction -Properties of materials change with temperature, i.e., the vibrational motion of electrons and nuclei. In a static thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. +Properties of materials change with temperature, i.e., the vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtain temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics [cite Tuckerman]. From da7d6d2dc0f33cdfb502224be08fd664b8684727 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 14:29:32 +0200 Subject: [PATCH 13/48] paper | add Matt Heine --- paper/paper.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/paper/paper.md b/paper/paper.md index 3783197c..e1a9118e 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -23,6 +23,9 @@ authors: - name: Matthieu J. Verstraete orcid: 0000-0001-6921-5163 affiliation: 3 + - name: Matthew Heine + orcid: 0000-0002-4882-6712 + affiliation: 5 - name: David Broido orcid: 0000-0003-0182-4450 affiliation: 5 From 7b986286cdf7d3399df06c177f301c2ca70dc0d9 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 14:29:56 +0200 Subject: [PATCH 14/48] paper | add bib --- paper/Makefile | 5 + paper/literature.bib | 494 +++++++++++++++++++++++++++++++++++++++++++ paper/paper.md | 6 +- 3 files changed, 502 insertions(+), 3 deletions(-) create mode 100644 paper/Makefile create mode 100644 paper/literature.bib diff --git a/paper/Makefile b/paper/Makefile new file mode 100644 index 00000000..d21ac3fe --- /dev/null +++ b/paper/Makefile @@ -0,0 +1,5 @@ +CMDbib = biber --tool --output_align --output_indent=2 --output_fieldcase=lower --output-legacy-dates --output-field-replace=journaltitle:journal + +bib: + ${CMDbib} paper_tdep_joss.bib + mv paper_tdep_joss_bibertool.bib literature.bib diff --git a/paper/literature.bib b/paper/literature.bib new file mode 100644 index 00000000..dff80c59 --- /dev/null +++ b/paper/literature.bib @@ -0,0 +1,494 @@ +@article{Zhou.2018, + abstract = {{Structural phase transitions and soft phonon modes pose a long-standing challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO3 is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200 K. Our calculations can accurately predict the temperature dependence of the electron mobility in SrTiO3 between 150–300 K, and reveal the microscopic origin of its roughly T-3 trend. Our approach enables first-principles calculations of e-ph interactions and charge transport in broad classes of crystals with phase transitions and strongly anharmonic phonons.}}, + author = {Zhou, Jin-Jian and Hellman, Olle and Bernardi, Marco}, + doi = {10.1103/physrevlett.121.226603}, + eprint = {1806.05775}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {22}, + pages = {226603}, + title = {{Electron-Phonon Scattering in the Presence of Soft Modes and Electron Mobility in SrTiO3 Perovskite from First Principles}}, + volume = {121}, + year = {2018}, +} + +@article{Werthamer.1970kr, + abstract = {{The self-consistent phonon theory of anharmonic lattice dynamics is derived via a stationary functional formulation. The crystal dynamics is approximated by a set of damped oscillators, and these are used to construct a trial action, analytically continued into the complex time-temperature plane. Using the action, a free-energy functional is required to be stationary with respect to the trial oscillators. The resulting phonon modes are undamped at the first order of approximation, whereas to second order the phonon spectral function is determined self-consistently. Expressions are obtained in first order for various thermodynamic derivatives, such as pressure, elastic constants, specific heats, and thermal expansion.}}, + author = {Werthamer, N. R.}, + doi = {10.1103/physrevb.1.572}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {2}, + pages = {572--581}, + title = {{Self-Consistent Phonon Formulation of Anharmonic Lattice Dynamics}}, + volume = {1}, + year = {1970}, +} + +@article{Souvatzis.2008, + abstract = {{Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self-consistently from first principles has been developed to address this issue. The method combines concepts from Born’s interatomic self-consistent phonon approach with first principles calculations of accurate interatomic forces in a supercell. The method has been tested on the high-temperature bcc phase of Ti, Zr, and Hf, as representative examples, and is found to reproduce the observed high-temperature phonon frequencies with good accuracy.}}, + author = {Souvatzis, P. and Eriksson, O. and Katsnelson, M. I. and Rudin, S. P.}, + doi = {10.1103/physrevlett.100.095901}, + eprint = {0803.1325}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {9}, + pages = {095901}, + title = {{Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory}}, + volume = {100}, + year = {2008}, +} + +@article{Shulumba.2016, + abstract = {{We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti1-xAlxN alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti1-xAlxN alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti0.5Al0.5N alloys agree with the calculated phase diagram.}}, + author = {Shulumba, Nina and Hellman, Olle and Raza, Zamaan and Alling, Björn and Barrirero, Jenifer and Mücklich, Frank and Abrikosov, Igor A. and Odén, Magnus}, + doi = {10.1103/physrevlett.117.205502}, + eprint = {1503.02459}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {20}, + pages = {205502}, + title = {{Lattice Vibrations Change the Solid Solubility of an Alloy at High Temperatures}}, + volume = {117}, + year = {2016}, +} + +@article{Shulumba.20179s8e, + abstract = {{Molecular crystals such as polyethylene are of intense interest as flexible thermal conductors, yet their intrinsic upper limits of thermal conductivity remain unknown. Here, we report a study of the vibrational properties and lattice thermal conductivity of a polyethylene molecular crystal using an ab initio approach that rigorously incorporates nuclear quantum motion and finite temperature effects. We obtain a thermal conductivity along the chain direction of around 160 W m−1 K−1 at room temperature, providing a firm upper bound for the thermal conductivity of this molecular crystal. Furthermore, we show that the inclusion of quantum nuclear effects significantly impacts the thermal conductivity by altering the phase space for three-phonon scattering. Our computational approach paves the way for ab initio studies and computational material discovery of molecular solids free of any adjustable parameters.}}, + author = {Shulumba, Nina and Hellman, Olle and Minnich, Austin J.}, + doi = {10.1103/physrevlett.119.185901}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {18}, + pages = {185901}, + title = {{Lattice Thermal Conductivity of Polyethylene Molecular Crystals from First-Principles Including Nuclear Quantum Effects}}, + volume = {119}, + year = {2017}, +} + +@article{Shulumba.2017, + abstract = {{Lead chalcogenides such as PbS, PbSe, and PbTe are of interest for their exceptional thermoelectric properties and strongly anharmonic lattice dynamics. Although PbTe has received the most attention, PbSe has a lower thermal conductivity and a nonlinear temperature dependence of thermal resistivity despite being stiffer, trends that prior first-principles calculations have not fully reproduced. Here, we use ab initio calculations that explicitly account for strong anharmonicity and a computationally efficient stochastic phase-space sampling scheme to identify the origin of this low thermal conductivity as an anomalously large anharmonic interaction, exceeding in strength that in PbTe, between the transverse optic and longitudinal acoustic branches. The strong anharmonicity is reflected in the striking observation of an intrinsic localized mode that forms in the acoustic frequencies. Our work shows the deep insights into thermal phonons that can be obtained from ab initio calculations that do not rely on perturbations from the ground-state phonon dispersion.}}, + author = {Shulumba, Nina and Hellman, Olle and Minnich, Austin J.}, + doi = {10.1103/physrevb.95.014302}, + eprint = {1609.08254}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {1}, + pages = {014302}, + title = {{Intrinsic localized mode and low thermal conductivity of PbSe}}, + volume = {95}, + year = {2017}, +} + +@article{Romero.2015, + abstract = {{We investigate the harmonic and anharmonic contributions to the phonon spectrum of lead telluride and perform a complete characterization of how thermal properties of PbTe evolve as temperature increases. We analyze the thermal resistivity's variation with temperature and clarify misconceptions about existing experimental literature. The resistivity initially increases sublinearly because of phase space effects and ultra strong anharmonic renormalizations of specific bands. This effect is the strongest factor in the favorable thermoelectric properties of PbTe, and it explains its limitations at higher T. This quantitative prediction opens the prospect of phonon phase space engineering to tailor the lifetimes of crucial heat carrying phonons by considering different structure or nanostructure geometries. We analyze the available scattering volume between TO and LA phonons as a function of temperature and correlate its changes to features in the thermal conductivity.}}, + author = {Romero, A. H. and Gross, E. K. U. and Verstraete, M. J. and Hellman, Olle}, + doi = {10.1103/physrevb.91.214310}, + eprint = {1402.5535}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {21}, + pages = {214310}, + title = {{Thermal conductivity in PbTe from first principles}}, + volume = {91}, + year = {2015}, +} + +@article{Reig.2022, + abstract = {{Understanding heat flow in layered transition metal dichalcogenide (TMD) crystals is crucial for applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood, in particular how transport is affected by material thickness and the material's environment. This combined experimental–theoretical study establishes a unifying physical picture of the intrinsic lattice thermal conductivity of the representative TMD MoSe2. Thermal conductivity measurements using Raman thermometry on a large set of clean, crystalline, suspended crystals with systematically varied thickness are combined with ab initio simulations with phonons at finite temperature. The results show that phonon dispersions and lifetimes change strongly with thickness, yet the thinnest TMD films exhibit an in‐plane thermal conductivity that is only marginally smaller than that of bulk crystals. This is the result of compensating phonon contributions, in particular heat‐carrying modes around ≈0.1 THz in (sub)nanometer thin films, with a surprisingly long mean free path of several micrometers. This behavior arises directly from the layered nature of the material. Furthermore, out‐of‐plane heat dissipation to air molecules is remarkably efficient, in particular for the thinnest crystals, increasing the apparent thermal conductivity of monolayer MoSe2 by an order of magnitude. These results are crucial for the design of (flexible) TMD‐based (opto‐)electronic applications. Combined experimental–theoretical study using Raman thermometry and ab initio simulations to unravel the heat transport properties of suspended MoSe2 crystals with systematic thickness variation down to the monolayer. Monolayer films have almost the same in‐plane thermal conductivity as bulk material thanks to an additional heat‐carrying low‐frequency mode. Out‐of‐plane heat dissipation to air is extremely efficient for the thinnest flakes.}}, + author = {Reig, David Saleta and Varghese, Sebin and Farris, Roberta and Block, Alexander and Mehew, Jake D. and Hellman, Olle and Woźniak, Paweł and Sledzinska, Marianna and Sachat, Alexandros El and Chávez‐Ángel, Emigdio and Valenzuela, Sergio O. and Hulst, Niek F. van and Ordejón, Pablo and Zanolli, Zeila and Torres, Clivia M. Sotomayor and Verstraete, Matthieu J. and Tielrooij, Klaas‐Jan}, + doi = {10.1002/adma.202108352}, + issn = {0935-9648}, + journal = {Advanced Materials}, + number = {10}, + pages = {2108352}, + title = {{Unraveling Heat Transport and Dissipation in Suspended MoSe2 from Bulk to Monolayer}}, + volume = {34}, + year = {2022}, +} + +@article{Reig.2021, + abstract = {{Understanding thermal transport in layered transition metal dichalcogenide (TMD) crystals is crucial for a myriad of applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood. Here, we present a combined experimental-theoretical study of the intrinsic lattice thermal conductivity of the representative TMD MoSe\$\_2\$, focusing on the effect of material thickness and the material's environment. We use Raman thermometry measurements on suspended crystals, where we identify and eliminate crucial artefacts, and perform \$ab\$ \$initio\$ simulations with phonons at finite, rather than zero, temperature. We find that phonon dispersions and lifetimes change strongly with thickness, yet (sub)nanometer thin TMD films exhibit a similar in-plane thermal conductivity (\$\textbackslashsim\$20\textbackslashtextasciitildeWm\$\textasciicircum\{-1\}\$K\$\textasciicircum\{-1\}\$) as bulk crystals (\$\textbackslashsim\$40\textbackslashtextasciitildeWm\$\textasciicircum\{-1\}\$K\$\textasciicircum\{-1\}\$). This is the result of compensating phonon contributions, in particular low-frequency modes with a surprisingly long mean free path of several micrometers that contribute significantly to thermal transport for monolayers. We furthermore demonstrate that out-of-plane heat dissipation to air is remarkably efficient, in particular for the thinnest crystals. These results are crucial for the design of TMD-based applications in thermal management, thermoelectrics and (opto)electronics.}}, + author = {Reig, D Saleta and Varghese, S and Farris, R and Block, A and Mehew, J D and Hellman, O and Woźniak, P and Sledzinska, M and Sachat, A El and Chávez-Ángel, E and Valenzuela, S O and Hulst, N F Van and Ordejón, P and Zanolli, Z and Torres, C M Sotomayor and Verstraete, M J and Tielrooij, K J}, + eprint = {2109.09225}, + journal = {arXiv}, + title = {{Unraveling heat transport and dissipation in suspended MoSe\$\_2\$ crystals from bulk to monolayer}}, + year = {2021}, +} + +@article{Menahem.2022, + abstract = {{The anharmonic lattice dynamics of oxide and halide perovskites play a crucial role in their mechanical and optical properties. Raman spectroscopy is one of the key methods used to study these structural dynamics. However, despite decades of research, existing interpretations cannot explain the temperature dependence of the observed Raman spectra. We demonstrate the non-monotonic evolution with temperature of the scattering intensity and present a model for 2nd-order Raman scattering that accounts for this unique trend. By invoking a low-frequency anharmonic feature, we are able to reproduce the Raman spectral line-shapes and integrated intensity temperature dependence. Numerical simulations support our interpretation of this low-frequency mode as a transition between two minima of a double-well potential surface. The model can be applied to other dynamically disordered crystal phases, providing a better understanding of the structural dynamics, leading to favorable electronic, optical, and mechanical properties in functional materials.}}, + author = {Menahem, Matan and Benshalom, Nimrod and Asher, Maor and Aharon, Sigalit and Korobko, Roman and Safran, Sam and Hellman, Olle and Yaffe, Omer}, + eprint = {2208.05563}, + journal = {arXiv}, + title = {{The Disorder Origin of Raman Scattering In Perovskites Single Crystals}}, + year = {2022}, +} + +@article{Mei.2015, + abstract = {{Structural phase transitions in epitaxial stoichiometric VN/MgO(011) thin films are investigated using temperature-dependent synchrotron x-ray diffraction (XRD), selected-area electron diffraction (SAED), resistivity measurements, high-resolution cross-sectional transmission electron microscopy, and ab initio molecular dynamics (AIMD). At room temperature, VN has the B1 NaCl structure. However, below Tc=250K, XRD and SAED results reveal forbidden (00l) reflections of mixed parity associated with a noncentrosymmetric tetragonal structure. The intensities of the forbidden reflections increase with decreasing temperature following the scaling behavior I∝(Tc−T)1/2. Resistivity measurements between 300 and 4 K consist of two linear regimes resulting from different electron/phonon coupling strengths in the cubic and tetragonal-VN phases. The VN transport Eliashberg spectral function αtr2F(ℏω), the product of the phonon density of states F(ℏω) and the transport electron/phonon coupling strength αtr2(ℏω), is determined and used in combination with AIMD renormalized phonon dispersion relations to show that anharmonic vibrations stabilize the NaCl structure at T>Tc. Free-energy contributions due to vibrational entropy, often neglected in theoretical modeling, are essential for understanding the room-temperature stability of NaCl-structure VN, and of strongly anharmonic systems in general.}}, + author = {Mei, A. B. and Hellman, O. and Wireklint, N. and Schlepütz, C. M. and Sangiovanni, D. G. and Alling, B. and Rockett, A. and Hultman, L. and Petrov, I. and Greene, J. E.}, + doi = {10.1103/physrevb.91.054101}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {5}, + pages = {054101}, + title = {{Dynamic and structural stability of cubic vanadium nitride}}, + volume = {91}, + year = {2015}, +} + +@article{Manley.2019, + abstract = {{Lead chalcogenides have exceptional thermoelectric properties and intriguing anharmonic lattice dynamics underlying their low thermal conductivities. An ideal material for thermoelectric efficiency is the phonon glass–electron crystal, which drives research on strategies to scatter or localize phonons while minimally disrupting electronic-transport. Anharmonicity can potentially do both, even in perfect crystals, and simulations suggest that PbSe is anharmonic enough to support intrinsic localized modes that halt transport. Here, we experimentally observe high-temperature localization in PbSe using neutron scattering but find that localization is not limited to isolated modes – zero group velocity develops for a significant section of the transverse optic phonon on heating above a transition in the anharmonic dynamics. Arrest of the optic phonon propagation coincides with unusual sharpening of the longitudinal acoustic mode due to a loss of phase space for scattering. Our study shows how nonlinear physics beyond conventional anharmonic perturbations can fundamentally alter vibrational transport properties. To optimize the performance of lead chalcogenides for thermoelectric applications, strategies to further reduce the crystal’s thermal conductivity is required. Here, the authors discover anharmonic localized vibrations in PbSe crystals for optimizing the crystal’s vibrational transport properties.}}, + author = {Manley, M. E. and Hellman, O. and Shulumba, N. and May, A. F. and Stonaha, P. J. and Lynn, J. W. and Garlea, V. O. and Alatas, A. and Hermann, R. P. and Budai, J. D. and Wang, H. and Sales, B. C. and Minnich, A. J.}, + doi = {10.1038/s41467-019-09921-4}, + journal = {Nature Communications}, + number = {1}, + pages = {1928}, + title = {{Intrinsic anharmonic localization in thermoelectric PbSe}}, + volume = {10}, + year = {2019}, +} + +@article{Levy.1984, + abstract = {{A quasi‐harmonic approximation is described for studying very low frequency vibrations and flexible paths in proteins. The force constants of the empirical potential function are quadratic approximations to the potentials of mean force; they are evaluated from a molecular dynamics simulation of a protein based on a detailed anharmonic potential. The method is used to identify very low frequency (∼1 cm−1) normal modes for the protein pancreatic trypsin inhibitor. A simplified model for the protein is used, for which each residue is represented by a single interaction center. The quasi‐harmonic force constants of the virtual internal coordinates are evaluated and the normal‐mode frequencies and eigenvectors are obtained. Conformations corresponding to distortions along selected low‐frequency modes are analyzed.}}, + author = {Levy, R. M. and Srinivasan, A. R. and Olson, W. K. and McCammon, J. A.}, + doi = {10.1002/bip.360230610}, + issn = {0006-3525}, + journal = {Biopolymers}, + number = {6}, + pages = {1099--1112}, + title = {{Quasi‐harmonic method for studying very low frequency modes in proteins}}, + volume = {23}, + year = {1984}, +} + +@article{Koehler.1966, + author = {Koehler, Thomas R.}, + doi = {10.1103/physrevlett.17.89}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {2}, + pages = {89--91}, + title = {{Theory of the Self-Consistent Harmonic Approximation with Application to Solid Neon}}, + volume = {17}, + year = {1966}, +} + +@article{Koehler.1971, + abstract = {{A theory is presented of the damping and frequency shift of phonons and of the ground-state energy corrections due to interactions between phonons in quantum crystals with singular forces. The technique begins with the adoption of a trial ground-state wave function of the Jastrow form, together with trial excited-state wave functions constructed to represent one-, two-, and three-phonon excitations. The Hamiltonian matrix in this restricted basis is diagonalized, and the basis is optimized by minimizing the lowest eigenvalue with respect to variational phonon parameters. Using a lowest-order cluster expansion, the unambiguous prescription is obtained that a specific effective potential, softened by the Jastrow correlation function, replaces everywhere the true potential in the existing self-consistent theory of phonon damping applicable to nonsingular forces. Close analogies are drawn with the correlated basis function treatment, of superfluid liquid helium.}}, + author = {Koehler, T. R. and Werthamer, N. R.}, + doi = {10.1103/physreva.3.2074}, + issn = {1050-2947}, + journal = {Physical Review A}, + number = {6}, + pages = {2074--2083}, + title = {{Phonon Spectral Functions and Ground-State Energy of Quantum Crystals in Perturbation Theory with a Variationally Optimum Correlated Basis Set}}, + volume = {3}, + year = {1971}, +} + +@article{Klein.1972, + author = {Klein, M. L. and Horton, G. K.}, + doi = {10.1007/bf00654839}, + issn = {0022-2291}, + journal = {Journal of Low Temperature Physics}, + number = {3-4}, + pages = {151--166}, + title = {{The rise of self-consistent phonon theory}}, + volume = {9}, + year = {1972}, +} + +@article{Klarbring.2020vk, + abstract = {{The lead-free halide double perovskite class of materials offers a promising venue for resolving issues related to toxicity of Pb and long-term stability of the lead-containing halide perovskites. We present a first-principles study of the lattice vibrations in Cs2AgBiBr6, the prototypical compound in this class and show that the lattice dynamics of Cs2AgBiBr6 is highly anharmonic, largely in regards to tilting of AgBr6 and BiBr6 octahedra. Using an energy- and temperature-dependent phonon spectral function, we then show how the experimentally observed cubic-to-tetragonal phase transformation is caused by the collapse of a soft phonon branch. We finally reveal that the softness and anharmonicity of Cs2AgBiBr6 yield an ultralow thermal conductivity, unexpected of high-symmetry cubic structures.}}, + author = {Klarbring, Johan and Hellman, Olle and Abrikosov, Igor A. and Simak, Sergei I.}, + doi = {10.1103/physrevlett.125.045701}, + eprint = {1912.05351}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {4}, + pages = {045701}, + title = {{Anharmonicity and Ultralow Thermal Conductivity in Lead-Free Halide Double Perovskites}}, + volume = {125}, + year = {2020}, +} + +@article{Kim.2018, + abstract = {{Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.}}, + author = {Kim, D. S. and Hellman, O. and Herriman, J. and Smith, H. L. and Lin, J. Y. Y. and Shulumba, N. and Niedziela, J. L. and Li, C. W. and Abernathy, D. L. and Fultz, B.}, + doi = {10.1073/pnas.1707745115}, + eprint = {1610.08737}, + issn = {0027-8424}, + journal = {Proceedings of the National Academy of Sciences}, + number = {9}, + pages = {201707745}, + title = {{Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon}}, + volume = {115}, + year = {2018}, +} + +@article{Horner.1972, + abstract = {{Numerical calculations of phonon spectra, including damping, are reported for bcc3He and4He and for fcc4He. Strong damping is found for the longitudinal branches near the boundary of the Brillouin zone. In the bcc phase anomalous dispersion occurs for several directions at long wavelengths, which is most pronounced in the lowest transverse branch in (110) direction. This leads to an anomaly in the specific heat at low temperatures. In this calculation anharmonicities and short-range correlations are treated in a self-consistent way.}}, + author = {Horner, Heinz}, + doi = {10.1007/bf00653877}, + issn = {0022-2291}, + journal = {Journal of Low Temperature Physics}, + number = {5-6}, + pages = {511--529}, + title = {{Phonons and thermal properties of bcc and fcc helium from a self-consistent anharmonic theory}}, + volume = {8}, + year = {1972}, +} + +@article{Hooton.1958, + abstract = {{Skyrme has recently discussed the use of a model in quantum mechanics. His method is applied to the case of the anharmonic vibrations of a crystal lattice, and compared with a previous treatment by the present author. Some remarks are added which give a new and more physical interpretation of the results of this earlier work.}}, + author = {Hooton, D. J.}, + doi = {10.1080/14786435808243224}, + issn = {0031-8086}, + journal = {Philosophical Magazine}, + number = {25}, + pages = {49--54}, + title = {{The use of a model in anharmonic lattice dynamics}}, + volume = {3}, + year = {1958}, +} + +@article{Hooton.2010, + abstract = {{The thermodynamical formulae of the previous paper are worked out with the help of an adaptation of Debye's continuum approximation ; in particular, the specific heat at constant volume is put into a form suitable for numerical calculation. This formula contains, however, a factor which expresses the (possibly strong) volume dependence of the relation between the new frequency spectrum and that of the customary lattice dynamics : the factor appears in addition to the Debye characteristic temperature θ and must be estimated in any particular application—for example, in the following consideration of solid helium it will be approximated from a linear chain model. The meaning of a Debye characteristic temperature in the anharnionic theory is discussed, and the place of an empirical Debye temperature, determined by fitting specific heat measurements to a theoretical specific heat formula, is also considered. A discussion of this fitted Debye temperature (due to Domb and Salter) is adapted to the anharmonic theory in order to give later a correct application to solid helium.}}, + author = {Hooton, D.J.}, + doi = {10.1080/14786440408520576}, + issn = {1941-5982}, + journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, + number = {375}, + pages = {433--442}, + title = {{LII. A new treatment of anharmonicity in lattice thermodynamics: II}}, + volume = {46}, + year = {2010}, +} + +@article{Hooton.2010mfn, + abstract = {{Born has given a method by which the anharmonic vibrational motion of the atoms in a crystal can be approximated in terms of an adapted set of harmonic oscillations, these differing from the usualmodes of vibration of harmonic lattice dynamics ; this method is here redeveloped from another standpoint and extended to give explicit results. The thermodynamical formulae of the anharmonic crystal can be given a simple form: they consist of the customary formulae for a set of harmonic oscillators, but now expressed in terms of new frequencies denned essentially from the quadratic and quartic terms in an expansion of the potential energy, plus correction terms which express the difference between the actual anharmonic motion and the harmonic approximation. For small anharmonicity the formulae reduce to thoseof the usual perturbation procedure (allowance for thermal expansion) with some extensions, but they also give a solution in the case of strong anharmonicity. This latter solution will later be used in a discussion of solid helium.}}, + author = {Hooton, D.J.}, + doi = {10.1080/14786440408520575}, + issn = {1941-5982}, + journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, + number = {375}, + pages = {422--432}, + title = {{LI. A new treatment of anharmonicity in lattice thermodynamics: I}}, + volume = {46}, + year = {2010}, +} + +@thesis{Hellman.2012, + author = {Hellman, Olle}, + title = {{Thermal properties of materials from first principles}}, + type = {phdthesis}, + year = {2012}, +} + +@article{Hellman.2013oi5, + abstract = {{The temperature-dependent effective potential (TDEP) method is generalized beyond pair interactions. The second- and third-order force constants are determined consistently from ab initio molecular dynamics simulations at finite temperature. The reliability of the approach is demonstrated by calculations of the mode Grüneisen parameters for Si. We show that the extension of TDEP to a higher order allows for an efficient calculation of the phonon life time, in Si as well as in ε-FeSi; a system that exhibits anomalous softening with temperature.}}, + author = {Hellman, Olle and Abrikosov, I. A.}, + doi = {10.1103/physrevb.88.144301}, + eprint = {1308.5436}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {14}, + pages = {144301}, + title = {{Temperature-dependent effective third-order interatomic force constants from first principles}}, + volume = {88}, + year = {2013}, +} + +@article{Hellman.2013, + abstract = {{We have developed a thorough and accurate method of determining anharmonic free energies, the temperature dependent effective potential technique (TDEP). It is based on ab initio molecular dynamics followed by a mapping onto a model Hamiltonian that describes the lattice dynamics. The formalism and the numerical aspects of the technique are described in detail. A number of practical examples are given, and results are presented, which confirm the usefulness of TDEP within ab initio and classical molecular dynamics frameworks. In particular, we examine from first principles the behavior of force constants upon the dynamical stabilization of the body centered phase of Zr, and show that they become more localized. We also calculate the phase diagram for 4He modeled with the Aziz et al. potential and obtain results which are in favorable agreement both with respect to experiment and established techniques.}}, + author = {Hellman, Olle and Steneteg, Peter and Abrikosov, I. A. and Simak, S. I.}, + doi = {10.1103/physrevb.87.104111}, + eprint = {1303.1145}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {10}, + pages = {104111}, + title = {{Temperature dependent effective potential method for accurate free energy calculations of solids}}, + volume = {87}, + year = {2013}, +} + +@article{Hellman.2011, + abstract = {{An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic—or higher order—potential energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated.}}, + author = {Hellman, O. and Abrikosov, I. A. and Simak, S. I.}, + doi = {10.1103/physrevb.84.180301}, + eprint = {1103.5590}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {18}, + pages = {180301}, + title = {{Lattice dynamics of anharmonic solids from first principles}}, + volume = {84}, + year = {2011}, +} + +@article{Heine.2021, + abstract = {{We put forth an ab initio framework to calculate local moment magnetic interaction parameters, renormalized to treat both the lattice and magnetic systems as a function of temperature T. For bcc Fe, magnetic and lattice thermal disorders act in opposition, the former strengthening the Heisenberg-like interactions, while the latter decreasing them. Below TC, J stays nearly independent of T, while around and above TC, it exhibits a sharp decrease. This remarkable behavior reflects an intricate spin-lattice coupling and its evolution with T, in which magnetic interactions and interatomic bonds are each renormalized by the other. This finding is consistent with magnetization data and with the observed softening of magnon and phonon modes at high temperatures. Magnetization as well as magnon and phonon mode softening are discussed.}}, + author = {Heine, Matthew and Hellman, Olle and Broido, David}, + doi = {10.1103/physrevb.103.184409}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {18}, + pages = {184409}, + title = {{Temperature-dependent renormalization of magnetic interactions by thermal, magnetic, and lattice disorder from first principles}}, + volume = {103}, + year = {2021}, +} + +@article{Heine.2019, + abstract = {{We present a first-principles theoretical approach to calculate temperature dependent phonon dispersions in bcc Fe, which captures finite temperature spin-lattice coupling by treating thermal disorder in both the spin and lattice systems simultaneously. With increasing temperature, thermal atomic displacements are found to induce increasingly large fluctuations in local magnetic moment magnitudes. The calculated phonon dispersions of bcc Fe show excellent agreement with measured data over a wide range of temperatures both above and below the magnetic and structural transition temperatures, suggesting the applicability of the developed approach to other magnetic materials.}}, + author = {Heine, Matthew and Hellman, Olle and Broido, David}, + doi = {10.1103/physrevb.100.104304}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {10}, + pages = {104304}, + title = {{Effect of thermal lattice and magnetic disorder on phonons in bcc Fe: A first-principles study}}, + volume = {100}, + year = {2019}, +} + +@article{Gillis.1967, + abstract = {{The self-consistent phonon theory of anharmonic lattice dynamics, devised independently by several authors using varying techniques and implemented computationally by Koehler, is here applied to the crystals of neon and argon. A Lennard-Jones 6-12 interatomic potential is assumed. The quantities calculated are the phonon spectrum and the bulk thermodynamic properties of thermal expansion, compressibility, and specific heat, all as a function of temperature at zero pressure. Although the computations are intended primarily to explore in detail the content of the self-consistent phonon approximation preparatory to incorporating the more elaborate expressions of the next higher approximation, comparison is made with the existing experimental data.}}, + author = {Gillis, N. S. and Werthamer, N. R. and Koehler, T. R.}, + doi = {10.1103/physrev.165.951}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {3}, + pages = {951--959}, + title = {{Properties of Crystalline Argon and Neon in the Self-Consistent Phonon Approximation}}, + volume = {165}, + year = {1967}, +} + +@article{Dove.1986, + abstract = {{As a contribution to the understanding of the incommensurate phase transitions in thiourea, we present a theoretical study of the crystallographic details of the parael ectric phase. A model intermolecular potential is developed, which includes a reasonable distribution of electrostatic multipole interactions as well as the standard dispersive and repulsive interactions. The model gives a satisfactory prediction of the structure of the para electric phase, and in particular explains the occurrence of the hydrogen-bond network. Calculations of phonon-dispersion curves predict a soft-phonon branch in the b direction with the same symmetry as that observed experimentally. Computer simulations predict reasonable values for the vibrational amplitudes, and show the existence of large-amplitude fluctuations of an harmonic quantities at incommensurate wave vectors. However, although the model displays a strong tendency towards incommensurate and lock-in ordering, it does not in fact give a phase transition at a finite temperature. This failure is attributed to the neglect of molecular polarizability, and it is concluded that this feature provides the mechanism that stabilizes the low-temperature phases.For the interested reader, full details of the molecular dynamics simulation technique using parallel processing are presented here. In particular, a method of extracting normal-mode eigenvectors from the results of the simulations is described.}}, + author = {Dove, Martin T. and Lynden-bell, Ruth M.}, + doi = {10.1080/13642818608236861}, + issn = {1364-2812}, + journal = {Philosophical Magazine Part B}, + number = {6}, + pages = {443--463}, + title = {{A model of the paraelectric phase of thiourea}}, + volume = {54}, + year = {1986}, +} + +@article{Dewandre.2016, + abstract = {{The interest in improving the thermoelectric response of bulk materials has received a boost after it has been recognized that layered materials, in particular SnSe, show a very large thermoelectric figure of merit. This result has received great attention while it is now possible to conceive other similar materials or experimental methods to improve this value. Before we can now think of engineering this material it is important we understand the basic mechanism that explains this unusual behavior, where very low thermal conductivity and a high thermopower result from a delicate balance between the crystal and electronic structure. In this Letter, we present a complete temperature evolution of the Seebeck coefficient as the material undergoes a soft crystal transformation and its consequences on other properties within SnSe by means of first-principles calculations. Our results are able to explain the full range of considered experimental temperatures.}}, + author = {Dewandre, Antoine and Hellman, Olle and Bhattacharya, Sandip and Romero, Aldo H. and Madsen, Georg K. H. and Verstraete, Matthieu J.}, + doi = {10.1103/physrevlett.117.276601}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {27}, + pages = {276601}, + title = {{Two-Step Phase Transition in SnSe and the Origins of its High Power Factor from First Principles}}, + volume = {117}, + year = {2016}, +} + +@article{Dangić.2021, + abstract = {{The proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity κ. However, the κ of GeTe increases at the ferroelectric phase transition near 700 K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in κ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Strong anharmonicity near the phase transition induces non-Lorentzian shapes of the phonon power spectra. To account for these effects, we implement a method of calculating κ based on the Green-Kubo approach and find that the Boltzmann transport equation underestimates κ near the phase transition. Our findings elucidate the influence of structural phase transitions on κ and provide guidance for design of better thermoelectric materials.}}, + author = {Dangić, Đorđe and Hellman, Olle and Fahy, Stephen and Savić, Ivana}, + doi = {10.1038/s41524-021-00523-7}, + journal = {npj Computational Materials}, + number = {1}, + pages = {57}, + title = {{The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe}}, + volume = {7}, + year = {2021}, +} + +@article{Cohen.2022, + abstract = {{Lead‐based halide perovskite crystals are shown to have strongly anharmonic structural dynamics. This behavior is important because it may be the origin of their exceptional photovoltaic properties. The double perovskite, Cs2AgBiBr6, has been recently studied as a lead‐free alternative for optoelectronic applications. However, it does not exhibit the excellent photovoltaic activity of the lead‐based halide perovskites. Therefore, to explore the correlation between the anharmonic structural dynamics and optoelectronic properties in lead‐based halide perovskites, the structural dynamics of Cs2AgBiBr6 are investigated and are compared to its lead‐based analog, CsPbBr3. Using temperature‐dependent Raman measurements, it is found that both materials are indeed strongly anharmonic. Nonetheless, the expression of their anharmonic behavior is markedly different. Cs2AgBiBr6 has well‐defined normal modes throughout the measured temperature range, while CsPbBr3 exhibits a complete breakdown of the normal‐mode picture above 200 K. It is suggested that the breakdown of the normal‐mode picture implies that the average crystal structure may not be a proper starting point to understand the electronic properties of the crystal. In addition to our main findings, an unreported phase of Cs2AgBiBr6 is also discovered below ≈37 K. Raman spectroscopy is used to compare the anharmonic expressions in the structural dynamics of two halide perovskites. In Cs2AgBiBr6, clear normal modes are observed in all measured temperatures. Contrary to this, the Raman spectrum of CsPbBr3 exhibits a breakdown of the normal‐mode picture above 200 K. Implications of these diverging behaviors on the electronic properties of the crystals is discussed.}}, + author = {Cohen, Adi and Brenner, Thomas M. and Klarbring, Johan and Sharma, Rituraj and Fabini, Douglas H. and Korobko, Roman and Nayak, Pabitra K. and Hellman, Olle and Yaffe, Omer}, + doi = {10.1002/adma.202107932}, + issn = {0935-9648}, + journal = {Advanced Materials}, + pages = {2107932}, + title = {{Diverging Expressions of Anharmonicity in Halide Perovskites}}, + year = {2022}, +} + +@book{Choquard.1967, + author = {Choquard, Philippe F.}, + publisher = {W.A. Benjamin, Inc.}, + title = {{The Anharmonic Crystal}}, + year = {1967}, +} + +@article{Cai.2021, + abstract = {{Phonon chirality has attracted intensive attention since it breaks the traditional cognition that phonons are linear propagating bosons. This new quasiparticle property has been extensively studied theoretically and experimentally. However, characterization of the phonon chirality throughout the full Brillouin zone is still not possible due to the lack of available experimental tools. In this work, phonon dispersion and chirality of tungsten carbide were investigated by millielectronvolt energy-resolution inelastic X-ray scattering. The atomistic calculation indicates that in-plane longitudinal and transverse acoustic phonons near K and K\$\textasciicircum\textbackslashprime\$ points are circularly polarized due to the broken inversion symmetry. Anomalous inelastic X-ray scattering by these circularly polarized phonons was observed and attributed to their chirality. Our results show that inelastic X-ray scattering can be utilized to characterize phonon chirality in materials and suggest that a revision to the phonon scattering function is necessary.}}, + author = {Cai, Qingan and Hellman, Olle and Wei, Bin and Sun, Qiyang and Said, Ayman H and Gog, Thomas and Winn, Barry and Li, Chen}, + eprint = {2108.06631}, + journal = {arXiv}, + title = {{Direct Observation of Chiral Phonons by Inelastic X-ray Scattering}}, + year = {2021}, +} + +@article{Born.1912, + author = {Born, M. and Karman, T. von}, + journal = {Physikalische Zeitschrift}, + pages = {297--309}, + title = {{Über Schwingungen in Raumgittern}}, + volume = {13}, + year = {1912}, +} + +@article{Born.1951, + author = {Born, Max and Brix, Peter and Kopfermann, Hans and Heisenberg, W. and Staudinger, Hermann and Stille, Hans and Weizsäcker, Carl Friedrich v. and Euler, Hans von and Hedvall, J. Arvid and Siegel, Carl Ludwig and Rellich, Franz and Nevanlinna, Rolf}, + doi = {10.1007/978-3-642-86703-3}, + title = {{Festschrift zur Feier des Zweihundertjährigen Bestehens der Akademie der Wissenschaften in Göttingen, I. Mathematisch-Physikalische Klasse}}, + year = {1951}, +} + +@article{Boer.1948, + abstract = {{It is shown in a quite general way, that the equation of states of the noble gases, H2, D2 and N2 can be written in a reduced form, in which the thermodynamic quantities T, P, V, etc. are expressed in “molecular units”, i.e. units obtained from the characteristics parameters of the intermolecular field. In general the reduced equation of states contains a parameter A∗, containing also h and the mass of the molecules, which measures essentially the influence of quantum mechanics on the phenomenon considered. Only when classical statistics can be applied and A∗ = 0, the reduced equation of states implies the law of corresponding states in its classical form.The reduction with molecular units is applied to the condensed phase of the substances mentioned above to study experimentally the thermodynamical properties as a function of A∗ and to obtain in this way information on the influence of quantum theory on these phenomena.}}, + author = {Boer, J De}, + doi = {10.1016/0031-8914(48)90032-9}, + issn = {0031-8914}, + journal = {Physica}, + number = {2-3}, + pages = {139--148}, + title = {{Quantum theory of condensed permanent gases I the law of corresponding states}}, + volume = {14}, + year = {1948}, +} + +@article{Benshalom.2021, + abstract = {{We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasi-harmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the temperature dependence of other material properties governed by it.}}, + author = {Benshalom, Nimrod and Reuveni, Guy and Korobko, Roman and Yaffe, Omer and Hellman, Olle}, + eprint = {2108.04589}, + journal = {arXiv}, + title = {{The dielectric response of rock-salt crystals at finite temperatures from first principles}}, + year = {2021}, +} + +@article{Benshalom.2022v0s, + abstract = {{We have found that the polarization dependence of the Raman signal in organic crystals can only be described by a fourth-rank formalism. The generalization from the traditional second-rank Raman tensor \$\textbackslashmathcal\{R\}\$ is physically motivated by consideration of the light scattering mechanism of anharmonic crystals at finite temperatures, and explained in terms of off-diagonal components of the crystal self-energy. We thus establish a novel manifestation of anharmonicity in inelastic light scattering, markedly separate from the better known phonon lifetime.}}, + author = {Benshalom, Nimrod and Asher, Maor and Jouclas, Rémy and Korobko, Roman and Schweicher, Guillaume and Liu, Jie and Geerts, Yves and Hellman, Olle and Yaffe, Omer}, + eprint = {2204.12528}, + journal = {arXiv}, + title = {{Phonon-phonon interactions in the polarizarion dependence of Raman scattering}}, + year = {2022}, +} + +@article{Benshalom.2022, + abstract = {{We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature-dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasiharmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the temperature dependence of other material properties governed by it.}}, + author = {Benshalom, Nimrod and Reuveni, Guy and Korobko, Roman and Yaffe, Omer and Hellman, Olle}, + doi = {10.1103/physrevmaterials.6.033607}, + journal = {Physical Review Materials}, + number = {3}, + pages = {033607}, + title = {{Dielectric response of rock-salt crystals at finite temperatures from first principles}}, + volume = {6}, + year = {2022}, +} + diff --git a/paper/paper.md b/paper/paper.md index e1a9118e..36ac88eb 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -58,18 +58,18 @@ affiliations: - name: College of Letters and Science, Department of Chemistry and Biochemistry, University of California, Los Angeles (UCLA), California 90025, USA index: 6 date: August 2023 -bibliography: paper.bib +bibliography: literature.bib --- # Introduction Properties of materials change with temperature, i.e., the vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. -In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtain temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics [cite Tuckerman]. +In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtain temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics. The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can provide _excellent_ qualitative microscopic insight into physical phenomena, and often even very good quantitative results, as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made, but the _precision_ is excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. -The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [CITE]. Alternatively, temperature-dependent _effective_, renormalized model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [CITE deBoer1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [CITE Born, Hooton]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [CITE Klein1972]. +The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent _effective_, renormalized model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [@Boer.1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [@Klein.1972]. # Statement of need From 907f1b8b5a8e8863465c873ece65269db3ea1520 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 15:11:54 +0200 Subject: [PATCH 15/48] paper | bib update --- paper/literature.bib | 735 ++++++++++++++++++++++++------------------- paper/paper.md | 2 +- 2 files changed, 416 insertions(+), 321 deletions(-) diff --git a/paper/literature.bib b/paper/literature.bib index dff80c59..d574ae69 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -1,56 +1,201 @@ -@article{Zhou.2018, - abstract = {{Structural phase transitions and soft phonon modes pose a long-standing challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO3 is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200 K. Our calculations can accurately predict the temperature dependence of the electron mobility in SrTiO3 between 150–300 K, and reveal the microscopic origin of its roughly T-3 trend. Our approach enables first-principles calculations of e-ph interactions and charge transport in broad classes of crystals with phase transitions and strongly anharmonic phonons.}}, - author = {Zhou, Jin-Jian and Hellman, Olle and Bernardi, Marco}, - doi = {10.1103/physrevlett.121.226603}, - eprint = {1806.05775}, - issn = {0031-9007}, - journal = {Physical Review Letters}, - number = {22}, - pages = {226603}, - title = {{Electron-Phonon Scattering in the Presence of Soft Modes and Electron Mobility in SrTiO3 Perovskite from First Principles}}, - volume = {121}, - year = {2018}, +@article{Reig.2022, + abstract = {{Understanding heat flow in layered transition metal dichalcogenide (TMD) crystals is crucial for applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood, in particular how transport is affected by material thickness and the material's environment. This combined experimental–theoretical study establishes a unifying physical picture of the intrinsic lattice thermal conductivity of the representative TMD MoSe2. Thermal conductivity measurements using Raman thermometry on a large set of clean, crystalline, suspended crystals with systematically varied thickness are combined with ab initio simulations with phonons at finite temperature. The results show that phonon dispersions and lifetimes change strongly with thickness, yet the thinnest TMD films exhibit an in‐plane thermal conductivity that is only marginally smaller than that of bulk crystals. This is the result of compensating phonon contributions, in particular heat‐carrying modes around ≈0.1 THz in (sub)nanometer thin films, with a surprisingly long mean free path of several micrometers. This behavior arises directly from the layered nature of the material. Furthermore, out‐of‐plane heat dissipation to air molecules is remarkably efficient, in particular for the thinnest crystals, increasing the apparent thermal conductivity of monolayer MoSe2 by an order of magnitude. These results are crucial for the design of (flexible) TMD‐based (opto‐)electronic applications. Combined experimental–theoretical study using Raman thermometry and ab initio simulations to unravel the heat transport properties of suspended MoSe2 crystals with systematic thickness variation down to the monolayer. Monolayer films have almost the same in‐plane thermal conductivity as bulk material thanks to an additional heat‐carrying low‐frequency mode. Out‐of‐plane heat dissipation to air is extremely efficient for the thinnest flakes.}}, + author = {Reig, David Saleta and Varghese, Sebin and Farris, Roberta and Block, Alexander and Mehew, Jake D. and Hellman, Olle and Woźniak, Paweł and Sledzinska, Marianna and Sachat, Alexandros El and Chávez‐Ángel, Emigdio and Valenzuela, Sergio O. and Hulst, Niek F. van and Ordejón, Pablo and Zanolli, Zeila and Torres, Clivia M. Sotomayor and Verstraete, Matthieu J. and Tielrooij, Klaas‐Jan}, + doi = {10.1002/adma.202108352}, + issn = {0935-9648}, + journal = {Advanced Materials}, + number = {10}, + pages = {2108352}, + title = {{Unraveling Heat Transport and Dissipation in Suspended MoSe2 from Bulk to Monolayer}}, + volume = {34}, + year = {2022}, } -@article{Werthamer.1970kr, - abstract = {{The self-consistent phonon theory of anharmonic lattice dynamics is derived via a stationary functional formulation. The crystal dynamics is approximated by a set of damped oscillators, and these are used to construct a trial action, analytically continued into the complex time-temperature plane. Using the action, a free-energy functional is required to be stationary with respect to the trial oscillators. The resulting phonon modes are undamped at the first order of approximation, whereas to second order the phonon spectral function is determined self-consistently. Expressions are obtained in first order for various thermodynamic derivatives, such as pressure, elastic constants, specific heats, and thermal expansion.}}, - author = {Werthamer, N. R.}, - doi = {10.1103/physrevb.1.572}, - issn = {1098-0121}, +@article{Menahem.2022, + abstract = {{The anharmonic lattice dynamics of oxide and halide perovskites play a crucial role in their mechanical and optical properties. Raman spectroscopy is one of the key methods used to study these structural dynamics. However, despite decades of research, existing interpretations cannot explain the temperature dependence of the observed Raman spectra. We demonstrate the non-monotonic evolution with temperature of the scattering intensity and present a model for 2nd-order Raman scattering that accounts for this unique trend. By invoking a low-frequency anharmonic feature, we are able to reproduce the Raman spectral line-shapes and integrated intensity temperature dependence. Numerical simulations support our interpretation of this low-frequency mode as a transition between two minima of a double-well potential surface. The model can be applied to other dynamically disordered crystal phases, providing a better understanding of the structural dynamics, leading to favorable electronic, optical, and mechanical properties in functional materials.}}, + author = {Menahem, Matan and Benshalom, Nimrod and Asher, Maor and Aharon, Sigalit and Korobko, Roman and Safran, Sam and Hellman, Olle and Yaffe, Omer}, + eprint = {2208.05563}, + journal = {arXiv}, + title = {{The Disorder Origin of Raman Scattering In Perovskites Single Crystals}}, + year = {2022}, +} + +@article{Benshalom.2022v0s, + abstract = {{We have found that the polarization dependence of the Raman signal in organic crystals can only be described by a fourth-rank formalism. The generalization from the traditional second-rank Raman tensor \$\textbackslashmathcal\{R\}\$ is physically motivated by consideration of the light scattering mechanism of anharmonic crystals at finite temperatures, and explained in terms of off-diagonal components of the crystal self-energy. We thus establish a novel manifestation of anharmonicity in inelastic light scattering, markedly separate from the better known phonon lifetime.}}, + author = {Benshalom, Nimrod and Asher, Maor and Jouclas, Rémy and Korobko, Roman and Schweicher, Guillaume and Liu, Jie and Geerts, Yves and Hellman, Olle and Yaffe, Omer}, + eprint = {2204.12528}, + journal = {arXiv}, + title = {{Phonon-phonon interactions in the polarizarion dependence of Raman scattering}}, + year = {2022}, +} + +@article{Cohen.2022, + abstract = {{Lead‐based halide perovskite crystals are shown to have strongly anharmonic structural dynamics. This behavior is important because it may be the origin of their exceptional photovoltaic properties. The double perovskite, Cs2AgBiBr6, has been recently studied as a lead‐free alternative for optoelectronic applications. However, it does not exhibit the excellent photovoltaic activity of the lead‐based halide perovskites. Therefore, to explore the correlation between the anharmonic structural dynamics and optoelectronic properties in lead‐based halide perovskites, the structural dynamics of Cs2AgBiBr6 are investigated and are compared to its lead‐based analog, CsPbBr3. Using temperature‐dependent Raman measurements, it is found that both materials are indeed strongly anharmonic. Nonetheless, the expression of their anharmonic behavior is markedly different. Cs2AgBiBr6 has well‐defined normal modes throughout the measured temperature range, while CsPbBr3 exhibits a complete breakdown of the normal‐mode picture above 200 K. It is suggested that the breakdown of the normal‐mode picture implies that the average crystal structure may not be a proper starting point to understand the electronic properties of the crystal. In addition to our main findings, an unreported phase of Cs2AgBiBr6 is also discovered below ≈37 K. Raman spectroscopy is used to compare the anharmonic expressions in the structural dynamics of two halide perovskites. In Cs2AgBiBr6, clear normal modes are observed in all measured temperatures. Contrary to this, the Raman spectrum of CsPbBr3 exhibits a breakdown of the normal‐mode picture above 200 K. Implications of these diverging behaviors on the electronic properties of the crystals is discussed.}}, + author = {Cohen, Adi and Brenner, Thomas M. and Klarbring, Johan and Sharma, Rituraj and Fabini, Douglas H. and Korobko, Roman and Nayak, Pabitra K. and Hellman, Olle and Yaffe, Omer}, + doi = {10.1002/adma.202107932}, + issn = {0935-9648}, + journal = {Advanced Materials}, + pages = {2107932}, + title = {{Diverging Expressions of Anharmonicity in Halide Perovskites}}, + year = {2022}, +} + +@article{Benshalom.2022, + abstract = {{We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature-dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasiharmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the temperature dependence of other material properties governed by it.}}, + author = {Benshalom, Nimrod and Reuveni, Guy and Korobko, Roman and Yaffe, Omer and Hellman, Olle}, + doi = {10.1103/physrevmaterials.6.033607}, + journal = {Physical Review Materials}, + number = {3}, + pages = {033607}, + title = {{Dielectric response of rock-salt crystals at finite temperatures from first principles}}, + volume = {6}, + year = {2022}, +} + +@article{Reig.2021, + abstract = {{Understanding thermal transport in layered transition metal dichalcogenide (TMD) crystals is crucial for a myriad of applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood. Here, we present a combined experimental-theoretical study of the intrinsic lattice thermal conductivity of the representative TMD MoSe\$\_2\$, focusing on the effect of material thickness and the material's environment. We use Raman thermometry measurements on suspended crystals, where we identify and eliminate crucial artefacts, and perform \$ab\$ \$initio\$ simulations with phonons at finite, rather than zero, temperature. We find that phonon dispersions and lifetimes change strongly with thickness, yet (sub)nanometer thin TMD films exhibit a similar in-plane thermal conductivity (\$\textbackslashsim\$20\textbackslashtextasciitildeWm\$\textasciicircum\{-1\}\$K\$\textasciicircum\{-1\}\$) as bulk crystals (\$\textbackslashsim\$40\textbackslashtextasciitildeWm\$\textasciicircum\{-1\}\$K\$\textasciicircum\{-1\}\$). This is the result of compensating phonon contributions, in particular low-frequency modes with a surprisingly long mean free path of several micrometers that contribute significantly to thermal transport for monolayers. We furthermore demonstrate that out-of-plane heat dissipation to air is remarkably efficient, in particular for the thinnest crystals. These results are crucial for the design of TMD-based applications in thermal management, thermoelectrics and (opto)electronics.}}, + author = {Reig, D Saleta and Varghese, S and Farris, R and Block, A and Mehew, J D and Hellman, O and Woźniak, P and Sledzinska, M and Sachat, A El and Chávez-Ángel, E and Valenzuela, S O and Hulst, N F Van and Ordejón, P and Zanolli, Z and Torres, C M Sotomayor and Verstraete, M J and Tielrooij, K J}, + eprint = {2109.09225}, + journal = {arXiv}, + title = {{Unraveling heat transport and dissipation in suspended MoSe\$\_2\$ crystals from bulk to monolayer}}, + year = {2021}, +} + +@article{Monacelli.2021, + abstract = {{The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approximation (SSCHA) method. This technique rigorously describes the full thermodynamics of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivatives with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles density-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to determine the phase diagram of any crystal at finite temperature. It enables the calculation of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon spectral functions. We review the theoretical framework of the SSCHA and its dynamical extension, making particular emphasis on the physical inter pretation of the variables present in the theory that can enlighten the comparison with any other anharmonic theory. A modular and flexible Python environment is used for the implementation, which allows for a clean interaction with other packages. We briefly present a toy-model calculation to illustrate the potential of the code. Several applications of the method in superconducting hydrides, charge-density-wave materials, and thermoelectric compounds are also reviewed.}}, + author = {Monacelli, Lorenzo and Bianco, Raffaello and Cherubini, Marco and Calandra, Matteo and Errea, Ion and Mauri, Francesco}, + doi = {10.1088/1361-648x/ac066b}, + eprint = {2103.03973}, + issn = {0953-8984}, + journal = {Journal of Physics: Condensed Matter}, + number = {36}, + pages = {363001}, + title = {{The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects}}, + volume = {33}, + year = {2021}, +} + +@article{Dangić.2021, + abstract = {{The proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity κ. However, the κ of GeTe increases at the ferroelectric phase transition near 700 K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in κ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Strong anharmonicity near the phase transition induces non-Lorentzian shapes of the phonon power spectra. To account for these effects, we implement a method of calculating κ based on the Green-Kubo approach and find that the Boltzmann transport equation underestimates κ near the phase transition. Our findings elucidate the influence of structural phase transitions on κ and provide guidance for design of better thermoelectric materials.}}, + author = {Dangić, Đorđe and Hellman, Olle and Fahy, Stephen and Savić, Ivana}, + doi = {10.1038/s41524-021-00523-7}, + journal = {npj Computational Materials}, + number = {1}, + pages = {57}, + title = {{The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe}}, + volume = {7}, + year = {2021}, +} + +@article{Benshalom.2021, + abstract = {{We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasi-harmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the temperature dependence of other material properties governed by it.}}, + author = {Benshalom, Nimrod and Reuveni, Guy and Korobko, Roman and Yaffe, Omer and Hellman, Olle}, + eprint = {2108.04589}, + journal = {arXiv}, + title = {{The dielectric response of rock-salt crystals at finite temperatures from first principles}}, + year = {2021}, +} + +@article{Heine.2021, + abstract = {{We put forth an ab initio framework to calculate local moment magnetic interaction parameters, renormalized to treat both the lattice and magnetic systems as a function of temperature T. For bcc Fe, magnetic and lattice thermal disorders act in opposition, the former strengthening the Heisenberg-like interactions, while the latter decreasing them. Below TC, J stays nearly independent of T, while around and above TC, it exhibits a sharp decrease. This remarkable behavior reflects an intricate spin-lattice coupling and its evolution with T, in which magnetic interactions and interatomic bonds are each renormalized by the other. This finding is consistent with magnetization data and with the observed softening of magnon and phonon modes at high temperatures. Magnetization as well as magnon and phonon mode softening are discussed.}}, + author = {Heine, Matthew and Hellman, Olle and Broido, David}, + doi = {10.1103/physrevb.103.184409}, + issn = {2469-9950}, journal = {Physical Review B}, - number = {2}, - pages = {572--581}, - title = {{Self-Consistent Phonon Formulation of Anharmonic Lattice Dynamics}}, - volume = {1}, - year = {1970}, + number = {18}, + pages = {184409}, + title = {{Temperature-dependent renormalization of magnetic interactions by thermal, magnetic, and lattice disorder from first principles}}, + volume = {103}, + year = {2021}, } -@article{Souvatzis.2008, - abstract = {{Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self-consistently from first principles has been developed to address this issue. The method combines concepts from Born’s interatomic self-consistent phonon approach with first principles calculations of accurate interatomic forces in a supercell. The method has been tested on the high-temperature bcc phase of Ti, Zr, and Hf, as representative examples, and is found to reproduce the observed high-temperature phonon frequencies with good accuracy.}}, - author = {Souvatzis, P. and Eriksson, O. and Katsnelson, M. I. and Rudin, S. P.}, - doi = {10.1103/physrevlett.100.095901}, - eprint = {0803.1325}, +@article{Roekeghem.2021, + abstract = {{The Quantum Self-Consistent Ab-Initio Lattice Dynamics package (QSCAILD) is a python library that computes temperature-dependent effective 2nd and 3rd order interatomic force constants in crystals, including anharmonic effects. QSCAILD’s approach is based on the quantum statistics of a harmonic model. The program requires the forces acting on displaced atoms of a solid as an input, which can be obtained from an external code based on density functional theory, or any other calculator. This article describes QSCAILD’s implementation, clarifies its connections to other methods, and illustrates its use in the case of the SrTiO3 cubic perovskite structure. Program Program Title: QSCAILD CPC Library link to program files: https://doi.org/10.17632/y4c922fwtf.1 Licensing provisions: GNU General Public License version 3.0 Programming language: Python External routines/libraries: MPI, NumPy, SciPy, spglib, phonopy, sklearn Nature of problem: Calculation of effective interatomic force constants at finite temperature Solution method: Regression analysis of forces from density functional theory coupled with a harmonic model of the quantum canonical ensemble, performed in an iterative way to achieve self-consistency of the phonon spectrum}}, + author = {Roekeghem, Ambroise van and Carrete, Jesús and Mingo, Natalio}, + doi = {10.1016/j.cpc.2021.107945}, + eprint = {2006.12867}, + issn = {0010-4655}, + journal = {Computer Physics Communications}, + pages = {107945}, + title = {{Quantum Self-Consistent Ab-Initio Lattice Dynamics}}, + volume = {263}, + year = {2021}, +} + +@article{Cai.2021, + abstract = {{Phonon chirality has attracted intensive attention since it breaks the traditional cognition that phonons are linear propagating bosons. This new quasiparticle property has been extensively studied theoretically and experimentally. However, characterization of the phonon chirality throughout the full Brillouin zone is still not possible due to the lack of available experimental tools. In this work, phonon dispersion and chirality of tungsten carbide were investigated by millielectronvolt energy-resolution inelastic X-ray scattering. The atomistic calculation indicates that in-plane longitudinal and transverse acoustic phonons near K and K\$\textasciicircum\textbackslashprime\$ points are circularly polarized due to the broken inversion symmetry. Anomalous inelastic X-ray scattering by these circularly polarized phonons was observed and attributed to their chirality. Our results show that inelastic X-ray scattering can be utilized to characterize phonon chirality in materials and suggest that a revision to the phonon scattering function is necessary.}}, + author = {Cai, Qingan and Hellman, Olle and Wei, Bin and Sun, Qiyang and Said, Ayman H and Gog, Thomas and Winn, Barry and Li, Chen}, + eprint = {2108.06631}, + journal = {arXiv}, + title = {{Direct Observation of Chiral Phonons by Inelastic X-ray Scattering}}, + year = {2021}, +} + +@article{Klarbring.2020vk, + abstract = {{The lead-free halide double perovskite class of materials offers a promising venue for resolving issues related to toxicity of Pb and long-term stability of the lead-containing halide perovskites. We present a first-principles study of the lattice vibrations in Cs2AgBiBr6, the prototypical compound in this class and show that the lattice dynamics of Cs2AgBiBr6 is highly anharmonic, largely in regards to tilting of AgBr6 and BiBr6 octahedra. Using an energy- and temperature-dependent phonon spectral function, we then show how the experimentally observed cubic-to-tetragonal phase transformation is caused by the collapse of a soft phonon branch. We finally reveal that the softness and anharmonicity of Cs2AgBiBr6 yield an ultralow thermal conductivity, unexpected of high-symmetry cubic structures.}}, + author = {Klarbring, Johan and Hellman, Olle and Abrikosov, Igor A. and Simak, Sergei I.}, + doi = {10.1103/physrevlett.125.045701}, + eprint = {1912.05351}, issn = {0031-9007}, journal = {Physical Review Letters}, - number = {9}, - pages = {095901}, - title = {{Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory}}, + number = {4}, + pages = {045701}, + title = {{Anharmonicity and Ultralow Thermal Conductivity in Lead-Free Halide Double Perovskites}}, + volume = {125}, + year = {2020}, +} + +@article{Manley.2019, + abstract = {{Lead chalcogenides have exceptional thermoelectric properties and intriguing anharmonic lattice dynamics underlying their low thermal conductivities. An ideal material for thermoelectric efficiency is the phonon glass–electron crystal, which drives research on strategies to scatter or localize phonons while minimally disrupting electronic-transport. Anharmonicity can potentially do both, even in perfect crystals, and simulations suggest that PbSe is anharmonic enough to support intrinsic localized modes that halt transport. Here, we experimentally observe high-temperature localization in PbSe using neutron scattering but find that localization is not limited to isolated modes – zero group velocity develops for a significant section of the transverse optic phonon on heating above a transition in the anharmonic dynamics. Arrest of the optic phonon propagation coincides with unusual sharpening of the longitudinal acoustic mode due to a loss of phase space for scattering. Our study shows how nonlinear physics beyond conventional anharmonic perturbations can fundamentally alter vibrational transport properties. To optimize the performance of lead chalcogenides for thermoelectric applications, strategies to further reduce the crystal’s thermal conductivity is required. Here, the authors discover anharmonic localized vibrations in PbSe crystals for optimizing the crystal’s vibrational transport properties.}}, + author = {Manley, M. E. and Hellman, O. and Shulumba, N. and May, A. F. and Stonaha, P. J. and Lynn, J. W. and Garlea, V. O. and Alatas, A. and Hermann, R. P. and Budai, J. D. and Wang, H. and Sales, B. C. and Minnich, A. J.}, + doi = {10.1038/s41467-019-09921-4}, + journal = {Nature Communications}, + number = {1}, + pages = {1928}, + title = {{Intrinsic anharmonic localization in thermoelectric PbSe}}, + volume = {10}, + year = {2019}, +} + +@article{Heine.2019, + abstract = {{We present a first-principles theoretical approach to calculate temperature dependent phonon dispersions in bcc Fe, which captures finite temperature spin-lattice coupling by treating thermal disorder in both the spin and lattice systems simultaneously. With increasing temperature, thermal atomic displacements are found to induce increasingly large fluctuations in local magnetic moment magnitudes. The calculated phonon dispersions of bcc Fe show excellent agreement with measured data over a wide range of temperatures both above and below the magnetic and structural transition temperatures, suggesting the applicability of the developed approach to other magnetic materials.}}, + author = {Heine, Matthew and Hellman, Olle and Broido, David}, + doi = {10.1103/physrevb.100.104304}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {10}, + pages = {104304}, + title = {{Effect of thermal lattice and magnetic disorder on phonons in bcc Fe: A first-principles study}}, volume = {100}, - year = {2008}, + year = {2019}, } -@article{Shulumba.2016, - abstract = {{We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti1-xAlxN alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti1-xAlxN alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti0.5Al0.5N alloys agree with the calculated phase diagram.}}, - author = {Shulumba, Nina and Hellman, Olle and Raza, Zamaan and Alling, Björn and Barrirero, Jenifer and Mücklich, Frank and Abrikosov, Igor A. and Odén, Magnus}, - doi = {10.1103/physrevlett.117.205502}, - eprint = {1503.02459}, +@article{Kim.2018, + abstract = {{Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.}}, + author = {Kim, D. S. and Hellman, O. and Herriman, J. and Smith, H. L. and Lin, J. Y. Y. and Shulumba, N. and Niedziela, J. L. and Li, C. W. and Abernathy, D. L. and Fultz, B.}, + doi = {10.1073/pnas.1707745115}, + eprint = {1610.08737}, + issn = {0027-8424}, + journal = {Proceedings of the National Academy of Sciences}, + number = {9}, + pages = {201707745}, + title = {{Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon}}, + volume = {115}, + year = {2018}, +} + +@article{Zhou.2018, + abstract = {{Structural phase transitions and soft phonon modes pose a long-standing challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO3 is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200 K. Our calculations can accurately predict the temperature dependence of the electron mobility in SrTiO3 between 150–300 K, and reveal the microscopic origin of its roughly T-3 trend. Our approach enables first-principles calculations of e-ph interactions and charge transport in broad classes of crystals with phase transitions and strongly anharmonic phonons.}}, + author = {Zhou, Jin-Jian and Hellman, Olle and Bernardi, Marco}, + doi = {10.1103/physrevlett.121.226603}, + eprint = {1806.05775}, issn = {0031-9007}, journal = {Physical Review Letters}, - number = {20}, - pages = {205502}, - title = {{Lattice Vibrations Change the Solid Solubility of an Alloy at High Temperatures}}, - volume = {117}, - year = {2016}, + number = {22}, + pages = {226603}, + title = {{Electron-Phonon Scattering in the Presence of Soft Modes and Electron Mobility in SrTiO3 Perovskite from First Principles}}, + volume = {121}, + year = {2018}, } @article{Shulumba.20179s8e, @@ -80,6 +225,33 @@ @article{Shulumba.2017 year = {2017}, } +@article{Dewandre.2016, + abstract = {{The interest in improving the thermoelectric response of bulk materials has received a boost after it has been recognized that layered materials, in particular SnSe, show a very large thermoelectric figure of merit. This result has received great attention while it is now possible to conceive other similar materials or experimental methods to improve this value. Before we can now think of engineering this material it is important we understand the basic mechanism that explains this unusual behavior, where very low thermal conductivity and a high thermopower result from a delicate balance between the crystal and electronic structure. In this Letter, we present a complete temperature evolution of the Seebeck coefficient as the material undergoes a soft crystal transformation and its consequences on other properties within SnSe by means of first-principles calculations. Our results are able to explain the full range of considered experimental temperatures.}}, + author = {Dewandre, Antoine and Hellman, Olle and Bhattacharya, Sandip and Romero, Aldo H. and Madsen, Georg K. H. and Verstraete, Matthieu J.}, + doi = {10.1103/physrevlett.117.276601}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {27}, + pages = {276601}, + title = {{Two-Step Phase Transition in SnSe and the Origins of its High Power Factor from First Principles}}, + volume = {117}, + year = {2016}, +} + +@article{Shulumba.2016, + abstract = {{We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti1-xAlxN alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti1-xAlxN alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti0.5Al0.5N alloys agree with the calculated phase diagram.}}, + author = {Shulumba, Nina and Hellman, Olle and Raza, Zamaan and Alling, Björn and Barrirero, Jenifer and Mücklich, Frank and Abrikosov, Igor A. and Odén, Magnus}, + doi = {10.1103/physrevlett.117.205502}, + eprint = {1503.02459}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {20}, + pages = {205502}, + title = {{Lattice Vibrations Change the Solid Solubility of an Alloy at High Temperatures}}, + volume = {117}, + year = {2016}, +} + @article{Romero.2015, abstract = {{We investigate the harmonic and anharmonic contributions to the phonon spectrum of lead telluride and perform a complete characterization of how thermal properties of PbTe evolve as temperature increases. We analyze the thermal resistivity's variation with temperature and clarify misconceptions about existing experimental literature. The resistivity initially increases sublinearly because of phase space effects and ultra strong anharmonic renormalizations of specific bands. This effect is the strongest factor in the favorable thermoelectric properties of PbTe, and it explains its limitations at higher T. This quantitative prediction opens the prospect of phonon phase space engineering to tailor the lifetimes of crucial heat carrying phonons by considering different structure or nanostructure geometries. We analyze the available scattering volume between TO and LA phonons as a function of temperature and correlate its changes to features in the thermal conductivity.}}, author = {Romero, A. H. and Gross, E. K. U. and Verstraete, M. J. and Hellman, Olle}, @@ -94,35 +266,18 @@ @article{Romero.2015 year = {2015}, } -@article{Reig.2022, - abstract = {{Understanding heat flow in layered transition metal dichalcogenide (TMD) crystals is crucial for applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood, in particular how transport is affected by material thickness and the material's environment. This combined experimental–theoretical study establishes a unifying physical picture of the intrinsic lattice thermal conductivity of the representative TMD MoSe2. Thermal conductivity measurements using Raman thermometry on a large set of clean, crystalline, suspended crystals with systematically varied thickness are combined with ab initio simulations with phonons at finite temperature. The results show that phonon dispersions and lifetimes change strongly with thickness, yet the thinnest TMD films exhibit an in‐plane thermal conductivity that is only marginally smaller than that of bulk crystals. This is the result of compensating phonon contributions, in particular heat‐carrying modes around ≈0.1 THz in (sub)nanometer thin films, with a surprisingly long mean free path of several micrometers. This behavior arises directly from the layered nature of the material. Furthermore, out‐of‐plane heat dissipation to air molecules is remarkably efficient, in particular for the thinnest crystals, increasing the apparent thermal conductivity of monolayer MoSe2 by an order of magnitude. These results are crucial for the design of (flexible) TMD‐based (opto‐)electronic applications. Combined experimental–theoretical study using Raman thermometry and ab initio simulations to unravel the heat transport properties of suspended MoSe2 crystals with systematic thickness variation down to the monolayer. Monolayer films have almost the same in‐plane thermal conductivity as bulk material thanks to an additional heat‐carrying low‐frequency mode. Out‐of‐plane heat dissipation to air is extremely efficient for the thinnest flakes.}}, - author = {Reig, David Saleta and Varghese, Sebin and Farris, Roberta and Block, Alexander and Mehew, Jake D. and Hellman, Olle and Woźniak, Paweł and Sledzinska, Marianna and Sachat, Alexandros El and Chávez‐Ángel, Emigdio and Valenzuela, Sergio O. and Hulst, Niek F. van and Ordejón, Pablo and Zanolli, Zeila and Torres, Clivia M. Sotomayor and Verstraete, Matthieu J. and Tielrooij, Klaas‐Jan}, - doi = {10.1002/adma.202108352}, - issn = {0935-9648}, - journal = {Advanced Materials}, - number = {10}, - pages = {2108352}, - title = {{Unraveling Heat Transport and Dissipation in Suspended MoSe2 from Bulk to Monolayer}}, - volume = {34}, - year = {2022}, -} - -@article{Reig.2021, - abstract = {{Understanding thermal transport in layered transition metal dichalcogenide (TMD) crystals is crucial for a myriad of applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood. Here, we present a combined experimental-theoretical study of the intrinsic lattice thermal conductivity of the representative TMD MoSe\$\_2\$, focusing on the effect of material thickness and the material's environment. We use Raman thermometry measurements on suspended crystals, where we identify and eliminate crucial artefacts, and perform \$ab\$ \$initio\$ simulations with phonons at finite, rather than zero, temperature. We find that phonon dispersions and lifetimes change strongly with thickness, yet (sub)nanometer thin TMD films exhibit a similar in-plane thermal conductivity (\$\textbackslashsim\$20\textbackslashtextasciitildeWm\$\textasciicircum\{-1\}\$K\$\textasciicircum\{-1\}\$) as bulk crystals (\$\textbackslashsim\$40\textbackslashtextasciitildeWm\$\textasciicircum\{-1\}\$K\$\textasciicircum\{-1\}\$). This is the result of compensating phonon contributions, in particular low-frequency modes with a surprisingly long mean free path of several micrometers that contribute significantly to thermal transport for monolayers. We furthermore demonstrate that out-of-plane heat dissipation to air is remarkably efficient, in particular for the thinnest crystals. These results are crucial for the design of TMD-based applications in thermal management, thermoelectrics and (opto)electronics.}}, - author = {Reig, D Saleta and Varghese, S and Farris, R and Block, A and Mehew, J D and Hellman, O and Woźniak, P and Sledzinska, M and Sachat, A El and Chávez-Ángel, E and Valenzuela, S O and Hulst, N F Van and Ordejón, P and Zanolli, Z and Torres, C M Sotomayor and Verstraete, M J and Tielrooij, K J}, - eprint = {2109.09225}, - journal = {arXiv}, - title = {{Unraveling heat transport and dissipation in suspended MoSe\$\_2\$ crystals from bulk to monolayer}}, - year = {2021}, -} - -@article{Menahem.2022, - abstract = {{The anharmonic lattice dynamics of oxide and halide perovskites play a crucial role in their mechanical and optical properties. Raman spectroscopy is one of the key methods used to study these structural dynamics. However, despite decades of research, existing interpretations cannot explain the temperature dependence of the observed Raman spectra. We demonstrate the non-monotonic evolution with temperature of the scattering intensity and present a model for 2nd-order Raman scattering that accounts for this unique trend. By invoking a low-frequency anharmonic feature, we are able to reproduce the Raman spectral line-shapes and integrated intensity temperature dependence. Numerical simulations support our interpretation of this low-frequency mode as a transition between two minima of a double-well potential surface. The model can be applied to other dynamically disordered crystal phases, providing a better understanding of the structural dynamics, leading to favorable electronic, optical, and mechanical properties in functional materials.}}, - author = {Menahem, Matan and Benshalom, Nimrod and Asher, Maor and Aharon, Sigalit and Korobko, Roman and Safran, Sam and Hellman, Olle and Yaffe, Omer}, - eprint = {2208.05563}, - journal = {arXiv}, - title = {{The Disorder Origin of Raman Scattering In Perovskites Single Crystals}}, - year = {2022}, +@article{Tadano.2015, + abstract = {{We present an ab initio framework to calculate anharmonic phonon frequency and phonon lifetime that is applicable to severely anharmonic systems. We employ self-consistent phonon (SCPH) theory with microscopic anharmonic force constants, which are extracted from density functional calculations using the least absolute shrinkage and selection operator technique. We apply the method to the high-temperature phase of SrTiO3 and obtain well-defined phonon quasiparticles that are free from imaginary frequencies. Here we show that the anharmonic phonon frequency of the antiferrodistortive mode depends significantly on the system size near the critical temperature of the cubic-to-tetragonal phase transition. By applying perturbation theory to the SCPH result, phonon lifetimes are calculated for cubic SrTiO3, which are then employed to predict lattice thermal conductivity using the Boltzmann transport equation within the relaxation-time approximation. The presented methodology is efficient and accurate, paving the way toward a reliable description of thermodynamic, dynamic, and transport properties of systems with severe anharmonicity, including thermoelectric, ferroelectric, and superconducting materials.}}, + author = {Tadano, Terumasa and Tsuneyuki, Shinji}, + doi = {10.1103/physrevb.92.054301}, + eprint = {1506.01781}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {5}, + pages = {054301}, + title = {{Self-consistent phonon calculations of lattice dynamical properties in cubic SrTiO3 with first-principles anharmonic force constants}}, + volume = {92}, + year = {2015}, } @article{Mei.2015, @@ -138,153 +293,31 @@ @article{Mei.2015 year = {2015}, } -@article{Manley.2019, - abstract = {{Lead chalcogenides have exceptional thermoelectric properties and intriguing anharmonic lattice dynamics underlying their low thermal conductivities. An ideal material for thermoelectric efficiency is the phonon glass–electron crystal, which drives research on strategies to scatter or localize phonons while minimally disrupting electronic-transport. Anharmonicity can potentially do both, even in perfect crystals, and simulations suggest that PbSe is anharmonic enough to support intrinsic localized modes that halt transport. Here, we experimentally observe high-temperature localization in PbSe using neutron scattering but find that localization is not limited to isolated modes – zero group velocity develops for a significant section of the transverse optic phonon on heating above a transition in the anharmonic dynamics. Arrest of the optic phonon propagation coincides with unusual sharpening of the longitudinal acoustic mode due to a loss of phase space for scattering. Our study shows how nonlinear physics beyond conventional anharmonic perturbations can fundamentally alter vibrational transport properties. To optimize the performance of lead chalcogenides for thermoelectric applications, strategies to further reduce the crystal’s thermal conductivity is required. Here, the authors discover anharmonic localized vibrations in PbSe crystals for optimizing the crystal’s vibrational transport properties.}}, - author = {Manley, M. E. and Hellman, O. and Shulumba, N. and May, A. F. and Stonaha, P. J. and Lynn, J. W. and Garlea, V. O. and Alatas, A. and Hermann, R. P. and Budai, J. D. and Wang, H. and Sales, B. C. and Minnich, A. J.}, - doi = {10.1038/s41467-019-09921-4}, - journal = {Nature Communications}, - number = {1}, - pages = {1928}, - title = {{Intrinsic anharmonic localization in thermoelectric PbSe}}, - volume = {10}, - year = {2019}, -} - -@article{Levy.1984, - abstract = {{A quasi‐harmonic approximation is described for studying very low frequency vibrations and flexible paths in proteins. The force constants of the empirical potential function are quadratic approximations to the potentials of mean force; they are evaluated from a molecular dynamics simulation of a protein based on a detailed anharmonic potential. The method is used to identify very low frequency (∼1 cm−1) normal modes for the protein pancreatic trypsin inhibitor. A simplified model for the protein is used, for which each residue is represented by a single interaction center. The quasi‐harmonic force constants of the virtual internal coordinates are evaluated and the normal‐mode frequencies and eigenvectors are obtained. Conformations corresponding to distortions along selected low‐frequency modes are analyzed.}}, - author = {Levy, R. M. and Srinivasan, A. R. and Olson, W. K. and McCammon, J. A.}, - doi = {10.1002/bip.360230610}, - issn = {0006-3525}, - journal = {Biopolymers}, - number = {6}, - pages = {1099--1112}, - title = {{Quasi‐harmonic method for studying very low frequency modes in proteins}}, - volume = {23}, - year = {1984}, -} - -@article{Koehler.1966, - author = {Koehler, Thomas R.}, - doi = {10.1103/physrevlett.17.89}, - issn = {0031-9007}, - journal = {Physical Review Letters}, - number = {2}, - pages = {89--91}, - title = {{Theory of the Self-Consistent Harmonic Approximation with Application to Solid Neon}}, - volume = {17}, - year = {1966}, -} - -@article{Koehler.1971, - abstract = {{A theory is presented of the damping and frequency shift of phonons and of the ground-state energy corrections due to interactions between phonons in quantum crystals with singular forces. The technique begins with the adoption of a trial ground-state wave function of the Jastrow form, together with trial excited-state wave functions constructed to represent one-, two-, and three-phonon excitations. The Hamiltonian matrix in this restricted basis is diagonalized, and the basis is optimized by minimizing the lowest eigenvalue with respect to variational phonon parameters. Using a lowest-order cluster expansion, the unambiguous prescription is obtained that a specific effective potential, softened by the Jastrow correlation function, replaces everywhere the true potential in the existing self-consistent theory of phonon damping applicable to nonsingular forces. Close analogies are drawn with the correlated basis function treatment, of superfluid liquid helium.}}, - author = {Koehler, T. R. and Werthamer, N. R.}, - doi = {10.1103/physreva.3.2074}, - issn = {1050-2947}, - journal = {Physical Review A}, - number = {6}, - pages = {2074--2083}, - title = {{Phonon Spectral Functions and Ground-State Energy of Quantum Crystals in Perturbation Theory with a Variationally Optimum Correlated Basis Set}}, - volume = {3}, - year = {1971}, -} - -@article{Klein.1972, - author = {Klein, M. L. and Horton, G. K.}, - doi = {10.1007/bf00654839}, - issn = {0022-2291}, - journal = {Journal of Low Temperature Physics}, - number = {3-4}, - pages = {151--166}, - title = {{The rise of self-consistent phonon theory}}, - volume = {9}, - year = {1972}, -} - -@article{Klarbring.2020vk, - abstract = {{The lead-free halide double perovskite class of materials offers a promising venue for resolving issues related to toxicity of Pb and long-term stability of the lead-containing halide perovskites. We present a first-principles study of the lattice vibrations in Cs2AgBiBr6, the prototypical compound in this class and show that the lattice dynamics of Cs2AgBiBr6 is highly anharmonic, largely in regards to tilting of AgBr6 and BiBr6 octahedra. Using an energy- and temperature-dependent phonon spectral function, we then show how the experimentally observed cubic-to-tetragonal phase transformation is caused by the collapse of a soft phonon branch. We finally reveal that the softness and anharmonicity of Cs2AgBiBr6 yield an ultralow thermal conductivity, unexpected of high-symmetry cubic structures.}}, - author = {Klarbring, Johan and Hellman, Olle and Abrikosov, Igor A. and Simak, Sergei I.}, - doi = {10.1103/physrevlett.125.045701}, - eprint = {1912.05351}, +@article{Zhang.2014up, + abstract = {{We use a hybrid strategy to obtain anharmonic frequency shifts and lifetimes of phonon quasiparticles from first principles molecular dynamics simulations in modest size supercells. This approach is effective irrespective of crystal structure complexity and facilitates calculation of full anharmonic phonon dispersions, as long as phonon quasiparticles are well defined. We validate this approach to obtain anharmonic effects with calculations in MgSiO3 perovskite, the major Earth forming mineral phase. First, we reproduce irregular thermal frequency shifts of well characterized Raman modes. Second, we combine the phonon gas model (PGM) with quasiparticle frequencies and reproduce free energies obtained using thermodynamic integration. Combining thoroughly sampled quasiparticle dispersions with the PGM we then obtain first-principles anharmonic free energy in the thermodynamic limit (N→∞).}}, + author = {Zhang, Dong-Bo and Sun, Tao and Wentzcovitch, Renata M.}, + doi = {10.1103/physrevlett.112.058501}, + eprint = {1312.7490}, issn = {0031-9007}, journal = {Physical Review Letters}, - number = {4}, - pages = {045701}, - title = {{Anharmonicity and Ultralow Thermal Conductivity in Lead-Free Halide Double Perovskites}}, - volume = {125}, - year = {2020}, -} - -@article{Kim.2018, - abstract = {{Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.}}, - author = {Kim, D. S. and Hellman, O. and Herriman, J. and Smith, H. L. and Lin, J. Y. Y. and Shulumba, N. and Niedziela, J. L. and Li, C. W. and Abernathy, D. L. and Fultz, B.}, - doi = {10.1073/pnas.1707745115}, - eprint = {1610.08737}, - issn = {0027-8424}, - journal = {Proceedings of the National Academy of Sciences}, - number = {9}, - pages = {201707745}, - title = {{Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon}}, - volume = {115}, - year = {2018}, -} - -@article{Horner.1972, - abstract = {{Numerical calculations of phonon spectra, including damping, are reported for bcc3He and4He and for fcc4He. Strong damping is found for the longitudinal branches near the boundary of the Brillouin zone. In the bcc phase anomalous dispersion occurs for several directions at long wavelengths, which is most pronounced in the lowest transverse branch in (110) direction. This leads to an anomaly in the specific heat at low temperatures. In this calculation anharmonicities and short-range correlations are treated in a self-consistent way.}}, - author = {Horner, Heinz}, - doi = {10.1007/bf00653877}, - issn = {0022-2291}, - journal = {Journal of Low Temperature Physics}, - number = {5-6}, - pages = {511--529}, - title = {{Phonons and thermal properties of bcc and fcc helium from a self-consistent anharmonic theory}}, - volume = {8}, - year = {1972}, -} - -@article{Hooton.1958, - abstract = {{Skyrme has recently discussed the use of a model in quantum mechanics. His method is applied to the case of the anharmonic vibrations of a crystal lattice, and compared with a previous treatment by the present author. Some remarks are added which give a new and more physical interpretation of the results of this earlier work.}}, - author = {Hooton, D. J.}, - doi = {10.1080/14786435808243224}, - issn = {0031-8086}, - journal = {Philosophical Magazine}, - number = {25}, - pages = {49--54}, - title = {{The use of a model in anharmonic lattice dynamics}}, - volume = {3}, - year = {1958}, -} - -@article{Hooton.2010, - abstract = {{The thermodynamical formulae of the previous paper are worked out with the help of an adaptation of Debye's continuum approximation ; in particular, the specific heat at constant volume is put into a form suitable for numerical calculation. This formula contains, however, a factor which expresses the (possibly strong) volume dependence of the relation between the new frequency spectrum and that of the customary lattice dynamics : the factor appears in addition to the Debye characteristic temperature θ and must be estimated in any particular application—for example, in the following consideration of solid helium it will be approximated from a linear chain model. The meaning of a Debye characteristic temperature in the anharnionic theory is discussed, and the place of an empirical Debye temperature, determined by fitting specific heat measurements to a theoretical specific heat formula, is also considered. A discussion of this fitted Debye temperature (due to Domb and Salter) is adapted to the anharmonic theory in order to give later a correct application to solid helium.}}, - author = {Hooton, D.J.}, - doi = {10.1080/14786440408520576}, - issn = {1941-5982}, - journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, - number = {375}, - pages = {433--442}, - title = {{LII. A new treatment of anharmonicity in lattice thermodynamics: II}}, - volume = {46}, - year = {2010}, -} - -@article{Hooton.2010mfn, - abstract = {{Born has given a method by which the anharmonic vibrational motion of the atoms in a crystal can be approximated in terms of an adapted set of harmonic oscillations, these differing from the usualmodes of vibration of harmonic lattice dynamics ; this method is here redeveloped from another standpoint and extended to give explicit results. The thermodynamical formulae of the anharmonic crystal can be given a simple form: they consist of the customary formulae for a set of harmonic oscillators, but now expressed in terms of new frequencies denned essentially from the quadratic and quartic terms in an expansion of the potential energy, plus correction terms which express the difference between the actual anharmonic motion and the harmonic approximation. For small anharmonicity the formulae reduce to thoseof the usual perturbation procedure (allowance for thermal expansion) with some extensions, but they also give a solution in the case of strong anharmonicity. This latter solution will later be used in a discussion of solid helium.}}, - author = {Hooton, D.J.}, - doi = {10.1080/14786440408520575}, - issn = {1941-5982}, - journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, - number = {375}, - pages = {422--432}, - title = {{LI. A new treatment of anharmonicity in lattice thermodynamics: I}}, - volume = {46}, - year = {2010}, -} - -@thesis{Hellman.2012, - author = {Hellman, Olle}, - title = {{Thermal properties of materials from first principles}}, - type = {phdthesis}, - year = {2012}, + number = {5}, + pages = {058501}, + title = {{Phonon Quasiparticles and Anharmonic Free Energy in Complex Systems}}, + volume = {112}, + year = {2014}, +} + +@article{Tadano.2014, + abstract = {{A systematic method to calculate anharmonic force constants of crystals is presented. The method employs the direct-method approach, where anharmonic force constants are extracted from the trajectory of first-principles molecular dynamics simulations at high temperature. The method is applied to Si where accurate cubic and quartic force constants are obtained. We observe that higher-order correction is crucial to obtain accurate force constants from the trajectory with large atomic displacements. The calculated harmonic and anharmonic force constants are, then, combined with the Boltzmann transport equation (BTE) and non-equilibrium molecular dynamics (NEMD) methods in calculating the thermal conductivity. The BTE approach successfully predicts the lattice thermal conductivity of bulk Si, whereas NEMD shows considerable underestimates. To evaluate the linear extrapolation method employed in NEMD to estimate bulk values, we analyze the size dependence in NEMD based on BTE calculations. We observe strong nonlinearity in the size dependence of NEMD in Si, which can be ascribed to acoustic phonons having long mean-free-paths and carrying considerable heat. Subsequently, we also apply the whole method to a thermoelectric material Mg2Si and demonstrate the reliability of the NEMD method for systems with low thermal conductivities.}}, + author = {Tadano, T and Gohda, Y and Tsuneyuki, S}, + doi = {10.1088/0953-8984/26/22/225402}, + issn = {0953-8984}, + journal = {Journal of Physics: Condensed Matter}, + number = {22}, + pages = {225402}, + title = {{Anharmonic force constants extracted from first-principles molecular dynamics: applications to heat transfer simulations}}, + volume = {26}, + year = {2014}, } @article{Hellman.2013oi5, @@ -315,6 +348,27 @@ @article{Hellman.2013 year = {2013}, } +@article{Errea.2013, + abstract = {{Palladium hydrides display the largest isotope effect anomaly known in the literature. Replacement of hydrogen with the heavier isotopes leads to higher superconducting temperatures, a behavior inconsistent with harmonic theory. Solving the self-consistent harmonic approximation by a stochastic approach, we obtain the anharmonic free energy, the thermal expansion, and the superconducting properties fully ab initio. We find that the phonon spectra are strongly renormalized by anharmonicity far beyond the perturbative regime. Superconductivity is phonon mediated, but the harmonic approximation largely overestimates the superconducting critical temperatures. We explain the inverse isotope effect, obtaining a -0.38 value for the isotope coefficient in good agreement with experiments, hydrogen anharmonicity being mainly responsible for the isotope anomaly.}}, + author = {Errea, Ion and Calandra, Matteo and Mauri, Francesco}, + doi = {10.1103/physrevlett.111.177002}, + eprint = {1305.7123}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {17}, + pages = {177002}, + title = {{First-Principles Theory of Anharmonicity and the Inverse Isotope Effect in Superconducting Palladium-Hydride Compounds}}, + volume = {111}, + year = {2013}, +} + +@thesis{Hellman.2012, + author = {Hellman, Olle}, + title = {{Thermal properties of materials from first principles}}, + type = {phdthesis}, + year = {2012}, +} + @article{Hellman.2011, abstract = {{An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic—or higher order—potential energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated.}}, author = {Hellman, O. and Abrikosov, I. A. and Simak, S. I.}, @@ -329,43 +383,44 @@ @article{Hellman.2011 year = {2011}, } -@article{Heine.2021, - abstract = {{We put forth an ab initio framework to calculate local moment magnetic interaction parameters, renormalized to treat both the lattice and magnetic systems as a function of temperature T. For bcc Fe, magnetic and lattice thermal disorders act in opposition, the former strengthening the Heisenberg-like interactions, while the latter decreasing them. Below TC, J stays nearly independent of T, while around and above TC, it exhibits a sharp decrease. This remarkable behavior reflects an intricate spin-lattice coupling and its evolution with T, in which magnetic interactions and interatomic bonds are each renormalized by the other. This finding is consistent with magnetization data and with the observed softening of magnon and phonon modes at high temperatures. Magnetization as well as magnon and phonon mode softening are discussed.}}, - author = {Heine, Matthew and Hellman, Olle and Broido, David}, - doi = {10.1103/physrevb.103.184409}, - issn = {2469-9950}, - journal = {Physical Review B}, - number = {18}, - pages = {184409}, - title = {{Temperature-dependent renormalization of magnetic interactions by thermal, magnetic, and lattice disorder from first principles}}, - volume = {103}, - year = {2021}, +@article{Hooton.2010, + abstract = {{The thermodynamical formulae of the previous paper are worked out with the help of an adaptation of Debye's continuum approximation ; in particular, the specific heat at constant volume is put into a form suitable for numerical calculation. This formula contains, however, a factor which expresses the (possibly strong) volume dependence of the relation between the new frequency spectrum and that of the customary lattice dynamics : the factor appears in addition to the Debye characteristic temperature θ and must be estimated in any particular application—for example, in the following consideration of solid helium it will be approximated from a linear chain model. The meaning of a Debye characteristic temperature in the anharnionic theory is discussed, and the place of an empirical Debye temperature, determined by fitting specific heat measurements to a theoretical specific heat formula, is also considered. A discussion of this fitted Debye temperature (due to Domb and Salter) is adapted to the anharmonic theory in order to give later a correct application to solid helium.}}, + author = {Hooton, D.J.}, + doi = {10.1080/14786440408520576}, + issn = {1941-5982}, + journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, + number = {375}, + pages = {433--442}, + title = {{LII. A new treatment of anharmonicity in lattice thermodynamics: II}}, + volume = {46}, + year = {2010}, } -@article{Heine.2019, - abstract = {{We present a first-principles theoretical approach to calculate temperature dependent phonon dispersions in bcc Fe, which captures finite temperature spin-lattice coupling by treating thermal disorder in both the spin and lattice systems simultaneously. With increasing temperature, thermal atomic displacements are found to induce increasingly large fluctuations in local magnetic moment magnitudes. The calculated phonon dispersions of bcc Fe show excellent agreement with measured data over a wide range of temperatures both above and below the magnetic and structural transition temperatures, suggesting the applicability of the developed approach to other magnetic materials.}}, - author = {Heine, Matthew and Hellman, Olle and Broido, David}, - doi = {10.1103/physrevb.100.104304}, - issn = {2469-9950}, - journal = {Physical Review B}, - number = {10}, - pages = {104304}, - title = {{Effect of thermal lattice and magnetic disorder on phonons in bcc Fe: A first-principles study}}, - volume = {100}, - year = {2019}, +@article{Hooton.2010mfn, + abstract = {{Born has given a method by which the anharmonic vibrational motion of the atoms in a crystal can be approximated in terms of an adapted set of harmonic oscillations, these differing from the usualmodes of vibration of harmonic lattice dynamics ; this method is here redeveloped from another standpoint and extended to give explicit results. The thermodynamical formulae of the anharmonic crystal can be given a simple form: they consist of the customary formulae for a set of harmonic oscillators, but now expressed in terms of new frequencies denned essentially from the quadratic and quartic terms in an expansion of the potential energy, plus correction terms which express the difference between the actual anharmonic motion and the harmonic approximation. For small anharmonicity the formulae reduce to thoseof the usual perturbation procedure (allowance for thermal expansion) with some extensions, but they also give a solution in the case of strong anharmonicity. This latter solution will later be used in a discussion of solid helium.}}, + author = {Hooton, D.J.}, + doi = {10.1080/14786440408520575}, + issn = {1941-5982}, + journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, + number = {375}, + pages = {422--432}, + title = {{LI. A new treatment of anharmonicity in lattice thermodynamics: I}}, + volume = {46}, + year = {2010}, } -@article{Gillis.1967, - abstract = {{The self-consistent phonon theory of anharmonic lattice dynamics, devised independently by several authors using varying techniques and implemented computationally by Koehler, is here applied to the crystals of neon and argon. A Lennard-Jones 6-12 interatomic potential is assumed. The quantities calculated are the phonon spectrum and the bulk thermodynamic properties of thermal expansion, compressibility, and specific heat, all as a function of temperature at zero pressure. Although the computations are intended primarily to explore in detail the content of the self-consistent phonon approximation preparatory to incorporating the more elaborate expressions of the next higher approximation, comparison is made with the existing experimental data.}}, - author = {Gillis, N. S. and Werthamer, N. R. and Koehler, T. R.}, - doi = {10.1103/physrev.165.951}, - issn = {0031-899X}, - journal = {Physical Review}, - number = {3}, - pages = {951--959}, - title = {{Properties of Crystalline Argon and Neon in the Self-Consistent Phonon Approximation}}, - volume = {165}, - year = {1967}, +@article{Souvatzis.2008, + abstract = {{Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self-consistently from first principles has been developed to address this issue. The method combines concepts from Born’s interatomic self-consistent phonon approach with first principles calculations of accurate interatomic forces in a supercell. The method has been tested on the high-temperature bcc phase of Ti, Zr, and Hf, as representative examples, and is found to reproduce the observed high-temperature phonon frequencies with good accuracy.}}, + author = {Souvatzis, P. and Eriksson, O. and Katsnelson, M. I. and Rudin, S. P.}, + doi = {10.1103/physrevlett.100.095901}, + eprint = {0803.1325}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {9}, + pages = {095901}, + title = {{Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory}}, + volume = {100}, + year = {2008}, } @article{Dove.1986, @@ -381,40 +436,68 @@ @article{Dove.1986 year = {1986}, } -@article{Dewandre.2016, - abstract = {{The interest in improving the thermoelectric response of bulk materials has received a boost after it has been recognized that layered materials, in particular SnSe, show a very large thermoelectric figure of merit. This result has received great attention while it is now possible to conceive other similar materials or experimental methods to improve this value. Before we can now think of engineering this material it is important we understand the basic mechanism that explains this unusual behavior, where very low thermal conductivity and a high thermopower result from a delicate balance between the crystal and electronic structure. In this Letter, we present a complete temperature evolution of the Seebeck coefficient as the material undergoes a soft crystal transformation and its consequences on other properties within SnSe by means of first-principles calculations. Our results are able to explain the full range of considered experimental temperatures.}}, - author = {Dewandre, Antoine and Hellman, Olle and Bhattacharya, Sandip and Romero, Aldo H. and Madsen, Georg K. H. and Verstraete, Matthieu J.}, - doi = {10.1103/physrevlett.117.276601}, - issn = {0031-9007}, - journal = {Physical Review Letters}, - number = {27}, - pages = {276601}, - title = {{Two-Step Phase Transition in SnSe and the Origins of its High Power Factor from First Principles}}, - volume = {117}, - year = {2016}, +@article{Levy.1984, + abstract = {{A quasi‐harmonic approximation is described for studying very low frequency vibrations and flexible paths in proteins. The force constants of the empirical potential function are quadratic approximations to the potentials of mean force; they are evaluated from a molecular dynamics simulation of a protein based on a detailed anharmonic potential. The method is used to identify very low frequency (∼1 cm−1) normal modes for the protein pancreatic trypsin inhibitor. A simplified model for the protein is used, for which each residue is represented by a single interaction center. The quasi‐harmonic force constants of the virtual internal coordinates are evaluated and the normal‐mode frequencies and eigenvectors are obtained. Conformations corresponding to distortions along selected low‐frequency modes are analyzed.}}, + author = {Levy, R. M. and Srinivasan, A. R. and Olson, W. K. and McCammon, J. A.}, + doi = {10.1002/bip.360230610}, + issn = {0006-3525}, + journal = {Biopolymers}, + number = {6}, + pages = {1099--1112}, + title = {{Quasi‐harmonic method for studying very low frequency modes in proteins}}, + volume = {23}, + year = {1984}, } -@article{Dangić.2021, - abstract = {{The proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity κ. However, the κ of GeTe increases at the ferroelectric phase transition near 700 K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in κ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Strong anharmonicity near the phase transition induces non-Lorentzian shapes of the phonon power spectra. To account for these effects, we implement a method of calculating κ based on the Green-Kubo approach and find that the Boltzmann transport equation underestimates κ near the phase transition. Our findings elucidate the influence of structural phase transitions on κ and provide guidance for design of better thermoelectric materials.}}, - author = {Dangić, Đorđe and Hellman, Olle and Fahy, Stephen and Savić, Ivana}, - doi = {10.1038/s41524-021-00523-7}, - journal = {npj Computational Materials}, - number = {1}, - pages = {57}, - title = {{The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe}}, - volume = {7}, - year = {2021}, +@article{Klein.1972, + author = {Klein, M. L. and Horton, G. K.}, + doi = {10.1007/bf00654839}, + issn = {0022-2291}, + journal = {Journal of Low Temperature Physics}, + number = {3-4}, + pages = {151--166}, + title = {{The rise of self-consistent phonon theory}}, + volume = {9}, + year = {1972}, } -@article{Cohen.2022, - abstract = {{Lead‐based halide perovskite crystals are shown to have strongly anharmonic structural dynamics. This behavior is important because it may be the origin of their exceptional photovoltaic properties. The double perovskite, Cs2AgBiBr6, has been recently studied as a lead‐free alternative for optoelectronic applications. However, it does not exhibit the excellent photovoltaic activity of the lead‐based halide perovskites. Therefore, to explore the correlation between the anharmonic structural dynamics and optoelectronic properties in lead‐based halide perovskites, the structural dynamics of Cs2AgBiBr6 are investigated and are compared to its lead‐based analog, CsPbBr3. Using temperature‐dependent Raman measurements, it is found that both materials are indeed strongly anharmonic. Nonetheless, the expression of their anharmonic behavior is markedly different. Cs2AgBiBr6 has well‐defined normal modes throughout the measured temperature range, while CsPbBr3 exhibits a complete breakdown of the normal‐mode picture above 200 K. It is suggested that the breakdown of the normal‐mode picture implies that the average crystal structure may not be a proper starting point to understand the electronic properties of the crystal. In addition to our main findings, an unreported phase of Cs2AgBiBr6 is also discovered below ≈37 K. Raman spectroscopy is used to compare the anharmonic expressions in the structural dynamics of two halide perovskites. In Cs2AgBiBr6, clear normal modes are observed in all measured temperatures. Contrary to this, the Raman spectrum of CsPbBr3 exhibits a breakdown of the normal‐mode picture above 200 K. Implications of these diverging behaviors on the electronic properties of the crystals is discussed.}}, - author = {Cohen, Adi and Brenner, Thomas M. and Klarbring, Johan and Sharma, Rituraj and Fabini, Douglas H. and Korobko, Roman and Nayak, Pabitra K. and Hellman, Olle and Yaffe, Omer}, - doi = {10.1002/adma.202107932}, - issn = {0935-9648}, - journal = {Advanced Materials}, - pages = {2107932}, - title = {{Diverging Expressions of Anharmonicity in Halide Perovskites}}, - year = {2022}, +@article{Horner.1972, + abstract = {{Numerical calculations of phonon spectra, including damping, are reported for bcc3He and4He and for fcc4He. Strong damping is found for the longitudinal branches near the boundary of the Brillouin zone. In the bcc phase anomalous dispersion occurs for several directions at long wavelengths, which is most pronounced in the lowest transverse branch in (110) direction. This leads to an anomaly in the specific heat at low temperatures. In this calculation anharmonicities and short-range correlations are treated in a self-consistent way.}}, + author = {Horner, Heinz}, + doi = {10.1007/bf00653877}, + issn = {0022-2291}, + journal = {Journal of Low Temperature Physics}, + number = {5-6}, + pages = {511--529}, + title = {{Phonons and thermal properties of bcc and fcc helium from a self-consistent anharmonic theory}}, + volume = {8}, + year = {1972}, +} + +@article{Koehler.1971, + abstract = {{A theory is presented of the damping and frequency shift of phonons and of the ground-state energy corrections due to interactions between phonons in quantum crystals with singular forces. The technique begins with the adoption of a trial ground-state wave function of the Jastrow form, together with trial excited-state wave functions constructed to represent one-, two-, and three-phonon excitations. The Hamiltonian matrix in this restricted basis is diagonalized, and the basis is optimized by minimizing the lowest eigenvalue with respect to variational phonon parameters. Using a lowest-order cluster expansion, the unambiguous prescription is obtained that a specific effective potential, softened by the Jastrow correlation function, replaces everywhere the true potential in the existing self-consistent theory of phonon damping applicable to nonsingular forces. Close analogies are drawn with the correlated basis function treatment, of superfluid liquid helium.}}, + author = {Koehler, T. R. and Werthamer, N. R.}, + doi = {10.1103/physreva.3.2074}, + issn = {1050-2947}, + journal = {Physical Review A}, + number = {6}, + pages = {2074--2083}, + title = {{Phonon Spectral Functions and Ground-State Energy of Quantum Crystals in Perturbation Theory with a Variationally Optimum Correlated Basis Set}}, + volume = {3}, + year = {1971}, +} + +@article{Werthamer.1970kr, + abstract = {{The self-consistent phonon theory of anharmonic lattice dynamics is derived via a stationary functional formulation. The crystal dynamics is approximated by a set of damped oscillators, and these are used to construct a trial action, analytically continued into the complex time-temperature plane. Using the action, a free-energy functional is required to be stationary with respect to the trial oscillators. The resulting phonon modes are undamped at the first order of approximation, whereas to second order the phonon spectral function is determined self-consistently. Expressions are obtained in first order for various thermodynamic derivatives, such as pressure, elastic constants, specific heats, and thermal expansion.}}, + author = {Werthamer, N. R.}, + doi = {10.1103/physrevb.1.572}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {2}, + pages = {572--581}, + title = {{Self-Consistent Phonon Formulation of Anharmonic Lattice Dynamics}}, + volume = {1}, + year = {1970}, } @book{Choquard.1967, @@ -424,22 +507,55 @@ @book{Choquard.1967 year = {1967}, } -@article{Cai.2021, - abstract = {{Phonon chirality has attracted intensive attention since it breaks the traditional cognition that phonons are linear propagating bosons. This new quasiparticle property has been extensively studied theoretically and experimentally. However, characterization of the phonon chirality throughout the full Brillouin zone is still not possible due to the lack of available experimental tools. In this work, phonon dispersion and chirality of tungsten carbide were investigated by millielectronvolt energy-resolution inelastic X-ray scattering. The atomistic calculation indicates that in-plane longitudinal and transverse acoustic phonons near K and K\$\textasciicircum\textbackslashprime\$ points are circularly polarized due to the broken inversion symmetry. Anomalous inelastic X-ray scattering by these circularly polarized phonons was observed and attributed to their chirality. Our results show that inelastic X-ray scattering can be utilized to characterize phonon chirality in materials and suggest that a revision to the phonon scattering function is necessary.}}, - author = {Cai, Qingan and Hellman, Olle and Wei, Bin and Sun, Qiyang and Said, Ayman H and Gog, Thomas and Winn, Barry and Li, Chen}, - eprint = {2108.06631}, - journal = {arXiv}, - title = {{Direct Observation of Chiral Phonons by Inelastic X-ray Scattering}}, - year = {2021}, +@article{Gillis.1967, + abstract = {{The self-consistent phonon theory of anharmonic lattice dynamics, devised independently by several authors using varying techniques and implemented computationally by Koehler, is here applied to the crystals of neon and argon. A Lennard-Jones 6-12 interatomic potential is assumed. The quantities calculated are the phonon spectrum and the bulk thermodynamic properties of thermal expansion, compressibility, and specific heat, all as a function of temperature at zero pressure. Although the computations are intended primarily to explore in detail the content of the self-consistent phonon approximation preparatory to incorporating the more elaborate expressions of the next higher approximation, comparison is made with the existing experimental data.}}, + author = {Gillis, N. S. and Werthamer, N. R. and Koehler, T. R.}, + doi = {10.1103/physrev.165.951}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {3}, + pages = {951--959}, + title = {{Properties of Crystalline Argon and Neon in the Self-Consistent Phonon Approximation}}, + volume = {165}, + year = {1967}, } -@article{Born.1912, - author = {Born, M. and Karman, T. von}, - journal = {Physikalische Zeitschrift}, - pages = {297--309}, - title = {{Über Schwingungen in Raumgittern}}, - volume = {13}, - year = {1912}, +@article{Koehler.1966, + author = {Koehler, Thomas R.}, + doi = {10.1103/physrevlett.17.89}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {2}, + pages = {89--91}, + title = {{Theory of the Self-Consistent Harmonic Approximation with Application to Solid Neon}}, + volume = {17}, + year = {1966}, +} + +@article{Hooton.1958, + abstract = {{Skyrme has recently discussed the use of a model in quantum mechanics. His method is applied to the case of the anharmonic vibrations of a crystal lattice, and compared with a previous treatment by the present author. Some remarks are added which give a new and more physical interpretation of the results of this earlier work.}}, + author = {Hooton, D. J.}, + doi = {10.1080/14786435808243224}, + issn = {0031-8086}, + journal = {Philosophical Magazine}, + number = {25}, + pages = {49--54}, + title = {{The use of a model in anharmonic lattice dynamics}}, + volume = {3}, + year = {1958}, +} + +@article{Hooton.1955, + abstract = {{Eine neue Methode zur Beschreibung anharmonischer Gitterschwingungen, die aufMax Born zurückgeht, wird hier von einem anderen Gesichtspunkt aus betrachtet und weiterentwickelt. Es werden effektive harmonische Schwingungen definiert, durch welche sich die freie Energie darstellen läßt; es werden die Fälle schwacher und starker Anharmonizität betrachtet. Die Formeln werden für das Beispiel einer linearen Kette explizit gelöst und an Hand von Werten des festen Heliums numerisch illustriert.}}, + author = {Hooton, D. J.}, + doi = {10.1007/bf01330055}, + issn = {0044-3328}, + journal = {Zeitschrift für Physik}, + number = {1}, + pages = {42--57}, + title = {{Anharmonische Gitterschwingungen und die lineare Kette}}, + volume = {142}, + year = {1955}, } @article{Born.1951, @@ -462,33 +578,12 @@ @article{Boer.1948 year = {1948}, } -@article{Benshalom.2021, - abstract = {{We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasi-harmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the temperature dependence of other material properties governed by it.}}, - author = {Benshalom, Nimrod and Reuveni, Guy and Korobko, Roman and Yaffe, Omer and Hellman, Olle}, - eprint = {2108.04589}, - journal = {arXiv}, - title = {{The dielectric response of rock-salt crystals at finite temperatures from first principles}}, - year = {2021}, -} - -@article{Benshalom.2022v0s, - abstract = {{We have found that the polarization dependence of the Raman signal in organic crystals can only be described by a fourth-rank formalism. The generalization from the traditional second-rank Raman tensor \$\textbackslashmathcal\{R\}\$ is physically motivated by consideration of the light scattering mechanism of anharmonic crystals at finite temperatures, and explained in terms of off-diagonal components of the crystal self-energy. We thus establish a novel manifestation of anharmonicity in inelastic light scattering, markedly separate from the better known phonon lifetime.}}, - author = {Benshalom, Nimrod and Asher, Maor and Jouclas, Rémy and Korobko, Roman and Schweicher, Guillaume and Liu, Jie and Geerts, Yves and Hellman, Olle and Yaffe, Omer}, - eprint = {2204.12528}, - journal = {arXiv}, - title = {{Phonon-phonon interactions in the polarizarion dependence of Raman scattering}}, - year = {2022}, -} - -@article{Benshalom.2022, - abstract = {{We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature-dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasiharmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the temperature dependence of other material properties governed by it.}}, - author = {Benshalom, Nimrod and Reuveni, Guy and Korobko, Roman and Yaffe, Omer and Hellman, Olle}, - doi = {10.1103/physrevmaterials.6.033607}, - journal = {Physical Review Materials}, - number = {3}, - pages = {033607}, - title = {{Dielectric response of rock-salt crystals at finite temperatures from first principles}}, - volume = {6}, - year = {2022}, +@article{Born.1912, + author = {Born, M. and Karman, T. von}, + journal = {Physikalische Zeitschrift}, + pages = {297--309}, + title = {{Über Schwingungen in Raumgittern}}, + volume = {13}, + year = {1912}, } diff --git a/paper/paper.md b/paper/paper.md index 36ac88eb..969a63ef 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -75,7 +75,7 @@ The parameters in the lattice dynamics Hamiltonian, called _force constants_, ca # Statement of need The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve temperature-dependent, effective lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. -As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [CITE SCAILD/qSCAILD, SCHA/SSCHA, SCP/Alamode]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [cite Levy1984, Dove1986]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [cite Hellman2011, 2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [Shulumba2017, Benshalom2022]. +As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008,@Errea.2013,@Tadano.2015,@Roekeghem.2021,@Monacelli.2021,@Tadano.2014]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984,@Dove.1986,@Zhang.2014up]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [cite Hellman2011, 2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [Shulumba2017, Benshalom2022]. While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants up to fourth order [CITE Cowley, Hellman2013, Feng2016 ...]. These can be used to get better approximations to the free energy [CITE Wallace], describe thermal transport [CITE Broido, Romero], and linewidth broadening in spectroscopic experiments [CITE neutrons + Raman]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [CITE Castellano]. From b922a717c968ae663fb20694cdcc7b8b6f2b5864 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 15:16:29 +0200 Subject: [PATCH 16/48] paper | update bib --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 969a63ef..1e738a4f 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -75,7 +75,7 @@ The parameters in the lattice dynamics Hamiltonian, called _force constants_, ca # Statement of need The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve temperature-dependent, effective lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. -As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008,@Errea.2013,@Tadano.2015,@Roekeghem.2021,@Monacelli.2021,@Tadano.2014]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984,@Dove.1986,@Zhang.2014up]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [cite Hellman2011, 2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [Shulumba2017, Benshalom2022]. +As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986; @Zhang.2014up]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017, @Benshalom.2022]. While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants up to fourth order [CITE Cowley, Hellman2013, Feng2016 ...]. These can be used to get better approximations to the free energy [CITE Wallace], describe thermal transport [CITE Broido, Romero], and linewidth broadening in spectroscopic experiments [CITE neutrons + Raman]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [CITE Castellano]. From 0318f967b80d0eba60581fed46c09f2225156c0b Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 15:35:13 +0200 Subject: [PATCH 17/48] update --- paper/literature.bib | 94 ++++++++++++++++++++++++++++++++++++++++++++ paper/paper.md | 8 ++-- 2 files changed, 98 insertions(+), 4 deletions(-) diff --git a/paper/literature.bib b/paper/literature.bib index d574ae69..b83757ae 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -1,3 +1,13 @@ +@article{Castellano.2023, + abstract = {{The dynamical properties of nuclei, carried by the concept of phonon quasiparticles, are central to the field of condensed matter. While the harmonic approximation can reproduce a number of properties observed in real crystals, the inclusion of anharmonicity in lattice dynamics is essential to accurately predict properties such as heat transport or thermal expansion. For highly anharmonic systems, non perturbative approaches are needed, which result in renormalized theories of lattice dynamics. In this article, we apply the Mori-Zwanzig projector formalism to derive an exact generalized Langevin equation describing the quantum dynamics of nuclei in a crystal. By projecting this equation on quasiparticles in reciprocal space, and with results from linear response theory, we obtain a formulation of vibrational spectra that fully accounts for the anharmonicity. Using a mode-coupling approach, we construct a systematic perturbative expansion in which each new order is built to minimize the following ones. With a truncation to the lowest order, we show how to obtain a set of self-consistent equations that can describe the lineshapes of quasiparticles. The only inputs needed for the resulting set of equations are the static Kubo correlation functions, which can be computed using path-integral molecular dynamics or approximated with (classical or ab initio) molecular dynamics.}}, + author = {Castellano, Aloïs and Batista, José and Verstraete, Matthieu J}, + doi = {10.48550/arxiv.2303.10621}, + eprint = {2303.10621}, + journal = {arXiv}, + title = {{Mode-coupling theory of lattice dynamics for classical and quantum crystals}}, + year = {2023}, +} + @article{Reig.2022, abstract = {{Understanding heat flow in layered transition metal dichalcogenide (TMD) crystals is crucial for applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood, in particular how transport is affected by material thickness and the material's environment. This combined experimental–theoretical study establishes a unifying physical picture of the intrinsic lattice thermal conductivity of the representative TMD MoSe2. Thermal conductivity measurements using Raman thermometry on a large set of clean, crystalline, suspended crystals with systematically varied thickness are combined with ab initio simulations with phonons at finite temperature. The results show that phonon dispersions and lifetimes change strongly with thickness, yet the thinnest TMD films exhibit an in‐plane thermal conductivity that is only marginally smaller than that of bulk crystals. This is the result of compensating phonon contributions, in particular heat‐carrying modes around ≈0.1 THz in (sub)nanometer thin films, with a surprisingly long mean free path of several micrometers. This behavior arises directly from the layered nature of the material. Furthermore, out‐of‐plane heat dissipation to air molecules is remarkably efficient, in particular for the thinnest crystals, increasing the apparent thermal conductivity of monolayer MoSe2 by an order of magnitude. These results are crucial for the design of (flexible) TMD‐based (opto‐)electronic applications. Combined experimental–theoretical study using Raman thermometry and ab initio simulations to unravel the heat transport properties of suspended MoSe2 crystals with systematic thickness variation down to the monolayer. Monolayer films have almost the same in‐plane thermal conductivity as bulk material thanks to an additional heat‐carrying low‐frequency mode. Out‐of‐plane heat dissipation to air is extremely efficient for the thinnest flakes.}}, author = {Reig, David Saleta and Varghese, Sebin and Farris, Roberta and Block, Alexander and Mehew, Jake D. and Hellman, Olle and Woźniak, Paweł and Sledzinska, Marianna and Sachat, Alexandros El and Chávez‐Ángel, Emigdio and Valenzuela, Sergio O. and Hulst, Niek F. van and Ordejón, Pablo and Zanolli, Zeila and Torres, Clivia M. Sotomayor and Verstraete, Matthieu J. and Tielrooij, Klaas‐Jan}, @@ -29,6 +39,19 @@ @article{Benshalom.2022v0s year = {2022}, } +@article{Lin.2022, + abstract = {{The long-wavelength behavior of vibrational modes plays a central role in carrier transport, phonon-assisted optical properties, superconductivity, and thermomechanical and thermoelectric properties of materials. Here, we present general invariance and equilibrium conditions of the lattice potential; these allow to recover the quadratic dispersions of flexural phonons in low-dimensional materials, in agreement with the phenomenological model for long-wavelength bending modes. We also prove that for any low-dimensional material the bending modes can have a purely out-of-plane polarization in the vacuum direction and a quadratic dispersion in the long-wavelength limit. In addition, we propose an effective approach to treat invariance conditions in crystals with non-vanishing Born effective charges where the long-range dipole-dipole interactions induce a contribution to the lattice potential and stress tensor. Our approach is successfully applied to the phonon dispersions of 158 two-dimensional materials, highlighting its critical relevance in the study of phonon-mediated properties of low-dimensional materials.}}, + author = {Lin, Changpeng and Poncé, Samuel and Marzari, Nicola}, + doi = {10.1038/s41524-022-00920-6}, + eprint = {2209.09520}, + journal = {npj Computational Materials}, + number = {1}, + pages = {236}, + title = {{General invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials}}, + volume = {8}, + year = {2022}, +} + @article{Cohen.2022, abstract = {{Lead‐based halide perovskite crystals are shown to have strongly anharmonic structural dynamics. This behavior is important because it may be the origin of their exceptional photovoltaic properties. The double perovskite, Cs2AgBiBr6, has been recently studied as a lead‐free alternative for optoelectronic applications. However, it does not exhibit the excellent photovoltaic activity of the lead‐based halide perovskites. Therefore, to explore the correlation between the anharmonic structural dynamics and optoelectronic properties in lead‐based halide perovskites, the structural dynamics of Cs2AgBiBr6 are investigated and are compared to its lead‐based analog, CsPbBr3. Using temperature‐dependent Raman measurements, it is found that both materials are indeed strongly anharmonic. Nonetheless, the expression of their anharmonic behavior is markedly different. Cs2AgBiBr6 has well‐defined normal modes throughout the measured temperature range, while CsPbBr3 exhibits a complete breakdown of the normal‐mode picture above 200 K. It is suggested that the breakdown of the normal‐mode picture implies that the average crystal structure may not be a proper starting point to understand the electronic properties of the crystal. In addition to our main findings, an unreported phase of Cs2AgBiBr6 is also discovered below ≈37 K. Raman spectroscopy is used to compare the anharmonic expressions in the structural dynamics of two halide perovskites. In Cs2AgBiBr6, clear normal modes are observed in all measured temperatures. Contrary to this, the Raman spectrum of CsPbBr3 exhibits a breakdown of the normal‐mode picture above 200 K. Implications of these diverging behaviors on the electronic properties of the crystals is discussed.}}, author = {Cohen, Adi and Brenner, Thomas M. and Klarbring, Johan and Sharma, Rituraj and Fabini, Douglas H. and Korobko, Roman and Nayak, Pabitra K. and Hellman, Olle and Yaffe, Omer}, @@ -145,6 +168,20 @@ @article{Klarbring.2020vk year = {2020}, } +@article{Eriksson.2019, + abstract = {{The efficient extraction of force constants (FCs) is crucial for the analysis of many thermodynamic materials properties. Approaches based on the systematic enumeration of finite differences scale poorly with system size and can rarely extend beyond third order when input data is obtained from first‐principles calculations. Methods based on parameter fitting in the spirit of interatomic potentials, on the other hand, can extract FC parameters from semi‐random configurations of high information density and advanced regularized regression methods can recover physical solutions from a limited amount of data. Here, the hiphive Python package, that enables the construction of force constant models up to arbitrary order is presented. hiphive exploits crystal symmetries to reduce the number of free parameters and then employs advanced machine learning algorithms to extract the force constants. Depending on the problem at hand, both over and underdetermined systems are handled efficiently. The FCs can be subsequently analyzed directly and or be used to carry out, for example, molecular dynamics simulations. The utility of this approach is demonstrated via several examples including ideal and defective monolayers of MoS2 as well as bulk nickel. The hiphive package is a powerful tool for the efficient extraction of high‐order force constants. It thereby enables modeling the thermodynamic and vibrational properties of, for example, large, low‐symmetry systems and strongly anharmonic materials. This ultimately includes, for example, temperature‐dependent phonon dispersions, life times, and the thermal conductivity.}}, + author = {Eriksson, Fredrik and Fransson, Erik and Erhart, Paul}, + doi = {10.1002/adts.201800184}, + eprint = {1811.09267}, + issn = {2513-0390}, + journal = {Advanced Theory and Simulations}, + number = {5}, + pages = {1800184}, + title = {{The Hiphive Package for the Extraction of High‐Order Force Constants by Machine Learning}}, + volume = {2}, + year = {2019}, +} + @article{Manley.2019, abstract = {{Lead chalcogenides have exceptional thermoelectric properties and intriguing anharmonic lattice dynamics underlying their low thermal conductivities. An ideal material for thermoelectric efficiency is the phonon glass–electron crystal, which drives research on strategies to scatter or localize phonons while minimally disrupting electronic-transport. Anharmonicity can potentially do both, even in perfect crystals, and simulations suggest that PbSe is anharmonic enough to support intrinsic localized modes that halt transport. Here, we experimentally observe high-temperature localization in PbSe using neutron scattering but find that localization is not limited to isolated modes – zero group velocity develops for a significant section of the transverse optic phonon on heating above a transition in the anharmonic dynamics. Arrest of the optic phonon propagation coincides with unusual sharpening of the longitudinal acoustic mode due to a loss of phase space for scattering. Our study shows how nonlinear physics beyond conventional anharmonic perturbations can fundamentally alter vibrational transport properties. To optimize the performance of lead chalcogenides for thermoelectric applications, strategies to further reduce the crystal’s thermal conductivity is required. Here, the authors discover anharmonic localized vibrations in PbSe crystals for optimizing the crystal’s vibrational transport properties.}}, author = {Manley, M. E. and Hellman, O. and Shulumba, N. and May, A. F. and Stonaha, P. J. and Lynn, J. W. and Garlea, V. O. and Alatas, A. and Hermann, R. P. and Budai, J. D. and Wang, H. and Sales, B. C. and Minnich, A. J.}, @@ -238,6 +275,19 @@ @article{Dewandre.2016 year = {2016}, } +@article{Feng.2016, + abstract = {{Recently, first principle-based predictions of lattice thermal conductivity κ from perturbation theory have achieved significant success. However, it only includes three-phonon scattering due to the assumption that four-phonon and higher-order processes are generally unimportant. Also, directly evaluating the scattering rates of four-phonon and higher-order processes has been a long-standing challenge. In this work, however, we have developed a formalism to explicitly determine quantum mechanical scattering probability matrices for four-phonon scattering in the full Brillouin zone, and by mitigating the computational challenge we have directly calculated four-phonon scattering rates. We find that four-phonon scattering rates are comparable to three-phonon scattering rates at medium and high temperatures, and they increase quadratically with temperature. As a consequence, κ of Lennard-Jones argon is reduced by more than 60\% at 80 K when four-phonon scattering is included. Also, in less anharmonic materials—diamond, silicon, and germanium—κ is still reduced considerably at high temperature by four-phonon scattering by using the classical Tersoff potentials. Also, the thermal conductivity of optical phonons is dominated by the fourth- and higher-orders phonon scattering even at low temperature.}}, + author = {Feng, Tianli and Ruan, Xiulin}, + doi = {10.1103/physrevb.93.045202}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {4}, + pages = {045202}, + title = {{Quantum mechanical prediction of four-phonon scattering rates and reduced thermal conductivity of solids}}, + volume = {93}, + year = {2016}, +} + @article{Shulumba.2016, abstract = {{We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti1-xAlxN alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti1-xAlxN alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti0.5Al0.5N alloys agree with the calculated phase diagram.}}, author = {Shulumba, Nina and Hellman, Olle and Raza, Zamaan and Alling, Björn and Barrirero, Jenifer and Mücklich, Frank and Abrikosov, Igor A. and Odén, Magnus}, @@ -423,6 +473,19 @@ @article{Souvatzis.2008 year = {2008}, } +@article{Broido.2007, + abstract = {{We present an ab initio theoretical approach to accurately describe phonon thermal transport in semiconductors and insulators free of adjustable parameters. This technique combines a Boltzmann formalism with density functional calculations of harmonic and anharmonic interatomic force constants. Without any fitting parameters, we obtain excellent agreement (<5\% difference at room temperature) between the calculated and measured intrinsic lattice thermal conductivities of silicon and germanium. As such, this method may provide predictive theoretical guidance to experimental thermal transport studies of bulk and nanomaterials as well as facilitating the design of new materials.}}, + author = {Broido, D. A. and Malorny, M. and Birner, G. and Mingo, Natalio and Stewart, D. A.}, + doi = {10.1063/1.2822891}, + issn = {0003-6951}, + journal = {Applied Physics Letters}, + number = {23}, + pages = {231922}, + title = {{Intrinsic lattice thermal conductivity of semiconductors from first principles}}, + volume = {91}, + year = {2007}, +} + @article{Dove.1986, abstract = {{As a contribution to the understanding of the incommensurate phase transitions in thiourea, we present a theoretical study of the crystallographic details of the parael ectric phase. A model intermolecular potential is developed, which includes a reasonable distribution of electrostatic multipole interactions as well as the standard dispersive and repulsive interactions. The model gives a satisfactory prediction of the structure of the para electric phase, and in particular explains the occurrence of the hydrogen-bond network. Calculations of phonon-dispersion curves predict a soft-phonon branch in the b direction with the same symmetry as that observed experimentally. Computer simulations predict reasonable values for the vibrational amplitudes, and show the existence of large-amplitude fluctuations of an harmonic quantities at incommensurate wave vectors. However, although the model displays a strong tendency towards incommensurate and lock-in ordering, it does not in fact give a phase transition at a finite temperature. This failure is attributed to the neglect of molecular polarizability, and it is concluded that this feature provides the mechanism that stabilizes the low-temperature phases.For the interested reader, full details of the molecular dynamics simulation technique using parallel processing are presented here. In particular, a method of extracting normal-mode eigenvectors from the results of the simulations is described.}}, author = {Dove, Martin T. and Lynden-bell, Ruth M.}, @@ -449,6 +512,15 @@ @article{Levy.1984 year = {1984}, } +@book{Wallace.1972, + author = {Wallace, Duane C.}, + location = {New York}, + publisher = {John Wiley \& Sons, Inc.}, + note = {Read up on operator-renormalization method - pressure: p. 74, 154, 192, 193}, + title = {{Thermodynamics of Crystals}}, + year = {1972}, +} + @article{Klein.1972, author = {Klein, M. L. and Horton, G. K.}, doi = {10.1007/bf00654839}, @@ -532,6 +604,19 @@ @article{Koehler.1966 year = {1966}, } +@article{Cowley.1963, + abstract = {{The theory of the physical properties of an anharmonic crystal is discussed by using the thermodynamic Green's functions for the phonons. A perturbation procedure is developed to obtain the Green's functions and it is shown that for some purposes a quasi-harmonic approximation is useful, in which the frequencies of the normal modes are those determined by infra-red or neutron spectrometry. The thermodynamic, elastic, dielectric and scattering properties of an anharmonic crystal are discussed in terms of the Green's functions, and detailed expressions are given for the more important contributions. Detailed numerical calculations are presented of the thermal expansion, dielectric properties and shapes of some of the inelastically scattered neutron groups, for sodium iodide and potassium bromide. The calculations, which give reasonable agreement with experiment, show that even at quite low temperatures, the lifetimes of some of the normal modes can be quite short. By using the quasi-harmonic approximation it is shown that the large temperature dependence of the normal modes in a ferroelectric crystal can be treated adequately.}}, + author = {Cowley, R.A.}, + doi = {10.1080/00018736300101333}, + issn = {0001-8732}, + journal = {Advances in Physics}, + number = {48}, + pages = {421--480}, + title = {{The lattice dynamics of an anharmonic crystal}}, + volume = {12}, + year = {1963}, +} + @article{Hooton.1958, abstract = {{Skyrme has recently discussed the use of a model in quantum mechanics. His method is applied to the case of the anharmonic vibrations of a crystal lattice, and compared with a previous treatment by the present author. Some remarks are added which give a new and more physical interpretation of the results of this earlier work.}}, author = {Hooton, D. J.}, @@ -558,6 +643,15 @@ @article{Hooton.1955 year = {1955}, } +@book{Born.1954, + author = {Born, Max and Huang, Kun}, + location = {Oxford}, + publisher = {Clarendon Press}, + note = {Grilnoisc11,E., 21, 49, 50, 52, 60, 187, 188.}, + title = {{Dynamical theory of crystal lattices}}, + year = {1954}, +} + @article{Born.1951, author = {Born, Max and Brix, Peter and Kopfermann, Hans and Heisenberg, W. and Staudinger, Hermann and Stille, Hans and Weizsäcker, Carl Friedrich v. and Euler, Hans von and Hedvall, J. Arvid and Siegel, Carl Ludwig and Rellich, Franz and Nevanlinna, Rolf}, doi = {10.1007/978-3-642-86703-3}, diff --git a/paper/paper.md b/paper/paper.md index 1e738a4f..2896e6fd 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -75,13 +75,13 @@ The parameters in the lattice dynamics Hamiltonian, called _force constants_, ca # Statement of need The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve temperature-dependent, effective lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. -As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986; @Zhang.2014up]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017, @Benshalom.2022]. +As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986; @Zhang.2014up]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. -While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants up to fourth order [CITE Cowley, Hellman2013, Feng2016 ...]. These can be used to get better approximations to the free energy [CITE Wallace], describe thermal transport [CITE Broido, Romero], and linewidth broadening in spectroscopic experiments [CITE neutrons + Raman]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [CITE Castellano]. +While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants up to fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [@Castellano.2023]. -To extract force constants from thermal snapshots efficiently, TDEP employs the spacegroup symmetry of a given system to rigorously reduce the free parameters in the model to an irreducible set _before_ fitting the model parameters. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [cite Hellman2013b]. Furthermore, additional lattice dynamics sum rules such as acoustic (translational) and rotational invariances, as well the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [CITE BornHuang]. While TDEP was probably the first approach to exploit all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [CITE hiphive, Ponce]. +To extract force constants from thermal snapshots efficiently, TDEP employs the spacegroup symmetry of a given system to rigorously reduce the free parameters in the model to an irreducible set _before_ fitting the model parameters. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [cite Hellman2013b]. Furthermore, additional lattice dynamics sum rules such as acoustic (translational) and rotational invariances, as well the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was probably the first approach to exploit all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. -TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both extracting force constants, as well as analyzing (effective) harmonic phonons and explicit anharmonic properties such as thermal transport and the full phonon spectral function across the Brillouin zone, from which spectroscopic properties can be obtained. This allows simulations even for complex bulk materials with reduced symmetry in practice. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [CITE Benshalom]. We highlight some applications and results below. +TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both extracting force constants, as well as analyzing (effective) harmonic phonons and explicit anharmonic properties such as thermal transport and the full phonon spectral function across the Brillouin zone, from which spectroscopic properties can be obtained. This allows simulations even for complex bulk materials with reduced symmetry in practice. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. We highlight some applications and results below. Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readbale formats like csv, or self-documented HDF5 files for larger datasets. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for higher-order force constants. From acce6bb7476929961ef33221c74590698f01073b Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 16:14:38 +0200 Subject: [PATCH 18/48] paper | finalize bib --- paper/literature.bib | 20 ++++++++++++++++++++ paper/paper.md | 6 +++--- 2 files changed, 23 insertions(+), 3 deletions(-) diff --git a/paper/literature.bib b/paper/literature.bib index b83757ae..77c75896 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -1,3 +1,10 @@ +@misc{tdeptools, + author = {Knoop, F.}, + publisher = {GitHub}, + url = {https://github.com/flokno/tools.tdep}, + title = {{tdeptools: tools for TDEP}}, +} + @article{Castellano.2023, abstract = {{The dynamical properties of nuclei, carried by the concept of phonon quasiparticles, are central to the field of condensed matter. While the harmonic approximation can reproduce a number of properties observed in real crystals, the inclusion of anharmonicity in lattice dynamics is essential to accurately predict properties such as heat transport or thermal expansion. For highly anharmonic systems, non perturbative approaches are needed, which result in renormalized theories of lattice dynamics. In this article, we apply the Mori-Zwanzig projector formalism to derive an exact generalized Langevin equation describing the quantum dynamics of nuclei in a crystal. By projecting this equation on quasiparticles in reciprocal space, and with results from linear response theory, we obtain a formulation of vibrational spectra that fully accounts for the anharmonicity. Using a mode-coupling approach, we construct a systematic perturbative expansion in which each new order is built to minimize the following ones. With a truncation to the lowest order, we show how to obtain a set of self-consistent equations that can describe the lineshapes of quasiparticles. The only inputs needed for the resulting set of equations are the static Kubo correlation functions, which can be computed using path-integral molecular dynamics or approximated with (classical or ab initio) molecular dynamics.}}, author = {Castellano, Aloïs and Batista, José and Verstraete, Matthieu J}, @@ -235,6 +242,19 @@ @article{Zhou.2018 year = {2018}, } +@article{Larsen.2017, + abstract = {{The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.}}, + author = {Larsen, Ask Hjorth and Mortensen, Jens Jørgen and Blomqvist, Jakob and Castelli, Ivano E and Christensen, Rune and Dułak, Marcin and Friis, Jesper and Groves, Michael N and Hammer, Bjørk and Hargus, Cory and Hermes, Eric D and Jennings, Paul C and Jensen, Peter Bjerre and Kermode, James and Kitchin, John R and Kolsbjerg, Esben Leonhard and Kubal, Joseph and Kaasbjerg, Kristen and Lysgaard, Steen and Maronsson, Jón Bergmann and Maxson, Tristan and Olsen, Thomas and Pastewka, Lars and Peterson, Andrew and Rostgaard, Carsten and Schiøtz, Jakob and Schütt, Ole and Strange, Mikkel and Thygesen, Kristian S and Vegge, Tejs and Vilhelmsen, Lasse and Walter, Michael and Zeng, Zhenhua and Jacobsen, Karsten W}, + doi = {10.1088/1361-648x/aa680e}, + issn = {0953-8984}, + journal = {Journal of Physics: Condensed Matter}, + number = {27}, + pages = {273002}, + title = {{The atomic simulation environment—a Python library for working with atoms}}, + volume = {29}, + year = {2017}, +} + @article{Shulumba.20179s8e, abstract = {{Molecular crystals such as polyethylene are of intense interest as flexible thermal conductors, yet their intrinsic upper limits of thermal conductivity remain unknown. Here, we report a study of the vibrational properties and lattice thermal conductivity of a polyethylene molecular crystal using an ab initio approach that rigorously incorporates nuclear quantum motion and finite temperature effects. We obtain a thermal conductivity along the chain direction of around 160 W m−1 K−1 at room temperature, providing a firm upper bound for the thermal conductivity of this molecular crystal. Furthermore, we show that the inclusion of quantum nuclear effects significantly impacts the thermal conductivity by altering the phase space for three-phonon scattering. Our computational approach paves the way for ab initio studies and computational material discovery of molecular solids free of any adjustable parameters.}}, author = {Shulumba, Nina and Hellman, Olle and Minnich, Austin J.}, diff --git a/paper/paper.md b/paper/paper.md index 2896e6fd..db0f8533 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -100,7 +100,7 @@ Here we list the most important codes that are shipped with the TDEP code and ex - `canonical_configuration`: Create supercells with thermal displacements from the force constants via Monte Carlo sampling from a classical and quantum canonical distribution. - `generate_structure`: Generate supercells of target size that are as cubic as possible to maximize the largest possible real-space cutoff for the force constants. -A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [CITE Ask], as well as processing and further analysis of TDEP output files is available as well [CITE tdeptools]. +A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. ## Overview of results @@ -112,7 +112,7 @@ A separate python library for interfacing with different DFT and force field cod The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name as described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to a more in-depth discussion of the theory is given in the introduction. # Acknowledgements -- SeRC -- VR grants + +F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. # References From 0d2cb4f2806cff5c16a80bb7a89bc249c8d2e0ac Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 16:38:50 +0200 Subject: [PATCH 19/48] paper | polish --- paper/literature.bib | 14 ++++++++++++++ paper/paper.md | 19 +++++++++---------- 2 files changed, 23 insertions(+), 10 deletions(-) diff --git a/paper/literature.bib b/paper/literature.bib index 77c75896..d388ce98 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -46,6 +46,20 @@ @article{Benshalom.2022v0s year = {2022}, } +@article{Laniel.2022, + abstract = {{The lanthanum-hydrogen system has attracted significant attention following the report of superconductivity in LaH10 at near-ambient temperatures and high pressures. Phases other than LaH10 are suspected to be synthesized based on both powder X-ray diffraction and resistivity data, although they have not yet been identified. Here, we present the results of our single-crystal X-ray diffraction studies on this system, supported by density functional theory calculations, which reveal an unexpected chemical and structural diversity of lanthanum hydrides synthesized in the range of 50 to 180 GPa. Seven lanthanum hydrides were produced, LaH3, LaH\textbackslashtextasciitilde4, LaH4+δ, La4H23, LaH6+δ, LaH9+δ, and LaH10+δ, and the atomic coordinates of lanthanum in their structures determined. The regularities in rare-earth element hydrides unveiled here provide clues to guide the search for other synthesizable hydrides and candidate high-temperature superconductors. The hydrogen content variability in lanthanum hydrides and the samples’ phase heterogeneity underline the challenges related to assessing potentially superconducting phases and the nature of electronic transitions in high-pressure hydrides. The lanthanum-hydrogen system has attracted attention following the observation of superconductivity in LaH10 at near-ambient temperatures and high pressures. Here authors describe the high-pressure syntheses of seven La-H phases; they report crystal structures and remarkable regularities in rare-earth element hydrides.}}, + author = {Laniel, Dominique and Trybel, Florian and Winkler, Bjoern and Knoop, Florian and Fedotenko, Timofey and Khandarkhaeva, Saiana and Aslandukova, Alena and Meier, Thomas and Chariton, Stella and Glazyrin, Konstantin and Milman, Victor and Prakapenka, Vitali and Abrikosov, Igor A. and Dubrovinsky, Leonid and Dubrovinskaia, Natalia}, + doi = {10.1038/s41467-022-34755-y}, + eprint = {2208.10418}, + journal = {Nature Communications}, + keywords = {me}, + number = {1}, + pages = {6987}, + title = {{High-pressure synthesis of seven lanthanum hydrides with a significant variability of hydrogen content}}, + volume = {13}, + year = {2022}, +} + @article{Lin.2022, abstract = {{The long-wavelength behavior of vibrational modes plays a central role in carrier transport, phonon-assisted optical properties, superconductivity, and thermomechanical and thermoelectric properties of materials. Here, we present general invariance and equilibrium conditions of the lattice potential; these allow to recover the quadratic dispersions of flexural phonons in low-dimensional materials, in agreement with the phenomenological model for long-wavelength bending modes. We also prove that for any low-dimensional material the bending modes can have a purely out-of-plane polarization in the vacuum direction and a quadratic dispersion in the long-wavelength limit. In addition, we propose an effective approach to treat invariance conditions in crystals with non-vanishing Born effective charges where the long-range dipole-dipole interactions induce a contribution to the lattice potential and stress tensor. Our approach is successfully applied to the phonon dispersions of 158 two-dimensional materials, highlighting its critical relevance in the study of phonon-mediated properties of low-dimensional materials.}}, author = {Lin, Changpeng and Poncé, Samuel and Marzari, Nicola}, diff --git a/paper/paper.md b/paper/paper.md index db0f8533..069a3f3e 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -63,25 +63,25 @@ bibliography: literature.bib # Introduction -Properties of materials change with temperature, i.e., the vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. +Properties of materials change with temperature, i.e., the thermal vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. -In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtain temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics. +In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics. -The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, in practice the phonon picture is a good starting point for a wide range of materials, and lattice dynamics can provide _excellent_ qualitative microscopic insight into physical phenomena, and often even very good quantitative results, as detailed below. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made, but the _precision_ is excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. +The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, the phonon picture is a good starting point for a wide range of materials properties in practice. Lattice dynamics can provide _excellent_ qualitative microscopic insight into physical phenomena, and often even very good quantitative results. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made, but the _precision_ is excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. -The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent _effective_, renormalized model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [@Boer.1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [@Klein.1972]. +The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [@Boer.1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [@Klein.1972]. # Statement of need The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve temperature-dependent, effective lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. -As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986; @Zhang.2014up]. The idea was extended later in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where instead of MD simulations, thermal samples are created from the model Hamiltonian itself, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. +As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants up to fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [@Castellano.2023]. -To extract force constants from thermal snapshots efficiently, TDEP employs the spacegroup symmetry of a given system to rigorously reduce the free parameters in the model to an irreducible set _before_ fitting the model parameters. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [cite Hellman2013b]. Furthermore, additional lattice dynamics sum rules such as acoustic (translational) and rotational invariances, as well the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was probably the first approach to exploit all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. +To extract force constants from thermal snapshots efficiently, TDEP employs the spacegroup symmetry of a given system to rigorously reduce the free parameters in the model to an irreducible set _before_ fitting the model parameters. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Furthermore, additional lattice dynamics sum rules such as acoustic (translational) and rotational invariances, as well the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was probably the first approach to exploit all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. -TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both extracting force constants, as well as analyzing (effective) harmonic phonons and explicit anharmonic properties such as thermal transport and the full phonon spectral function across the Brillouin zone, from which spectroscopic properties can be obtained. This allows simulations even for complex bulk materials with reduced symmetry in practice. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. We highlight some applications and results below. +TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both the extraction of force constants and their subsequent treatment. This allows simulations even for complex bulk materials with reduced symmetry in practice. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readbale formats like csv, or self-documented HDF5 files for larger datasets. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for higher-order force constants. @@ -102,14 +102,13 @@ Here we list the most important codes that are shipped with the TDEP code and ex A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. - ## Overview of results -- some results? +**Do we want to highlight some results here?** # Summary -The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name as described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to a more in-depth discussion of the theory is given in the introduction. +The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to a more in-depth discussion of the theory are given. # Acknowledgements From 97944d4ca44eaf60ad9d6f2b9fb2f4a0956aede5 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 16:51:49 +0200 Subject: [PATCH 20/48] paper | polish --- paper/paper.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 069a3f3e..418a5094 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -65,9 +65,9 @@ bibliography: literature.bib Properties of materials change with temperature, i.e., the thermal vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. -In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables in equilibrium through static thermal expectation values, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics. +In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables in equilibrium through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics. -The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, the phonon picture is a good starting point for a wide range of materials properties in practice. Lattice dynamics can provide _excellent_ qualitative microscopic insight into physical phenomena, and often even very good quantitative results. Compared to MD simulations, one can say that the _accuracy_ is potentially limited because more approximations are made, but the _precision_ is excellent because the statistical error can be tightly controlled in the analytic setting, whereas MD approaches, in particular purely _ab initio_ MD, will typically suffer from much larger statistical noise. +The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, the phonon picture is a good starting point for a wide range of materials properties in practice. Lattice dynamics can provide precise microscopic insight into physical phenomena, and often even reach excellent accuracy on par with MD. The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [@Boer.1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [@Klein.1972]. @@ -108,7 +108,7 @@ A separate python library for interfacing with different DFT and force field cod # Summary -The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to a more in-depth discussion of the theory are given. +The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. # Acknowledgements From acd633c14a22bf36db1b8513b0faf2e3d7ea7e62 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 17:04:10 +0200 Subject: [PATCH 21/48] paper | polish --- paper/paper.md | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 418a5094..64fc462f 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -6,7 +6,9 @@ tags: - Phonons - Temperature - Anharmonicity + - Thermal transport - Neutron spectroscopy + - Raman spectroscopy authors: - name: Florian Knoop orcid: 0000-0002-7132-039X @@ -67,7 +69,7 @@ Properties of materials change with temperature, i.e., the thermal vibrational m In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables in equilibrium through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics. -The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion, typically by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, the phonon picture is a good starting point for a wide range of materials properties in practice. Lattice dynamics can provide precise microscopic insight into physical phenomena, and often even reach excellent accuracy on par with MD. +The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, the phonon picture is a good starting point for a wide range of materials properties in practice. Lattice dynamics can provide precise microscopic insight into physical phenomena, and often even reach excellent accuracy on par with MD. The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [@Boer.1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [@Klein.1972]. @@ -77,13 +79,13 @@ The Temperature Dependent Effective Potentials (TDEP) method is a framework to c As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to phonon-phonon interactions can be included by using higher-order force constants up to fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [@Castellano.2023]. +While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [@Castellano.2023]. To extract force constants from thermal snapshots efficiently, TDEP employs the spacegroup symmetry of a given system to rigorously reduce the free parameters in the model to an irreducible set _before_ fitting the model parameters. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Furthermore, additional lattice dynamics sum rules such as acoustic (translational) and rotational invariances, as well the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was probably the first approach to exploit all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. -TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for both the extraction of force constants and their subsequent treatment. This allows simulations even for complex bulk materials with reduced symmetry in practice. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism. This allows simulations even for complex bulk materials with reduced symmetry in practice. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. -Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readbale formats like csv, or self-documented HDF5 files for larger datasets. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for higher-order force constants. +Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readbale formats like csv, or self-documented HDF5 files for larger datasets. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for anharmonic force constants. Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good simulation cells, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. From 50c39fe8f7e6b43e149da6aa49bd101b079e309c Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 17:12:50 +0200 Subject: [PATCH 22/48] fix year? --- paper/literature.bib | 1 + 1 file changed, 1 insertion(+) diff --git a/paper/literature.bib b/paper/literature.bib index d388ce98..fa25b8f9 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -3,6 +3,7 @@ @misc{tdeptools publisher = {GitHub}, url = {https://github.com/flokno/tools.tdep}, title = {{tdeptools: tools for TDEP}}, + year = 2023, } @article{Castellano.2023, From 777122db23ff7a8cf61e5737d90c3e18c7396c4a Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 21 Sep 2023 17:56:34 +0200 Subject: [PATCH 23/48] paper | add Roberta --- paper/paper.md | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/paper/paper.md b/paper/paper.md index 64fc462f..e9ff2b02 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -22,6 +22,9 @@ authors: - name: J. P. Alvarinhas Batista orcid: 0000-0002-3314-249X affiliation: 3 + - name: Roberta Farris + orcid: 0000-0001-6710-0100 + affiliation: 7 - name: Matthieu J. Verstraete orcid: 0000-0001-6921-5163 affiliation: 3 @@ -59,6 +62,8 @@ affiliations: index: 5 - name: College of Letters and Science, Department of Chemistry and Biochemistry, University of California, Los Angeles (UCLA), California 90025, USA index: 6 + - name: Catalan Institute of Nanoscience and Nanotechnology - ICN2 (BIST and CSIC), Campus UAB, 08193 Bellaterra (Barcelona), Spain + index: 7 date: August 2023 bibliography: literature.bib --- From 44e69853fc3d9c2751b11ed65ccbb2a98e9c0063 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 2 Oct 2023 11:07:19 +0200 Subject: [PATCH 24/48] paper | add references for binaries --- paper/literature.bib | 15 ++++++++++++++- paper/paper.md | 18 +++++++----------- 2 files changed, 21 insertions(+), 12 deletions(-) diff --git a/paper/literature.bib b/paper/literature.bib index fa25b8f9..2e80de49 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -3,7 +3,7 @@ @misc{tdeptools publisher = {GitHub}, url = {https://github.com/flokno/tools.tdep}, title = {{tdeptools: tools for TDEP}}, - year = 2023, + year = {2023}, } @article{Castellano.2023, @@ -521,6 +521,19 @@ @article{Broido.2007 year = {2007}, } +@article{West.2006, + abstract = {{The vibrational lifetimes and decay channels of local vibrational modes are calculated from first principles at various temperatures. Our method can be used to predict the temperature dependence of the lifetime of any normal mode in any crystal. We focus here on the stretch modes of H2*, HBC+, and VH·HV in Si. The frequencies are almost identical, but the lifetimes vary from 4 to 295 ps. The calculations correctly predict the lifetimes for T>50 K and illustrate the critical importance of pseudolocal modes in the decay processes of high-frequency local vibrational modes.}}, + author = {West, D. and Estreicher, S. K.}, + doi = {10.1103/physrevlett.96.115504}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {11}, + pages = {115504}, + title = {{First-Principles Calculations of Vibrational Lifetimes and Decay Channels: Hydrogen-Related Modes in Si}}, + volume = {96}, + year = {2006}, +} + @article{Dove.1986, abstract = {{As a contribution to the understanding of the incommensurate phase transitions in thiourea, we present a theoretical study of the crystallographic details of the parael ectric phase. A model intermolecular potential is developed, which includes a reasonable distribution of electrostatic multipole interactions as well as the standard dispersive and repulsive interactions. The model gives a satisfactory prediction of the structure of the para electric phase, and in particular explains the occurrence of the hydrogen-bond network. Calculations of phonon-dispersion curves predict a soft-phonon branch in the b direction with the same symmetry as that observed experimentally. Computer simulations predict reasonable values for the vibrational amplitudes, and show the existence of large-amplitude fluctuations of an harmonic quantities at incommensurate wave vectors. However, although the model displays a strong tendency towards incommensurate and lock-in ordering, it does not in fact give a phase transition at a finite temperature. This failure is attributed to the neglect of molecular polarizability, and it is concluded that this feature provides the mechanism that stabilizes the low-temperature phases.For the interested reader, full details of the molecular dynamics simulation technique using parallel processing are presented here. In particular, a method of extracting normal-mode eigenvectors from the results of the simulations is described.}}, author = {Dove, Martin T. and Lynden-bell, Ruth M.}, diff --git a/paper/paper.md b/paper/paper.md index e9ff2b02..eae0d2b4 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -96,23 +96,19 @@ Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell ## Features -Here we list the most important codes that are shipped with the TDEP code and explain their purpose. Are more detailed explanation of all features can be found in the online documentation. +Here we list the most important codes that are shipped with the TDEP code, explain their purpose, and list the respective references in the literature. Are more detailed explanation of all features can be found in the online documentation. -- `extract_forceconstants`: Obtain force constants up to fourths order from a set of snapshots with positions and forces. +- `extract_forceconstants`: Obtain (effective) harmonic force constants from a set of snapshots with positions and forces [@Hellman.2013]. Optionally fit higher-order force constants [@Hellman.2013oi5], or dielectric tensor properties [@Benshalom.2022]. -- `phonon_dispersion_relations`: Calculate phonon dispersion relations and related harmonic thermodynamic properties from the second-order force constants. +- `phonon_dispersion_relations`: Calculate phonon dispersion relations and related harmonic thermodynamic properties from the second-order force constants [@Hellman.2013], including Grüneisen parameters from third-order force constants [@Hellman.2013oi5]. -- `thermal_conductivity`: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of third-order anharmonicity. -- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone. -- `canonical_configuration`: Create supercells with thermal displacements from the force constants via Monte Carlo sampling from a classical and quantum canonical distribution. -- `generate_structure`: Generate supercells of target size that are as cubic as possible to maximize the largest possible real-space cutoff for the force constants. +- `thermal_conductivity`: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of third-order anharmonicity [@Broido.2007; @Romero.2015]. +- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone [@Romero.2015; @Shulumba.2017]. Grid mode computes spectral thermal transport properties [@Dangić.2021]. +- `canonical_configuration`: Create supercells with thermal displacements from the force constants via Monte Carlo sampling from a classical and quantum canonical distribution [@West.2006; @Shulumba.2017]. Using sTDEP to perform self-consistent sampling is explained in detail in [@Benshalom.2022]. +- `generate_structure`: Generate supercells of target size that are as cubic as possible to maximize the largest possible real-space cutoff for the force constants [@Hellman.2011]. A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. -## Overview of results - -**Do we want to highlight some results here?** - # Summary The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. From b884132f45ded7885232371c2b9fcaff1dba8932 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Tue, 3 Oct 2023 10:52:15 +0200 Subject: [PATCH 25/48] paper | add Esfarjani, polish --- paper/literature.bib | 13 +++++++++++++ paper/paper.md | 6 +++--- 2 files changed, 16 insertions(+), 3 deletions(-) diff --git a/paper/literature.bib b/paper/literature.bib index 2e80de49..7e03fc11 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -494,6 +494,19 @@ @article{Hooton.2010mfn year = {2010}, } +@article{Esfarjani.2008, + abstract = {{A method for extracting force constants (FCs) from first principles is introduced. In principle, provided that forces are accurate enough, it can extract harmonic as well as anharmonic FCs up to any neighbor shell. Symmetries of the FCs as well as those of the lattice are used to reduce the number of parameters to be calculated. The results are illustrated for the case of the Lennard-Jones potential, wherein forces are exact and FCs can be analytically calculated, and Si in the diamond structure. The latter are compared to the previously calculated harmonic FCs.}}, + author = {Esfarjani, Keivan and Stokes, Harold T.}, + doi = {10.1103/physrevb.77.144112}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {14}, + pages = {144112}, + title = {{Method to extract anharmonic force constants from first principles calculations}}, + volume = {77}, + year = {2008}, +} + @article{Souvatzis.2008, abstract = {{Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self-consistently from first principles has been developed to address this issue. The method combines concepts from Born’s interatomic self-consistent phonon approach with first principles calculations of accurate interatomic forces in a supercell. The method has been tested on the high-temperature bcc phase of Ti, Zr, and Hf, as representative examples, and is found to reproduce the observed high-temperature phonon frequencies with good accuracy.}}, author = {Souvatzis, P. and Eriksson, O. and Katsnelson, M. I. and Rudin, S. P.}, diff --git a/paper/paper.md b/paper/paper.md index eae0d2b4..4df4a4b3 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -84,11 +84,11 @@ The Temperature Dependent Effective Potentials (TDEP) method is a framework to c As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [@Castellano.2023]. +While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. -To extract force constants from thermal snapshots efficiently, TDEP employs the spacegroup symmetry of a given system to rigorously reduce the free parameters in the model to an irreducible set _before_ fitting the model parameters. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Furthermore, additional lattice dynamics sum rules such as acoustic (translational) and rotational invariances, as well the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was probably the first approach to exploit all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. +To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set before fitting the model parameters [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, and the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. -TDEP delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism. This allows simulations even for complex bulk materials with reduced symmetry in practice. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +The TDEP code delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for these methods. This allows for materials simulations of simple elemental solids up to complex compounds with reduced symmetry. Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readbale formats like csv, or self-documented HDF5 files for larger datasets. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for anharmonic force constants. From c2e8e0d014c729dfeb89ba9dbcb19d9c96e979aa Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Tue, 3 Oct 2023 11:03:40 +0200 Subject: [PATCH 26/48] paper | add aTDEP --- paper/literature.bib | 12 ++++++++++++ paper/paper.md | 2 ++ 2 files changed, 14 insertions(+) diff --git a/paper/literature.bib b/paper/literature.bib index 7e03fc11..193f8e0a 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -190,6 +190,18 @@ @article{Klarbring.2020vk year = {2020}, } +@article{Bottin.2020rn5, + abstract = {{In this paper, we present the a-TDEP post-process code implemented in the Abinit package. This one is able to capture the explicit thermal effects in solid state physics and to produce a large number of temperature dependent thermodynamic quantities, including the so-called anharmonic effects. Its use is straightforward and require only a single ab initio molecular dynamic (AIMD) trajectory. A Graphical User Interface (GUI) is also available, making the use even easier. We detail our home made implementation of the original “Temperature Dependent Effective Potential” method proposed by Hellman et al. (2011). In particular, we present the various algorithms and schemes used in a-TDEP which enable to obtain the effective Interatomic Force Constants (IFC). The 2nd and 3rd order effective IFC are produced self-consistently using a least-square method, fitting the AIMD forces on a model Hamiltonian function of the displacements. In addition, we stress that we face to a constrained least-square problem since all the effective IFC have to fulfill the several symmetry rules imposed by the space group, by the translation or rotation invariances of the system and by others. Numerous thermodynamic quantities can be computed starting from the 2nd order effective IFC. The first one is the phonon spectrum, from which a large number of other quantities flow : internal energy, entropy, free energy, specific heat... The elastic constants and other usual elastic moduli (the bulk, shear and Young moduli) can also be produced at this level. Using the 3rd order effective IFC, we show how to extract the thermodynamic Grüneisen parameter, the thermal expansion, the sound velocities... and in particular, how to take into account the anisotropy of the system within. As representative applications of a-TDEP capabilities, we show the thermal evolution of the soft phonon mode of α -U, the thermal stabilization of the bcc phase of Zr and the thermal expansion of diamond Si. All these features highlight the strong anharmonicity included in these systems.}}, + author = {Bottin, François and Bieder, Jordan and Bouchet, Johann}, + doi = {10.1016/j.cpc.2020.107301}, + issn = {0010-4655}, + journal = {Computer Physics Communications}, + pages = {107301}, + title = {{a-TDEP: Temperature Dependent Effective Potential for Abinit – Lattice dynamic properties including anharmonicity}}, + volume = {254}, + year = {2020}, +} + @article{Eriksson.2019, abstract = {{The efficient extraction of force constants (FCs) is crucial for the analysis of many thermodynamic materials properties. Approaches based on the systematic enumeration of finite differences scale poorly with system size and can rarely extend beyond third order when input data is obtained from first‐principles calculations. Methods based on parameter fitting in the spirit of interatomic potentials, on the other hand, can extract FC parameters from semi‐random configurations of high information density and advanced regularized regression methods can recover physical solutions from a limited amount of data. Here, the hiphive Python package, that enables the construction of force constant models up to arbitrary order is presented. hiphive exploits crystal symmetries to reduce the number of free parameters and then employs advanced machine learning algorithms to extract the force constants. Depending on the problem at hand, both over and underdetermined systems are handled efficiently. The FCs can be subsequently analyzed directly and or be used to carry out, for example, molecular dynamics simulations. The utility of this approach is demonstrated via several examples including ideal and defective monolayers of MoS2 as well as bulk nickel. The hiphive package is a powerful tool for the efficient extraction of high‐order force constants. It thereby enables modeling the thermodynamic and vibrational properties of, for example, large, low‐symmetry systems and strongly anharmonic materials. This ultimately includes, for example, temperature‐dependent phonon dispersions, life times, and the thermal conductivity.}}, author = {Eriksson, Fredrik and Fransson, Erik and Erhart, Paul}, diff --git a/paper/paper.md b/paper/paper.md index 4df4a4b3..6fbe6dd3 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -109,6 +109,8 @@ Here we list the most important codes that are shipped with the TDEP code, expla A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. +We note that parts of the TDEP method have been implemented in other code packages as well [@Bottin.2020rn5]. + # Summary The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. From 0e5ea8533230cf1c40c626e2a139faa4ca156475 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Tue, 3 Oct 2023 11:22:20 +0200 Subject: [PATCH 27/48] paper | remove old bib --- paper/paper.bib | 343 ------------------------------------------------ 1 file changed, 343 deletions(-) delete mode 100644 paper/paper.bib diff --git a/paper/paper.bib b/paper/paper.bib deleted file mode 100644 index 0e07ccef..00000000 --- a/paper/paper.bib +++ /dev/null @@ -1,343 +0,0 @@ -@article{Togo2018, - author = {Atsushi Togo and Isao Tanaka}, - eid = {arXiv:1808.01590}, - eprint = {1808.01590}, - eprintclass = {cond-mat.mtrl-sci}, - eprinttype = {arXiv}, - journaltitle = {arXiv e-prints}, - pages = {arXiv:1808.01590}, - title = {Spglib: a software library for crystal symmetry search}, - year = {2018}, -} - -@article{Knoop2020, - title = {Anharmonicity measure for materials}, - author = {Knoop, Florian and Purcell, Thomas A. R. and Scheffler, Matthias and Carbogno, Christian}, - journal = {Phys. Rev. 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Benefiting from the increased size and improved qualities, additional properties have been characterized. Important factors related to boron arsenide, remaining challenges, and the future outlook are addressed in this minireview.}, -author = {Tian, Fei and Ren, Zhifeng}, -doi = {10.1002/anie.201812112}, -issn = {15213773}, -journal = {Angewandte Chemie - International Edition}, -keywords = {III–V compounds,boron arsenide,crystal growth,semiconductors,thermal conductivity}, -month = {apr}, -number = {18}, -pages = {5824--5831}, -pmid = {30523650}, -publisher = {Wiley-VCH Verlag}, -title = {{High Thermal Conductivity in Boron Arsenide: From Prediction to Reality}}, -url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201812112}, -volume = {58}, -year = {2019} -} - - -@article{Salzillo2016, -abstract = {Raman microscopy in the lattice phonon region coupled with X-ray diffraction have been used to study the polymorphism in crystals and microcrystals of the organic semiconductor 9,10-diphenylanthracene (DPA) obtained by various methods. While solution grown specimens all display the well-known monoclinic structure widely reported in the literature, by varying the growth conditions two more polymorphs have been obtained, either from the melt or by sublimation. By injecting water as a nonsolvent in a DPA solution, one of the two new polymorphs was predominantly obtained in the shape of microribbons. Lattice energy calculations allow us to assess the relative thermodynamic stability of the polymorphs and verify that the energies of the different phases are very sensitive to the details of the molecular geometry adopted in the solid state. The mobility channels of DPA polymorphs are shortly investigated.}, -author = {Salzillo, Tommaso and {Della Valle}, Raffaele Guido and Venuti, Elisabetta and Brillante, Aldo and Siegrist, Theo and Masino, Matteo and Mezzadri, Francesco and Girlando, Alberto}, -doi = {10.1021/acs.jpcc.5b11115}, -file = {:home/purcell/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Salzillo et al. - 2016 - Two New Polymorphs of the Organic Semiconductor 9,10-Diphenylanthracene Raman and X-ray Analysis.pdf:pdf}, -issn = {19327455}, -journal = {Journal of Physical Chemistry C}, -number = {3}, -pages = {1831--1840}, -publisher = {UTC}, -title = {{Two new polymorphs of the organic semiconductor 9,10-diphenylanthracene: Raman and X-ray analysis}}, -url = {https://pubs.acs.org/sharingguidelines}, -volume = {120}, -year = {2016} -} - -@article{Snyder2008, -abstract = {Thermoelectric materials, which can generate electricity from waste heat or be used as solid-state Peltier coolers, could play an important role in a global sustainable energy solution. Such a development is contingent on identifying materials with higher thermoelectric efficiency than available at present, which is a challenge owing to the conflicting combination of material traits that are required. Nevertheless, because of modern synthesis and characterization techniques, particularly for nanoscale materials, a new era of complex thermoelectric materials is approaching. We review recent advances in the field, highlighting the strategies used to improve the thermopower and reduce the thermal conductivity.}, -author = {Snyder, G. Jeffrey and Toberer, Eric S.}, -doi = {10.1038/nmat2090}, -issn = {14761122}, -journal = {Nature Materials}, -keywords = {Biomaterials,Condensed Matter Physics,Materials Science,Nanotechnology,Optical and Electronic Materials,general}, -month = {feb}, -number = {2}, -pages = {105--114}, -pmid = {18219332}, -publisher = {Nature Publishing Group}, -title = {{Complex thermoelectric materials}}, -url = {www.nature.com/naturematerials}, -volume = {7}, -year = {2008} -} - -@article{Evans2008, -author = {Evans, AG and Clarke, DR and Levi, CG}, -title = {{The influence of oxides on the performance of advanced gas turbines}}, -journal = {J. Eur. Ceram. Soc.}, -year = {2008}, -volume = {28}, -number = {7}, -pages = {1405--1419}, -doi = {10.1016/j.jeurceramsoc.2007.12.023} -} - -@article{West2006, -author = {West, D. and Estreicher, S. K.}, -doi = {10.1103/PhysRevLett.96.115504}, -journal = {Phys. Rev. Lett.}, -number = {11}, -pages = {22--25}, -pmid = {16605840}, -title = {{First-principles calculations of vibrational lifetimes and decay channels: Hydrogen-related modes in Si}}, -volume = {96}, -year = {2006} -} - -@article{Turney2009, -author = {Turney, JE and Landry, ES and McGaughey, AJH and Amon, CH}, -title = {{Predicting phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations}}, -journal = {Phys. Rev. B}, -year = {2009}, -volume = {79}, -number = {6}, -pages = {64301}, -doi = {10.1103/physrevb.79.064301} - -} - -@article{Gonze2020, - Author = "Gonze, Xavier and Amadon, Bernard and Antonius, Gabriel and Arnardi, Frédéric and Baguet, Lucas and Beuken, Jean-Michel and Bieder, Jordan and Bottin, François and Bouchet, Johann and Bousquet, Eric and Brouwer, Nils and Bruneval, Fabien and Brunin, Guillaume and Cavignac, Théo and Charraud, Jean-Baptiste and Chen, Wei and Côté, Michel and Cottenier, Stefaan and Denier, Jules and Geneste, Grégory and Ghosez, Philippe and Giantomassi, Matteo and Gillet, Yannick and Gingras, Olivier and Hamann, Donald R. and Hautier, Geoffroy and He, Xu and Helbig, Nicole and Holzwarth, Natalie and Jia, Yongchao and Jollet, François and Lafargue-Dit-Hauret, William and Lejaeghere, Kurt and Marques, Miguel A. L. and Martin, Alexandre and Martins, Cyril and Miranda, Henrique P. C. and Naccarato, Francesco and Persson, Kristin and Petretto, Guido and Planes, Valentin and Pouillon, Yann and Prokhorenko, Sergei and Ricci, Fabio and Rignanese, Gian-Marco and Romero, Aldo H. and Schmitt, Michael Marcus and Torrent, Marc and van Setten, Michiel J. and Troeye, Benoit Van and Verstraete, Matthieu J. and Zérah, Gilles and Zwanziger, Josef W.", - Journal = "Comput. Phys. Commun.", - Pages = "107042", - Title = "The Abinit project: Impact, environment and recent developments", - Volume = "248", - Year = "2020", - url = "https://doi.org/10.1016/j.cpc.2019.107042" -} - -@article{Draxl2018, - doi = {10.1557/mrs.2018.208}, - url = {https://doi.org/10.1557/mrs.2018.208}, - year = {2018}, - month = sep, - publisher = {Cambridge University Press ({CUP})}, - volume = {43}, - number = {9}, - pages = {676--682}, - author = {Claudia Draxl and Matthias Scheffler}, - title = {{NOMAD}: The {FAIR} concept for big data-driven materials science}, - journal = {{MRS} Bulletin} -} - -@misc{AiiDA, -Author = {Sebastiaan. P. Huber and Spyros Zoupanos and Martin Uhrin and Leopold Talirz and Leonid Kahle and Rico Häuselmann and Dominik Gresch and Tiziano Müller and Aliaksandr V. Yakutovich and Casper W. Andersen and Francisco F. Ramirez and Carl S. Adorf and Fernando Gargiulo and Snehal Kumbhar and Elsa Passaro and Conrad Johnston and Andrius Merkys and Andrea Cepellotti and Nicolas Mounet and Nicola Marzari and Boris Kozinsky and Giovanni Pizzi}, -Title = {AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance}, -Year = {2020}, -Eprint = {arXiv:2003.12476}, -doi = {10.1038/s41597-020-00638-4}, -} - From 4cb4e0b092605357393824fd8ecae8c1c087423d Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Wed, 11 Oct 2023 09:52:55 +0200 Subject: [PATCH 28/48] paper | Roberta comments --- paper/paper.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 6fbe6dd3..8c952db6 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -70,9 +70,9 @@ bibliography: literature.bib # Introduction -Properties of materials change with temperature, i.e., the thermal vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. +Properties of materials change with temperature, i.e., the thermal vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. -In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly: This can be done by performing _molecular dynamics_ (MD) simulations which aims at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables in equilibrium through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics. +In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing _molecular dynamics_ (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables in equilibrium through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics. The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, the phonon picture is a good starting point for a wide range of materials properties in practice. Lattice dynamics can provide precise microscopic insight into physical phenomena, and often even reach excellent accuracy on par with MD. @@ -84,7 +84,7 @@ The Temperature Dependent Effective Potentials (TDEP) method is a framework to c As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of the authors in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set before fitting the model parameters [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, and the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. From 71f51f77ded147802fd0fbf26473927a99c308a3 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Wed, 11 Oct 2023 17:51:06 +0200 Subject: [PATCH 29/48] paper | Matthieu's changes --- paper/literature.bib | 26 ++++++++++++++++++++++++++ paper/paper.md | 44 +++++++++++++++++++++++++------------------- 2 files changed, 51 insertions(+), 19 deletions(-) diff --git a/paper/literature.bib b/paper/literature.bib index 193f8e0a..face3bed 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -677,6 +677,32 @@ @article{Koehler.1966 year = {1966}, } +@article{Kohn.1965, + abstract = {{From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of 23.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.}}, + author = {Kohn, W. and Sham, L. J.}, + doi = {10.1103/physrev.140.a1133}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {4A}, + pages = {A1133--A1138}, + title = {{Self-Consistent Equations Including Exchange and Correlation Effects}}, + volume = {140}, + year = {1965}, +} + +@article{Hohenberg.1964, + abstract = {{This paper deals with the ground state of an interacting electron gas in an external potential v(r). It is proved that there exists a universal functional of the density, F[n(r)], independent of v(r), such that the expression E≡∫v(r)n(r)dr+F[n(r)] has as its minimum value the correct ground-state energy associated with v(r). The functional F[n(r)] is then discussed for two situations: (1) n(r)=n0+ñ(r), ñn0≪1, and (2) n(r)=ϕ(rr0) with ϕ arbitrary and r0→∞. In both cases F can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.}}, + author = {Hohenberg, P. and Kohn, W.}, + doi = {10.1103/physrev.136.b864}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {3B}, + pages = {B864--B871}, + title = {{Inhomogeneous Electron Gas}}, + volume = {136}, + year = {1964}, +} + @article{Cowley.1963, abstract = {{The theory of the physical properties of an anharmonic crystal is discussed by using the thermodynamic Green's functions for the phonons. A perturbation procedure is developed to obtain the Green's functions and it is shown that for some purposes a quasi-harmonic approximation is useful, in which the frequencies of the normal modes are those determined by infra-red or neutron spectrometry. The thermodynamic, elastic, dielectric and scattering properties of an anharmonic crystal are discussed in terms of the Green's functions, and detailed expressions are given for the more important contributions. Detailed numerical calculations are presented of the thermal expansion, dielectric properties and shapes of some of the inelastically scattered neutron groups, for sodium iodide and potassium bromide. The calculations, which give reasonable agreement with experiment, show that even at quite low temperatures, the lifetimes of some of the normal modes can be quite short. By using the quasi-harmonic approximation it is shown that the large temperature dependence of the normal modes in a ferroelectric crystal can be treated adequately.}}, author = {Cowley, R.A.}, diff --git a/paper/paper.md b/paper/paper.md index 8c952db6..5c6e2260 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -27,7 +27,7 @@ authors: affiliation: 7 - name: Matthieu J. Verstraete orcid: 0000-0001-6921-5163 - affiliation: 3 + affiliation: 3, 8 - name: Matthew Heine orcid: 0000-0002-4882-6712 affiliation: 5 @@ -64,48 +64,54 @@ affiliations: index: 6 - name: Catalan Institute of Nanoscience and Nanotechnology - ICN2 (BIST and CSIC), Campus UAB, 08193 Bellaterra (Barcelona), Spain index: 7 -date: August 2023 + - name: ITP, Physics Department, University of Utrecht, 3584 CC Utrecht, the Netherlands + index: 8 +date: 2023 bibliography: literature.bib --- # Introduction -Properties of materials change with temperature, i.e., the thermal vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat through the sample, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties both in applied and fundamental sciences. +The properties of materials change both qualitatively and quantitatively with temperature, i.e., the macroscopic manifestation of the microscopic vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, the temperature influences the response of the material to the perturbation, for example its ability to conduct heat, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties, both in applied and fundamental sciences. -In _ab initio_ materials modeling, the electronic temperature contribution is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing _molecular dynamics_ (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables in equilibrium through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the thermal relaxation dynamics. +In _ab initio_ materials modeling, the _electronic_ temperature contribution is straightforward to include, through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing _molecular dynamics_ (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables either in equilibrium, through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the relaxation dynamics. -The alternative way is to construct approximate model Hamiltonians for the nuclear subsystem which enable an _analytic_ treatment of the nuclear motion by leveraging perturbation theory starting from an exactly solvable solution. This approach is called _lattice dynamics_, and the exact reference solution is given in terms of _phonons_ which are eigensolutions to a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the perturbative expansion grows very quickly with system size and perturbation order. It follows that the lattice dynamics approach is _not_ formally exact. However, the phonon picture is a good starting point for a wide range of materials properties in practice. Lattice dynamics can provide precise microscopic insight into physical phenomena, and often even reach excellent accuracy on par with MD. +An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ treatment of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach the exact reference solution is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The straightforward lattice dynamics approach is not formally exact, but the phonon picture is a good starting point for a wide range of materials properties in practice. Phonon lattice dynamics can further provide microscopic insight into physical phenomena, and often even reach excellent accuracy on par with MD-based methods. -The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example ist the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in dense solid He [@Boer.1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. At that time, it was most practical to obtain these effective phonons in a self-consistent way, hence denoted _self-consistent phonon theory_. An excellent review is given in Ref. [@Klein.1972]. +The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example is the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in the dense solid phase [@Boer.1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. It was shown to be practical to obtain these effective phonons in a self-consistent way, denoted _self-consistent phonon theory_, by sampling the force constants using a distribution of displacments obtained from the force constants from a previous iteration. An excellent review is given in Ref. [@Klein.1972]. # Statement of need -The Temperature Dependent Effective Potentials (TDEP) method is a framework to construct and solve temperature-dependent, effective lattice dynamics model Hamiltonians for a variety of properties, and the TDEP code described here is the respective reference implementation. +The Temperature Dependent Effective Potential (TDEP) method is a framework to construct and solve effective, temperature-dependent lattice dynamics model Hamiltonians for a variety of properties. The TDEP code described here is the respective reference implementation. -As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory is well-established since decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT). This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. +As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory has been well-established for decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -While effective phonons capture the effect of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or infinitesimal linewidth, respectively. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +While effective phonons capture the effects of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. -To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set before fitting the model parameters [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants in a bcc lattice with 4x4x4 supercell (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, and the Huang invariances which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. +To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set, before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. The TDEP code delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for these methods. This allows for materials simulations of simple elemental solids up to complex compounds with reduced symmetry. -Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readbale formats like csv, or self-documented HDF5 files for larger datasets. Thanks to exploiting the symmetry of force constants, the respective output files are very compact, even for anharmonic force constants. +Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readable formats like csv, or self-documented HDF5 files for larger datasets. Thanks to the exploitation of the force constant symmetries, the respective output files are very compact, even for anharmonic force constants. -Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good simulation cells, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. +Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good simulation (super)cells, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. ## Features -Here we list the most important codes that are shipped with the TDEP code, explain their purpose, and list the respective references in the literature. Are more detailed explanation of all features can be found in the online documentation. +Here we list the most important codes that are shipped with the TDEP code, explain their purpose, and list the respective references in the literature. A more detailed explanation of all features can be found in the online documentation. + +- `generate_structure`: Generate supercells of target size that are as cubic as possible to maximize the largest possible real-space cutoff for the force constants [@Hellman.2011]. + +- `canonical_configuration`: Create supercells with thermal displacements from the force constants via Monte Carlo sampling from a classical or quantum canonical distribution [@West.2006; @Shulumba.2017]. Using sTDEP to perform self-consistent sampling is explained in -- `extract_forceconstants`: Obtain (effective) harmonic force constants from a set of snapshots with positions and forces [@Hellman.2013]. Optionally fit higher-order force constants [@Hellman.2013oi5], or dielectric tensor properties [@Benshalom.2022]. +- `extract_forceconstants`: Obtain (effective) harmonic force constants from a set of supercell snapshots with displaced positions and forces [@Hellman.2013]. Optionally fit higher-order force constants [@Hellman.2013oi5], or dielectric tensor properties [@Benshalom.2022]. - `phonon_dispersion_relations`: Calculate phonon dispersion relations and related harmonic thermodynamic properties from the second-order force constants [@Hellman.2013], including Grüneisen parameters from third-order force constants [@Hellman.2013oi5]. - `thermal_conductivity`: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of third-order anharmonicity [@Broido.2007; @Romero.2015]. -- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone [@Romero.2015; @Shulumba.2017]. Grid mode computes spectral thermal transport properties [@Dangić.2021]. -- `canonical_configuration`: Create supercells with thermal displacements from the force constants via Monte Carlo sampling from a classical and quantum canonical distribution [@West.2006; @Shulumba.2017]. Using sTDEP to perform self-consistent sampling is explained in detail in [@Benshalom.2022]. -- `generate_structure`: Generate supercells of target size that are as cubic as possible to maximize the largest possible real-space cutoff for the force constants [@Hellman.2011]. + +- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone [@Romero.2015; @Shulumba.2017]. Grid mode computes _spectral_ thermal transport properties [@Dangić.2021]. +detail in [@Benshalom.2022]. A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. @@ -113,10 +119,10 @@ We note that parts of the TDEP method have been implemented in other code packag # Summary -The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory in self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. +The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory, in both self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. # Acknowledgements -F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. +F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. MJV, AC, and JPB acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. # References From 81e7d83992e749eab1e639ea9e9b679e9e27e5e8 Mon Sep 17 00:00:00 2001 From: johkl Date: Fri, 13 Oct 2023 11:02:58 +0100 Subject: [PATCH 30/48] Update paper.md Some edits to the paper --- paper/paper.md | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 5c6e2260..05f2bf8d 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -72,11 +72,11 @@ bibliography: literature.bib # Introduction -The properties of materials change both qualitatively and quantitatively with temperature, i.e., the macroscopic manifestation of the microscopic vibrational motion of electrons and nuclei. In thermal equilibrium, temperature determines the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, the temperature influences the response of the material to the perturbation, for example its ability to conduct heat, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of materials properties, both in applied and fundamental sciences. +The properties of materials change both qualitatively and quantitatively with temperature, i.e., the macroscopic manifestation of the microscopic vibrational motion of electrons and nuclei. In thermal equilibrium, temperature influences the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, for instance when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of both applied and fundamental materials science. -In _ab initio_ materials modeling, the _electronic_ temperature contribution is straightforward to include, through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing _molecular dynamics_ (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables either in equilibrium, through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the relaxation dynamics. +In _ab initio_ materials modeling, the contribution of _electronic_ temperature is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing _molecular dynamics_ (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables either in equilibrium, through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the relaxation dynamics. -An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ treatment of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach the exact reference solution is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The straightforward lattice dynamics approach is not formally exact, but the phonon picture is a good starting point for a wide range of materials properties in practice. Phonon lattice dynamics can further provide microscopic insight into physical phenomena, and often even reach excellent accuracy on par with MD-based methods. +An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ treatment of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach the exact reference solution is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included using established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The straightforward lattice dynamics approach is not formally exact, but the phonon picture is a good starting point for a wide range of materials properties in practice. Phonon lattice dynamics can further provide microscopic insight into physical phenomena, and often even reach excellent accuracy on par with MD-based methods. The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example is the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in the dense solid phase [@Boer.1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. It was shown to be practical to obtain these effective phonons in a self-consistent way, denoted _self-consistent phonon theory_, by sampling the force constants using a distribution of displacments obtained from the force constants from a previous iteration. An excellent review is given in Ref. [@Klein.1972]. @@ -90,9 +90,9 @@ While effective phonons capture the effects of anharmonic frequency renormalizat To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set, before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. -The TDEP code delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for these methods. This allows for materials simulations of simple elemental solids up to complex compounds with reduced symmetry. +The TDEP code delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for these methods. This allows for materials simulations of systems ranging from simple elemental solids up to complex compounds with reduced symmetry. -Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create or parse. These are either plain text formats, established human-readable formats like csv, or self-documented HDF5 files for larger datasets. Thanks to the exploitation of the force constant symmetries, the respective output files are very compact, even for anharmonic force constants. +Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create and parse. These are either plain text formats, established human-readable formats like csv, or self-documented HDF5 files for larger datasets. Thanks to the exploitation of the force constant symmetries, the respective output files are very compact, even for anharmonic force constants. Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good simulation (super)cells, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. @@ -102,7 +102,7 @@ Here we list the most important codes that are shipped with the TDEP code, expla - `generate_structure`: Generate supercells of target size that are as cubic as possible to maximize the largest possible real-space cutoff for the force constants [@Hellman.2011]. -- `canonical_configuration`: Create supercells with thermal displacements from the force constants via Monte Carlo sampling from a classical or quantum canonical distribution [@West.2006; @Shulumba.2017]. Using sTDEP to perform self-consistent sampling is explained in +- `canonical_configuration`: Create supercells with thermal displacements from the force constants using Monte Carlo sampling from a classical or quantum canonical distribution [@West.2006; @Shulumba.2017]. Using sTDEP to perform self-consistent sampling is explained in detail in [@Benshalom.2022]. - `extract_forceconstants`: Obtain (effective) harmonic force constants from a set of supercell snapshots with displaced positions and forces [@Hellman.2013]. Optionally fit higher-order force constants [@Hellman.2013oi5], or dielectric tensor properties [@Benshalom.2022]. @@ -110,8 +110,7 @@ Here we list the most important codes that are shipped with the TDEP code, expla - `thermal_conductivity`: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of third-order anharmonicity [@Broido.2007; @Romero.2015]. -- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone [@Romero.2015; @Shulumba.2017]. Grid mode computes _spectral_ thermal transport properties [@Dangić.2021]. -detail in [@Benshalom.2022]. +- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone [@Romero.2015; @Shulumba.2017]. The grid mode computes _spectral_ thermal transport properties [@Dangić.2021]. A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. @@ -123,6 +122,6 @@ The TDEP method is a versatile and efficient approach to perform temperature-dep # Acknowledgements -F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. MJV, AC, and JPB acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. +F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. MJV, AC, and JPB acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. # References From e2f3dbef7699b2c3e89828812ebdc9d97d2c5736 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Tue, 17 Oct 2023 09:50:56 +0200 Subject: [PATCH 31/48] paper | changes David 1 --- paper/literature.bib | 13 +++++++++++++ paper/paper.md | 16 ++++++++-------- 2 files changed, 21 insertions(+), 8 deletions(-) diff --git a/paper/literature.bib b/paper/literature.bib index face3bed..6c4a5eff 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -241,6 +241,19 @@ @article{Heine.2019 year = {2019}, } +@article{Ravichandran.2018, + abstract = {{The conventional first-principles theory for the thermal and thermodynamic properties of insulators is based on the perturbative treatment of the anharmonicity of crystal bonds. While this theory has been a successful predictive tool for strongly bonded solids such as diamond and silicon, here we show that it fails dramatically for strongly anharmonic (weakly bonded) materials, and that the conventional quasiparticle picture breaks down at relatively low temperatures. To address this failure, we present a unified first-principles theory of the thermodynamic and thermal properties of insulators that captures multiple thermal properties within the same framework across the full range of anharmonicity from strongly bonded to weakly bonded insulators. This theory features a new phonon renormalization approach derived from many-body physics that creates well-defined quasiparticles even at relatively high temperatures, and it accurately captures the effects of strongly anharmonic bonds on phonons and thermal transport. Using a prototypical strongly anharmonic material, sodium chloride (NaCl), as an example, we demonstrate that our new first-principles framework simultaneously captures the apparently contradictory experimental observations of large thermal expansion and low thermal conductivity of NaCl on the one hand, and anomalously weak temperature dependence of phonon modes on the other, while the conventional theory fails in all three cases. We demonstrate that four-phonon scattering due to higher-order anharmonicity significantly lowers the thermal conductivity of NaCl and is required for a proper comparison to experiment. Furthermore, we show that our renormalization framework, along with four-phonon scattering, also successfully predicts the measured phonon frequencies and thermal properties of a weakly anharmonic material, diamond, indicating universal applicability for thermal properties of insulators. Our work gives new insights into the physics of heat flow in solids, and presents a computationally efficient and rigorous framework that captures the thermal and thermodynamic properties of both weakly and strongly bonded insulators simultaneously.}}, + author = {Ravichandran, Navaneetha K. and Broido, David}, + doi = {10.1103/physrevb.98.085205}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {8}, + pages = {085205}, + title = {{Unified first-principles theory of thermal properties of insulators}}, + volume = {98}, + year = {2018}, +} + @article{Kim.2018, abstract = {{Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.}}, author = {Kim, D. S. and Hellman, O. and Herriman, J. and Smith, H. L. and Lin, J. Y. Y. and Shulumba, N. and Niedziela, J. L. and Li, C. W. and Abernathy, D. L. and Fultz, B.}, diff --git a/paper/paper.md b/paper/paper.md index 05f2bf8d..90ebfe19 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -70,15 +70,19 @@ date: 2023 bibliography: literature.bib --- +# Summary + +The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory, in both self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. + # Introduction The properties of materials change both qualitatively and quantitatively with temperature, i.e., the macroscopic manifestation of the microscopic vibrational motion of electrons and nuclei. In thermal equilibrium, temperature influences the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, for instance when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of both applied and fundamental materials science. In _ab initio_ materials modeling, the contribution of _electronic_ temperature is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing _molecular dynamics_ (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables either in equilibrium, through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the relaxation dynamics. -An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ treatment of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach the exact reference solution is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included using established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The straightforward lattice dynamics approach is not formally exact, but the phonon picture is a good starting point for a wide range of materials properties in practice. Phonon lattice dynamics can further provide microscopic insight into physical phenomena, and often even reach excellent accuracy on par with MD-based methods. +An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ description of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach, the starting point is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The lattice dynamics approach is therefore not formally exact. However, the phonon picture is useful for describing a wide range of materials properties in practice, and often reaches excellent accuracy in comparison to experiment while providing precise microscopic insight into the underlying physical phenomena. -The parameters in the lattice dynamics Hamiltonian, called _force constants_, can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion around the energetic minimum position. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classical example is the ⁴He problem in which a Taylor expansion does not yield well-defined phonons in the dense solid phase [@Boer.1948], whereas well-defined phonons that describe ⁴He satisfactorily can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. It was shown to be practical to obtain these effective phonons in a self-consistent way, denoted _self-consistent phonon theory_, by sampling the force constants using a distribution of displacments obtained from the force constants from a previous iteration. An excellent review is given in Ref. [@Klein.1972]. +The chemical bonding in the lattice dynamics Hamiltonian is represented through interatomic _force constants_. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem in which a Taylor expansion does not yield well-defined phonons in the dense solid phase [@Boer.1948], whereas well-defined phonons that describe $^4$He can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. It was shown to be practical to obtain these effective phonons in a self-consistent way, denoted _self-consistent phonon theory_, by sampling the force constants using a distribution of displacments obtained from the force constants from a previous iteration. An excellent review is given in Ref. [@Klein.1972]. # Statement of need @@ -86,9 +90,9 @@ The Temperature Dependent Effective Potential (TDEP) method is a framework to co As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory has been well-established for decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -While effective phonons capture the effects of anharmonic frequency renormalization, they are still non-interacting quasiparticles with inifite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +While effective phonons capture the effects of anharmonic frequency renormalization, they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that using effective force constants yields renormalized phonon quasiparticles that naturally interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where perturbation theory on top of bare phonons is no longer valid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. -To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set, before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns after employing symmetry arguments. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. +To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set, before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. The TDEP code delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for these methods. This allows for materials simulations of systems ranging from simple elemental solids up to complex compounds with reduced symmetry. @@ -116,10 +120,6 @@ A separate python library for interfacing with different DFT and force field cod We note that parts of the TDEP method have been implemented in other code packages as well [@Bottin.2020rn5]. -# Summary - -The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory, in both self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. - # Acknowledgements F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. MJV, AC, and JPB acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. From 10c2c54de5509b160771f6929c56e97e6ec29f00 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Tue, 17 Oct 2023 09:52:31 +0200 Subject: [PATCH 32/48] paper | restructuring David --- paper/paper.md | 15 ++++++--------- 1 file changed, 6 insertions(+), 9 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 90ebfe19..3e3289b3 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -72,7 +72,7 @@ bibliography: literature.bib # Summary -The TDEP method is a versatile and efficient approach to perform temperature-dependent materials simulations from first principles. This comprises thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation was briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory, in both self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. +The Temperature Dependent Effective Potential (TDEP) method is a versatile and efficient approach to include temperature in _ab initio_ materials simulations based on phonon theory. TDEP can be used to describe thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation is briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory, in both self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. # Introduction @@ -82,22 +82,19 @@ In _ab initio_ materials modeling, the contribution of _electronic_ temperature An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ description of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach, the starting point is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The lattice dynamics approach is therefore not formally exact. However, the phonon picture is useful for describing a wide range of materials properties in practice, and often reaches excellent accuracy in comparison to experiment while providing precise microscopic insight into the underlying physical phenomena. -The chemical bonding in the lattice dynamics Hamiltonian is represented through interatomic _force constants_. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem in which a Taylor expansion does not yield well-defined phonons in the dense solid phase [@Boer.1948], whereas well-defined phonons that describe $^4$He can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. It was shown to be practical to obtain these effective phonons in a self-consistent way, denoted _self-consistent phonon theory_, by sampling the force constants using a distribution of displacments obtained from the force constants from a previous iteration. An excellent review is given in Ref. [@Klein.1972]. +The chemical bonding in the lattice dynamics Hamiltonian is represented through _force constants_. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem in which a Taylor expansion does not yield well-defined phonons in the dense solid phase [@Boer.1948], whereas well-defined phonons that describe $^4$He can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. In these approaches, the effective phonons were obtained self-consistently using a variational principle. A excellent historical review of this _self-consistent phonon theory_ is given in Ref. [@Klein.1972]. +While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -# Statement of need -The Temperature Dependent Effective Potential (TDEP) method is a framework to construct and solve effective, temperature-dependent lattice dynamics model Hamiltonians for a variety of properties. The TDEP code described here is the respective reference implementation. +The effective phonons capture the effects of anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that using effective force constants yields renormalized phonon quasiparticles that naturally interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where perturbation theory on top of bare phonons is no longer valid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. -As discussed in the introduction, the theoretical foundation of (self-consistent) phonon theory has been well-established for decades. More recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -While effective phonons capture the effects of anharmonic frequency renormalization, they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that using effective force constants yields renormalized phonon quasiparticles that naturally interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where perturbation theory on top of bare phonons is no longer valid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +# Statement of need +The TDEP open source code is the reference implementation for the TDEP method introduced above. It delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism both for constructing and solving effective lattice-dynamics Hamiltonians. This allows for materials simulations of simple elemental solids up to complex compounds with reduced symmetry under realistic conditions. To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set, before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. -The TDEP code delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism for these methods. This allows for materials simulations of systems ranging from simple elemental solids up to complex compounds with reduced symmetry. - Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create and parse. These are either plain text formats, established human-readable formats like csv, or self-documented HDF5 files for larger datasets. Thanks to the exploitation of the force constant symmetries, the respective output files are very compact, even for anharmonic force constants. - Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good simulation (super)cells, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. ## Features From fcda82490125dac23d2cea52c1d4b7f088ac562c Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Tue, 17 Oct 2023 10:22:11 +0200 Subject: [PATCH 33/48] paper | streamline --- paper/paper.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 3e3289b3..7712a655 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -82,11 +82,11 @@ In _ab initio_ materials modeling, the contribution of _electronic_ temperature An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ description of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach, the starting point is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The lattice dynamics approach is therefore not formally exact. However, the phonon picture is useful for describing a wide range of materials properties in practice, and often reaches excellent accuracy in comparison to experiment while providing precise microscopic insight into the underlying physical phenomena. -The chemical bonding in the lattice dynamics Hamiltonian is represented through _force constants_. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem in which a Taylor expansion does not yield well-defined phonons in the dense solid phase [@Boer.1948], whereas well-defined phonons that describe $^4$He can be obtained from an effective, positive-definite second order Hamiltonian, as was shown by Born and coworkers in the 1950's [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. In these approaches, the effective phonons were obtained self-consistently using a variational principle. A excellent historical review of this _self-consistent phonon theory_ is given in Ref. [@Klein.1972]. +The chemical bonding in the lattice dynamics Hamiltonian is represented through _force constants_. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in Ref. [@Klein.1972]. While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -The effective phonons capture the effects of anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that using effective force constants yields renormalized phonon quasiparticles that naturally interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where perturbation theory on top of bare phonons is no longer valid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. # Statement of need @@ -95,6 +95,7 @@ The TDEP open source code is the reference implementation for the TDEP method in To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set, before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create and parse. These are either plain text formats, established human-readable formats like csv, or self-documented HDF5 files for larger datasets. Thanks to the exploitation of the force constant symmetries, the respective output files are very compact, even for anharmonic force constants. + Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good simulation (super)cells, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. ## Features From 725481396195032992579987f37539394c7f214b Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Tue, 17 Oct 2023 10:27:45 +0200 Subject: [PATCH 34/48] paper | affiliation Sergei --- paper/paper.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 7712a655..e1f11c0b 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -43,9 +43,9 @@ authors: - name: Igor Abrikosov orcid: 0000-0001-7551-4717 affiliation: 1 - - name: Sergei Simak + - name: Sergei I. Simak orcid: 0000-0002-1320-389X - affiliation: 1 + affiliation: 1, 9 - name: Olle Hellman orcid: 0000-0002-3453-2975 affiliation: 2 @@ -66,6 +66,8 @@ affiliations: index: 7 - name: ITP, Physics Department, University of Utrecht, 3584 CC Utrecht, the Netherlands index: 8 + - name: Department of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden + index: 9 date: 2023 bibliography: literature.bib --- From 08a466347b5212017fe1107e6e916c5716ffab4e Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Wed, 18 Oct 2023 14:41:19 +0200 Subject: [PATCH 35/48] paper | funding Roberta --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index e1f11c0b..12d0c16c 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -122,6 +122,6 @@ We note that parts of the TDEP method have been implemented in other code packag # Acknowledgements -F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. MJV, AC, and JPB acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. +F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. MJV, AC, and JPB acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. # References From 2ad81a77ce28dc15aca108c722ad5dfeda1d872a Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 23 Oct 2023 18:01:07 +0200 Subject: [PATCH 36/48] paper | comments Dennis --- paper/paper.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 12d0c16c..99021f51 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -104,9 +104,9 @@ Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell Here we list the most important codes that are shipped with the TDEP code, explain their purpose, and list the respective references in the literature. A more detailed explanation of all features can be found in the online documentation. -- `generate_structure`: Generate supercells of target size that are as cubic as possible to maximize the largest possible real-space cutoff for the force constants [@Hellman.2011]. +- `generate_structure`: Generate supercells of target size, with options to make them as cubic as possible to maximize the real-space cutoff for the force constants [@Hellman.2011]. -- `canonical_configuration`: Create supercells with thermal displacements from the force constants using Monte Carlo sampling from a classical or quantum canonical distribution [@West.2006; @Shulumba.2017]. Using sTDEP to perform self-consistent sampling is explained in detail in [@Benshalom.2022]. +- `canonical_configuration`: Create supercells with thermal displacements from an initial guess or existing force constants, using Monte Carlo sampling from a classical or quantum canonical distribution [@West.2006; @Shulumba.2017]. Self-consistent sampling with sTDEP is explained in detail in [@Benshalom.2022]. - `extract_forceconstants`: Obtain (effective) harmonic force constants from a set of supercell snapshots with displaced positions and forces [@Hellman.2013]. Optionally fit higher-order force constants [@Hellman.2013oi5], or dielectric tensor properties [@Benshalom.2022]. From b61428042e19abd82909de1b525dfb54d4528696 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Tue, 24 Oct 2023 19:25:42 +0200 Subject: [PATCH 37/48] paper | comments Igor --- paper/paper.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 99021f51..e089adc3 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -40,7 +40,7 @@ authors: - name: Johan Klarbring orcid: 0000-0002-6223-5812 affiliation: 1, 4 - - name: Igor Abrikosov + - name: Igor A. Abrikosov orcid: 0000-0001-7551-4717 affiliation: 1 - name: Sergei I. Simak @@ -80,13 +80,13 @@ The Temperature Dependent Effective Potential (TDEP) method is a versatile and e The properties of materials change both qualitatively and quantitatively with temperature, i.e., the macroscopic manifestation of the microscopic vibrational motion of electrons and nuclei. In thermal equilibrium, temperature influences the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, for instance when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of both applied and fundamental materials science. -In _ab initio_ materials modeling, the contribution of _electronic_ temperature is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing _molecular dynamics_ (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables either in equilibrium, through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the relaxation dynamics. +In _ab initio_ materials modeling, the contribution of electronic temperature is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing molecular dynamics (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables either in equilibrium, through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the relaxation dynamics. -An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ description of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach, the starting point is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of _harmonic_ form, i.e., _quadratic_ in the nuclear displacements. _Anharmonic_ contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The lattice dynamics approach is therefore not formally exact. However, the phonon picture is useful for describing a wide range of materials properties in practice, and often reaches excellent accuracy in comparison to experiment while providing precise microscopic insight into the underlying physical phenomena. +An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ description of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach, the starting point is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of harmonic form, i.e., quadratic in the nuclear displacements. Anharmonic contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The lattice dynamics approach is therefore not formally exact. However, the phonon picture is useful for describing a wide range of materials properties in practice, and often reaches excellent accuracy in comparison to experiment while providing precise microscopic insight into the underlying physical phenomena. -The chemical bonding in the lattice dynamics Hamiltonian is represented through _force constants_. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in Ref. [@Klein.1972]. +The chemical bonding in the lattice dynamics Hamiltonian is represented through force constants. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in Ref. [@Klein.1972]. -While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on _density functional theory_ (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. +While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. @@ -122,6 +122,6 @@ We note that parts of the TDEP method have been implemented in other code packag # Acknowledgements -F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. MJV, AC, and JPB acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. +F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). # References From 3491211abb98dd65e263adf184f9767b7c30acf0 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Tue, 24 Oct 2023 19:29:39 +0200 Subject: [PATCH 38/48] paper | update draft workflow --- .github/workflows/draft-pdf.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/draft-pdf.yml b/.github/workflows/draft-pdf.yml index f85b711e..eecf0d13 100644 --- a/.github/workflows/draft-pdf.yml +++ b/.github/workflows/draft-pdf.yml @@ -6,7 +6,7 @@ jobs: name: Paper Draft steps: - name: Checkout - uses: actions/checkout@v3 + uses: actions/checkout@v4 - name: Build draft PDF uses: openjournals/openjournals-draft-action@master with: From e29aeffb308edbea1b7c204803abf550a3d416bb Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Wed, 25 Oct 2023 14:48:21 +0200 Subject: [PATCH 39/48] paper | comments Sergei --- paper/paper.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index e089adc3..272d53ee 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -86,15 +86,15 @@ An alternative strategy is to construct approximate model Hamiltonians for the n The chemical bonding in the lattice dynamics Hamiltonian is represented through force constants. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in Ref. [@Klein.1972]. -While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. The idea was extended in the TDEP method to describe phonons in dynamically stabilized systems like Zirconium in the high-temperature bcc phase based on _ab initio_ MD simulations [@Hellman.2011; @Hellman.2013]. A self-consistent extension to TDEP was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself instead of using MD, and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. +While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. This idea was extended in the TDEP method to describe phonons in systems like Zirconium in the high-temperature body-centered cubic (bcc) phase, which is dynamically unstable at low temperatures [@Hellman.2011; @Hellman.2013]. While the initial TDEP method was based on _ab initio_ MD, a self-consistent extension was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Klarbring.2020vk; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. # Statement of need The TDEP open source code is the reference implementation for the TDEP method introduced above. It delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism both for constructing and solving effective lattice-dynamics Hamiltonians. This allows for materials simulations of simple elemental solids up to complex compounds with reduced symmetry under realistic conditions. -To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set, before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013oi5]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number and symmetry of elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. +To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set, before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number of independent elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create and parse. These are either plain text formats, established human-readable formats like csv, or self-documented HDF5 files for larger datasets. Thanks to the exploitation of the force constant symmetries, the respective output files are very compact, even for anharmonic force constants. @@ -122,6 +122,6 @@ We note that parts of the TDEP method have been implemented in other code packag # Acknowledgements -F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). +F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). S.I.S. acknowledges the support from Swedish Research Council (VR) (Project No. 2019-05551) and the ERC (synergy grant FASTCORR project 854843). # References From 0132549892ee8ad7d04fcc32d5488905eed41231 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Fri, 10 Nov 2023 12:59:49 +0100 Subject: [PATCH 40/48] paper | correct title? --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 272d53ee..53e002bb 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -1,5 +1,5 @@ --- -title: "TDEP: Temperature Dependent Effective Potenials" +title: "TDEP: Temperature Dependent Effective Potentials" tags: - Fortran - Physics From 481394f1611784ab9028134392431f5b8d8a629d Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 22 Jan 2024 11:20:20 +0100 Subject: [PATCH 41/48] paper | finalize literature * reformat names --- paper/literature.bib | 2 +- paper/literature_final.bib | 737 +++++++++++++++++++++++++++++++++++++ paper/paper.md | 6 +- 3 files changed, 741 insertions(+), 4 deletions(-) create mode 100644 paper/literature_final.bib diff --git a/paper/literature.bib b/paper/literature.bib index 6c4a5eff..710a0d92 100644 --- a/paper/literature.bib +++ b/paper/literature.bib @@ -120,7 +120,7 @@ @article{Monacelli.2021 year = {2021}, } -@article{Dangić.2021, +@article{Dangic.2021, abstract = {{The proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity κ. However, the κ of GeTe increases at the ferroelectric phase transition near 700 K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in κ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Strong anharmonicity near the phase transition induces non-Lorentzian shapes of the phonon power spectra. To account for these effects, we implement a method of calculating κ based on the Green-Kubo approach and find that the Boltzmann transport equation underestimates κ near the phase transition. Our findings elucidate the influence of structural phase transitions on κ and provide guidance for design of better thermoelectric materials.}}, author = {Dangić, Đorđe and Hellman, Olle and Fahy, Stephen and Savić, Ivana}, doi = {10.1038/s41524-021-00523-7}, diff --git a/paper/literature_final.bib b/paper/literature_final.bib new file mode 100644 index 00000000..3d58e117 --- /dev/null +++ b/paper/literature_final.bib @@ -0,0 +1,737 @@ +@misc{tdeptools, + author = {Knoop, F.}, + publisher = {GitHub}, + url = {https://github.com/flokno/tools.tdep}, + title = {{tdeptools: tools for TDEP}}, + year = {2023}, +} + +@article{Castellano.2023, + author = {Castellano, A. and Batista, J. and Verstraete, M. J.}, + doi = {10.48550/arxiv.2303.10621}, + eprint = {2303.10621}, + journal = {arXiv}, + title = {{Mode-coupling theory of lattice dynamics for classical and quantum crystals}}, + year = {2023}, +} + +@article{Reig.2022, + author = {Reig, D. 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M.}, + doi = {10.1103/physrevlett.112.058501}, + eprint = {1312.7490}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {5}, + pages = {058501}, + title = {{Phonon Quasiparticles and Anharmonic Free Energy in Complex Systems}}, + volume = {112}, + year = {2014}, +} + +@article{Tadano.2014, + author = {Tadano, T. and Gohda, Y. and Tsuneyuki, S.}, + doi = {10.1088/0953-8984/26/22/225402}, + issn = {0953-8984}, + journal = {Journal of Physics: Condensed Matter}, + number = {22}, + pages = {225402}, + title = {{Anharmonic force constants extracted from first-principles molecular dynamics: applications to heat transfer simulations}}, + volume = {26}, + year = {2014}, +} + +@article{Hellman.2013oi5, + author = {Hellman, O. and Abrikosov, I. A.}, + doi = {10.1103/physrevb.88.144301}, + eprint = {1308.5436}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {14}, + pages = {144301}, + title = {{Temperature-dependent effective third-order interatomic force constants from first principles}}, + volume = {88}, + year = {2013}, +} + +@article{Hellman.2013, + author = {Hellman, O. and Steneteg, P. and Abrikosov, I. A. and Simak, S. I.}, + doi = {10.1103/physrevb.87.104111}, + eprint = {1303.1145}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {10}, + pages = {104111}, + title = {{Temperature dependent effective potential method for accurate free energy calculations of solids}}, + volume = {87}, + year = {2013}, +} + +@article{Errea.2013, + author = {Errea, I. and Calandra, M. and Mauri, F.}, + doi = {10.1103/physrevlett.111.177002}, + eprint = {1305.7123}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {17}, + pages = {177002}, + title = {{First-Principles Theory of Anharmonicity and the Inverse Isotope Effect in Superconducting Palladium-Hydride Compounds}}, + volume = {111}, + year = {2013}, +} + +@thesis{Hellman.2012, + author = {Hellman, O.}, + title = {{Thermal properties of materials from first principles}}, + type = {phdthesis}, + year = {2012}, +} + +@article{Hellman.2011, + author = {Hellman, O. and Abrikosov, I. A. and Simak, S. I.}, + doi = {10.1103/physrevb.84.180301}, + eprint = {1103.5590}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {18}, + pages = {180301}, + title = {{Lattice dynamics of anharmonic solids from first principles}}, + volume = {84}, + year = {2011}, +} + +@article{Hooton.2010, + author = {Hooton, D.J.}, + doi = {10.1080/14786440408520576}, + issn = {1941-5982}, + journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, + number = {375}, + pages = {433--442}, + title = {{LII. A new treatment of anharmonicity in lattice thermodynamics: II}}, + volume = {46}, + year = {2010}, +} + +@article{Hooton.2010mfn, + author = {Hooton, D.J.}, + doi = {10.1080/14786440408520575}, + issn = {1941-5982}, + journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, + number = {375}, + pages = {422--432}, + title = {{LI. A new treatment of anharmonicity in lattice thermodynamics: I}}, + volume = {46}, + year = {2010}, +} + +@article{Esfarjani.2008, + author = {Esfarjani, K. and Stokes, H.T.}, + doi = {10.1103/physrevb.77.144112}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {14}, + pages = {144112}, + title = {{Method to extract anharmonic force constants from first principles calculations}}, + volume = {77}, + year = {2008}, +} + +@article{Souvatzis.2008, + author = {Souvatzis, P. and Eriksson, O. and Katsnelson, M.I. and Rudin, S.P.}, + doi = {10.1103/physrevlett.100.095901}, + eprint = {0803.1325}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {9}, + pages = {095901}, + title = {{Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory}}, + volume = {100}, + year = {2008}, +} + +@article{Broido.2007, + author = {Broido, D.A. and Malorny, M. and Birner, G. and Mingo, N. and Stewart, D.A.}, + doi = {10.1063/1.2822891}, + issn = {0003-6951}, + journal = {Applied Physics Letters}, + number = {23}, + pages = {231922}, + title = {{Intrinsic lattice thermal conductivity of semiconductors from first principles}}, + volume = {91}, + year = {2007}, +} + +@article{West.2006, + author = {West, D. and Estreicher, S.K.}, + doi = {10.1103/physrevlett.96.115504}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {11}, + pages = {115504}, + title = {{First-Principles Calculations of Vibrational Lifetimes and Decay Channels: Hydrogen-Related Modes in Si}}, + volume = {96}, + year = {2006}, +} + +@article{Dove.1986, + author = {Dove, M.T. and Lynden-bell, R.M.}, + doi = {10.1080/13642818608236861}, + issn = {1364-2812}, + journal = {Philosophical Magazine Part B}, + number = {6}, + pages = {443--463}, + title = {{A model of the paraelectric phase of thiourea}}, + volume = {54}, + year = {1986}, +} + +@article{Levy.1984, + author = {Levy, R.M. and Srinivasan, A.R. and Olson, W.K. and McCammon, J.A.}, + doi = {10.1002/bip.360230610}, + issn = {0006-3525}, + journal = {Biopolymers}, + number = {6}, + pages = {1099--1112}, + title = {{Quasi‐harmonic method for studying very low frequency modes in proteins}}, + volume = {23}, + year = {1984}, +} + +@book{Wallace.1972, + author = {Wallace, D.C.}, + location = {New York}, + publisher = {John Wiley \& Sons, Inc.}, + title = {{Thermodynamics of Crystals}}, + year = {1972}, +} + +@article{Klein.1972, + author = {Klein, M.L. and Horton, G.K.}, + doi = {10.1007/bf00654839}, + issn = {0022-2291}, + journal = {Journal of Low Temperature Physics}, + number = {3-4}, + pages = {151--166}, + title = {{The rise of self-consistent phonon theory}}, + volume = {9}, + year = {1972}, +} + +@article{Horner.1972, + author = {Horner, H.}, + doi = {10.1007/bf00653877}, + issn = {0022-2291}, + journal = {Journal of Low Temperature Physics}, + number = {5-6}, + pages = {511--529}, + title = {{Phonons and thermal properties of bcc and fcc helium from a self-consistent anharmonic theory}}, + volume = {8}, + year = {1972}, +} + +@article{Koehler.1971, + author = {Koehler, T.R. and Werthamer, N.R.}, + doi = {10.1103/physreva.3.2074}, + issn = {1050-2947}, + journal = {Physical Review A}, + number = {6}, + pages = {2074--2083}, + title = {{Phonon Spectral Functions and Ground-State Energy of Quantum Crystals in Perturbation Theory with a Variationally Optimum Correlated Basis Set}}, + volume = {3}, + year = {1971}, +} + +@article{Werthamer.1970kr, + author = {Werthamer, N.R.}, + doi = {10.1103/physrevb.1.572}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {2}, + pages = {572--581}, + title = {{Self-Consistent Phonon Formulation of Anharmonic Lattice Dynamics}}, + volume = {1}, + year = {1970}, +} + +@book{Choquard.1967, + author = {Choquard, P.F.}, + publisher = {W.A. Benjamin, Inc.}, + title = {{The Anharmonic Crystal}}, + year = {1967}, +} + +@article{Gillis.1967, + author = {Gillis, N.S. and Werthamer, N.R. and Koehler, T.R.}, + doi = {10.1103/physrev.165.951}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {3}, + pages = {951--959}, + title = {{Properties of Crystalline Argon and Neon in the Self-Consistent Phonon Approximation}}, + volume = {165}, + year = {1967}, +} + +@article{Koehler.1966, + author = {Koehler, T.R.}, + doi = {10.1103/physrevlett.17.89}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {2}, + pages = {89--91}, + title = {{Theory of the Self-Consistent Harmonic Approximation with Application to Solid Neon}}, + volume = {17}, + year = {1966}, +} + +@article{Kohn.1965, + author = {Kohn, W. and Sham, L.J.}, + doi = {10.1103/physrev.140.a1133}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {4A}, + pages = {A1133--A1138}, + title = {{Self-Consistent Equations Including Exchange and Correlation Effects}}, + volume = {140}, + year = {1965}, +} + +@article{Hohenberg.1964, + author = {Hohenberg, P. and Kohn, W.}, + doi = {10.1103/physrev.136.b864}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {3B}, + pages = {B864--B871}, + title = {{Inhomogeneous Electron Gas}}, + volume = {136}, + year = {1964}, +} + +@article{Cowley.1963, + author = {Cowley, R.A.}, + doi = {10.1080/00018736300101333}, + issn = {0001-8732}, + journal = {Advances in Physics}, + number = {48}, + pages = {421--480}, + title = {{The lattice dynamics of an anharmonic crystal}}, + volume = {12}, + year = {1963}, +} + +@article{Hooton.1958, + author = {Hooton, D.J.}, + doi = {10.1080/14786435808243224}, + issn = {0031-8086}, + journal = {Philosophical Magazine}, + number = {25}, + pages = {49--54}, + title = {{The use of a model in anharmonic lattice dynamics}}, + volume = {3}, + year = {1958}, +} + +@article{Hooton.1955, + author = {Hooton, D. J.}, + doi = {10.1007/bf01330055}, + issn = {0044-3328}, + journal = {Zeitschrift für Physik}, + number = {1}, + pages = {42--57}, + title = {Anharmonische Gitterschwingungen und die lineare Kette}, + volume = {142}, + year = {1955}, +} + +@book{Born.1954, + author = {Born, M. and Huang, K.}, + location = {Oxford}, + publisher = {Clarendon Press}, + title = {Dynamical theory of crystal lattices}, + year = {1954}, +} + +@article{Born.1951, + author = {Born, M. and Brix, P. and Kopfermann, H. and Heisenberg, W. and Staudinger, H. and Stille, H. and Weizsäcker, C. F. v. and Euler, H. v. and Hedvall, J. A. and Siegel, C. L. and Rellich, F. and Nevanlinna, R.}, + doi = {10.1007/978-3-642-86703-3}, + title = {Festschrift zur Feier des Zweihundertjährigen Bestehens der Akademie der Wissenschaften in Göttingen, I. Mathematisch-Physikalische Klasse}, + year = {1951}, +} + +@article{Boer.1948, + author = {De Boer, J.}, + doi = {10.1016/0031-8914(48)90032-9}, + issn = {0031-8914}, + journal = {Physica}, + number = {2-3}, + pages = {139--148}, + title = {Quantum theory of condensed permanent gases I: the law of corresponding states}, + volume = {14}, + year = {1948}, +} + +@article{Born.1912, + author = {Born, M. and Karman, T. v.}, + journal = {Physikalische Zeitschrift}, + pages = {297--309}, + title = {Über Schwingungen in Raumgittern}, + volume = {13}, + year = {1912}, +} + diff --git a/paper/paper.md b/paper/paper.md index 53e002bb..a69674d4 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -69,7 +69,7 @@ affiliations: - name: Department of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden index: 9 date: 2023 -bibliography: literature.bib +bibliography: literature_final.bib --- # Summary @@ -88,7 +88,7 @@ The chemical bonding in the lattice dynamics Hamiltonian is represented through While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. This idea was extended in the TDEP method to describe phonons in systems like Zirconium in the high-temperature body-centered cubic (bcc) phase, which is dynamically unstable at low temperatures [@Hellman.2011; @Hellman.2013]. While the initial TDEP method was based on _ab initio_ MD, a self-consistent extension was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Klarbring.2020vk; @Dangić.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Klarbring.2020vk; @Dangic.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. # Statement of need @@ -114,7 +114,7 @@ Here we list the most important codes that are shipped with the TDEP code, expla - `thermal_conductivity`: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of third-order anharmonicity [@Broido.2007; @Romero.2015]. -- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone [@Romero.2015; @Shulumba.2017]. The grid mode computes _spectral_ thermal transport properties [@Dangić.2021]. +- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone [@Romero.2015; @Shulumba.2017]. The grid mode computes _spectral_ thermal transport properties [@Dangic.2021]. A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. From 3ea3ee12757514013222b1835eeff467630ad460 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 22 Jan 2024 11:36:05 +0100 Subject: [PATCH 42/48] paper | fix bib --- paper/literature_final.bib | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/paper/literature_final.bib b/paper/literature_final.bib index 3d58e117..fa5d3732 100644 --- a/paper/literature_final.bib +++ b/paper/literature_final.bib @@ -694,7 +694,7 @@ @article{Hooton.1955 journal = {Zeitschrift für Physik}, number = {1}, pages = {42--57}, - title = {Anharmonische Gitterschwingungen und die lineare Kette}, + title = {{Anharmonische Gitterschwingungen und die lineare Kette}}, volume = {142}, year = {1955}, } @@ -703,34 +703,35 @@ @book{Born.1954 author = {Born, M. and Huang, K.}, location = {Oxford}, publisher = {Clarendon Press}, - title = {Dynamical theory of crystal lattices}, + title = {{Dynamical theory of crystal lattices}}, year = {1954}, + doi = {10.1093/oso/9780192670083.001.0001}, } @article{Born.1951, author = {Born, M. and Brix, P. and Kopfermann, H. and Heisenberg, W. and Staudinger, H. and Stille, H. and Weizsäcker, C. F. v. and Euler, H. v. and Hedvall, J. A. and Siegel, C. L. and Rellich, F. and Nevanlinna, R.}, doi = {10.1007/978-3-642-86703-3}, - title = {Festschrift zur Feier des Zweihundertjährigen Bestehens der Akademie der Wissenschaften in Göttingen, I. Mathematisch-Physikalische Klasse}, + title = {{Festschrift zur Feier des Zweihundertjährigen Bestehens der Akademie der Wissenschaften in Göttingen, I. Mathematisch-Physikalische Klasse}}, year = {1951}, } @article{Boer.1948, - author = {De Boer, J.}, + author = {de Boer, J.}, doi = {10.1016/0031-8914(48)90032-9}, issn = {0031-8914}, journal = {Physica}, number = {2-3}, pages = {139--148}, - title = {Quantum theory of condensed permanent gases I: the law of corresponding states}, + title = {{Quantum theory of condensed permanent gases I: the law of corresponding states}}, volume = {14}, year = {1948}, } @article{Born.1912, - author = {Born, M. and Karman, T. v.}, + author = {Born, M. and von Karman, T.}, journal = {Physikalische Zeitschrift}, pages = {297--309}, - title = {Über Schwingungen in Raumgittern}, + title = {{Über Schwingungen in Raumgittern}}, volume = {13}, year = {1912}, } From dcdd2f5592b86d49dcffbbea389d75c3fce7b10e Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 22 Jan 2024 11:43:05 +0100 Subject: [PATCH 43/48] paper | update bib --- paper/Makefile | 4 ++++ paper/literature_final.bib | 21 +++++++++++++-------- paper/paper.md | 2 +- 3 files changed, 18 insertions(+), 9 deletions(-) diff --git a/paper/Makefile b/paper/Makefile index d21ac3fe..735dae45 100644 --- a/paper/Makefile +++ b/paper/Makefile @@ -1,5 +1,9 @@ CMDbib = biber --tool --output_align --output_indent=2 --output_fieldcase=lower --output-legacy-dates --output-field-replace=journaltitle:journal +final: + ${CMDbib} literature_final.bib + mv literature_final_bibertool.bib literature_final.bib + bib: ${CMDbib} paper_tdep_joss.bib mv paper_tdep_joss_bibertool.bib literature.bib diff --git a/paper/literature_final.bib b/paper/literature_final.bib index fa5d3732..b1ea6db2 100644 --- a/paper/literature_final.bib +++ b/paper/literature_final.bib @@ -7,12 +7,17 @@ @misc{tdeptools } @article{Castellano.2023, - author = {Castellano, A. and Batista, J. and Verstraete, M. J.}, - doi = {10.48550/arxiv.2303.10621}, - eprint = {2303.10621}, - journal = {arXiv}, - title = {{Mode-coupling theory of lattice dynamics for classical and quantum crystals}}, - year = {2023}, + author = {Castellano, Aloïs and Batista, J. P. Alvarinhas and Verstraete, Matthieu J.}, + title = "{Mode-coupling theory of lattice dynamics for classical and quantum crystals}", + journal = {The Journal of Chemical Physics}, + volume = {159}, + number = {23}, + pages = {234501}, + year = {2023}, + month = {12}, + issn = {0021-9606}, + doi = {10.1063/5.0174255}, + url = {https://doi.org/10.1063/5.0174255}, } @article{Reig.2022, @@ -716,7 +721,7 @@ @article{Born.1951 } @article{Boer.1948, - author = {de Boer, J.}, + author = {{de Boer}, J.}, doi = {10.1016/0031-8914(48)90032-9}, issn = {0031-8914}, journal = {Physica}, @@ -728,7 +733,7 @@ @article{Boer.1948 } @article{Born.1912, - author = {Born, M. and von Karman, T.}, + author = {Born, M. and {von Karman}, T.}, journal = {Physikalische Zeitschrift}, pages = {297--309}, title = {{Über Schwingungen in Raumgittern}}, diff --git a/paper/paper.md b/paper/paper.md index a69674d4..7e10975e 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -88,7 +88,7 @@ The chemical bonding in the lattice dynamics Hamiltonian is represented through While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. This idea was extended in the TDEP method to describe phonons in systems like Zirconium in the high-temperature body-centered cubic (bcc) phase, which is dynamically unstable at low temperatures [@Hellman.2011; @Hellman.2013]. While the initial TDEP method was based on _ab initio_ MD, a self-consistent extension was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Klarbring.2020vk; @Dangic.2021], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Klarbring.2020vk; @Dangic.2021; @Reig.2022], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. # Statement of need From 9f3e66476745b968520f86797ce288d2760d993f Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 22 Jan 2024 11:56:50 +0100 Subject: [PATCH 44/48] paper | editorial comments --- paper/literature_final.bib | 2 +- paper/paper.md | 22 +++++++++++----------- 2 files changed, 12 insertions(+), 12 deletions(-) diff --git a/paper/literature_final.bib b/paper/literature_final.bib index b1ea6db2..226017b5 100644 --- a/paper/literature_final.bib +++ b/paper/literature_final.bib @@ -534,7 +534,7 @@ @article{West.2006 } @article{Dove.1986, - author = {Dove, M.T. and Lynden-bell, R.M.}, + author = {Dove, M.T. and Lynden-Bell, R.M.}, doi = {10.1080/13642818608236861}, issn = {1364-2812}, journal = {Philosophical Magazine Part B}, diff --git a/paper/paper.md b/paper/paper.md index 7e10975e..e7d532e4 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -78,37 +78,37 @@ The Temperature Dependent Effective Potential (TDEP) method is a versatile and e # Introduction -The properties of materials change both qualitatively and quantitatively with temperature, i.e., the macroscopic manifestation of the microscopic vibrational motion of electrons and nuclei. In thermal equilibrium, temperature influences the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, for instance when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of both applied and fundamental materials science. +The properties of materials change both qualitatively and quantitatively with temperature, i.e., the macroscopic manifestation of the microscopic vibrational motion of electrons and nuclei. In thermal equilibrium, temperature influences the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, for instance, when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of both applied and fundamental materials science. In _ab initio_ materials modeling, the contribution of electronic temperature is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing molecular dynamics (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables either in equilibrium, through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the relaxation dynamics. -An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ description of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest order model. In this approach, the starting point is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of harmonic form, i.e., quadratic in the nuclear displacements. Anharmonic contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The lattice dynamics approach is therefore not formally exact. However, the phonon picture is useful for describing a wide range of materials properties in practice, and often reaches excellent accuracy in comparison to experiment while providing precise microscopic insight into the underlying physical phenomena. +An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ description of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest-order model. In this approach, the starting point is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of harmonic form, i.e., quadratic in the nuclear displacements. Anharmonic contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The lattice-dynamics approach is therefore not formally exact. However, the phonon picture is useful for describing a wide range of materials properties in practice, and often reaches excellent accuracy in comparison to experiment while providing precise microscopic insight into the underlying physical phenomena. -The chemical bonding in the lattice dynamics Hamiltonian is represented through force constants. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in Ref. [@Klein.1972]. +The chemical bonding in the lattice dynamics Hamiltonian is represented through force constants. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged-atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem, in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in [@Klein.1972]. -While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_ self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. This idea was extended in the TDEP method to describe phonons in systems like Zirconium in the high-temperature body-centered cubic (bcc) phase, which is dynamically unstable at low temperatures [@Hellman.2011; @Hellman.2013]. While the initial TDEP method was based on _ab initio_ MD, a self-consistent extension was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. +While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_-self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. This idea was extended in the TDEP method to describe phonons in systems like Zirconium in the high-temperature body-centered cubic (bcc) phase, which is dynamically unstable at low temperatures [@Hellman.2011; @Hellman.2013]. While the initial TDEP method was based on _ab initio_ MD, a self-consistent extension was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. -Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Klarbring.2020vk; @Dangic.2021; @Reig.2022], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in Ref. [@Castellano.2023]. Explicitly incorporating dielectric response properties for light scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. +Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Klarbring.2020vk; @Dangic.2021; @Reig.2022], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in [@Castellano.2023]. Explicitly incorporating dielectric response properties for light-scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. # Statement of need -The TDEP open source code is the reference implementation for the TDEP method introduced above. It delivers a clean and fast Fortran implementation with message passing interface (MPI) parallelism both for constructing and solving effective lattice-dynamics Hamiltonians. This allows for materials simulations of simple elemental solids up to complex compounds with reduced symmetry under realistic conditions. +The TDEP open-source code is the reference implementation for the TDEP method introduced above. It delivers a clean and fast Fortran implementation with Message Passing Interface (MPI) parallelism both for constructing and solving effective lattice-dynamics Hamiltonians. This allows for materials simulations of simple elemental solids up to complex compounds with reduced symmetry under realistic conditions. -To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set, before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number of independent elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. +To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number of independent elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. -Another distinctive feature of TDEP is the use of plain input and output files which are code agnostic and easy to create and parse. These are either plain text formats, established human-readable formats like csv, or self-documented HDF5 files for larger datasets. Thanks to the exploitation of the force constant symmetries, the respective output files are very compact, even for anharmonic force constants. +Another distinctive feature of TDEP is the use of plain input and output files which are code-agnostic and easy to create and parse. These are either plain-text formats, established human-readable formats like CSV, or self-documented HDF5 files for larger datasets. Thanks to the exploitation of the force constant symmetries, the respective output files are very compact, even for anharmonic force constants. Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good simulation (super)cells, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. ## Features -Here we list the most important codes that are shipped with the TDEP code, explain their purpose, and list the respective references in the literature. A more detailed explanation of all features can be found in the online documentation. +Here we list the most important codes that are shipped with the TDEP package, explain their purpose, and list the respective references in the literature. A more detailed explanation of all features can be found in the online documentation. - `generate_structure`: Generate supercells of target size, with options to make them as cubic as possible to maximize the real-space cutoff for the force constants [@Hellman.2011]. - `canonical_configuration`: Create supercells with thermal displacements from an initial guess or existing force constants, using Monte Carlo sampling from a classical or quantum canonical distribution [@West.2006; @Shulumba.2017]. Self-consistent sampling with sTDEP is explained in detail in [@Benshalom.2022]. -- `extract_forceconstants`: Obtain (effective) harmonic force constants from a set of supercell snapshots with displaced positions and forces [@Hellman.2013]. Optionally fit higher-order force constants [@Hellman.2013oi5], or dielectric tensor properties [@Benshalom.2022]. +- `extract_forceconstants`: Obtain (effective) harmonic force constants from a set of supercell snapshots with displaced positions and forces [@Hellman.2013]. Optionally, fit higher-order force constants [@Hellman.2013oi5], or dielectric tensor properties [@Benshalom.2022]. - `phonon_dispersion_relations`: Calculate phonon dispersion relations and related harmonic thermodynamic properties from the second-order force constants [@Hellman.2013], including Grüneisen parameters from third-order force constants [@Hellman.2013oi5]. @@ -116,7 +116,7 @@ Here we list the most important codes that are shipped with the TDEP code, expla - `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone [@Romero.2015; @Shulumba.2017]. The grid mode computes _spectral_ thermal transport properties [@Dangic.2021]. -A separate python library for interfacing with different DFT and force field codes through the atomic simulation environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. +A separate python library for interfacing with different DFT and force field codes through the Atomic Simulation Environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. We note that parts of the TDEP method have been implemented in other code packages as well [@Bottin.2020rn5]. From e9a1afb916ae009f2542ba1e0f9fb767fa84ee57 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 22 Jan 2024 17:58:18 +0100 Subject: [PATCH 45/48] paper | typo --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index e7d532e4..a08168ad 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -84,7 +84,7 @@ In _ab initio_ materials modeling, the contribution of electronic temperature is An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ description of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest-order model. In this approach, the starting point is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of harmonic form, i.e., quadratic in the nuclear displacements. Anharmonic contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The lattice-dynamics approach is therefore not formally exact. However, the phonon picture is useful for describing a wide range of materials properties in practice, and often reaches excellent accuracy in comparison to experiment while providing precise microscopic insight into the underlying physical phenomena. -The chemical bonding in the lattice dynamics Hamiltonian is represented through force constants. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically arranged-atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem, in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in [@Klein.1972]. +The chemical bonding in the lattice dynamics Hamiltonian is represented through force constants. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically-arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem, in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in [@Klein.1972]. While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_-self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. This idea was extended in the TDEP method to describe phonons in systems like Zirconium in the high-temperature body-centered cubic (bcc) phase, which is dynamically unstable at low temperatures [@Hellman.2011; @Hellman.2013]. While the initial TDEP method was based on _ab initio_ MD, a self-consistent extension was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. From d9706317af24995df2964b14bac7dd53382171a9 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Mon, 22 Jan 2024 19:07:14 +0100 Subject: [PATCH 46/48] paper | post review 1, acknowledgement --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index a08168ad..917bdc40 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -122,6 +122,6 @@ We note that parts of the TDEP method have been implemented in other code packag # Acknowledgements -F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). S.I.S. acknowledges the support from Swedish Research Council (VR) (Project No. 2019-05551) and the ERC (synergy grant FASTCORR project 854843). +F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). S.I.S. acknowledges the support from Swedish Research Council (VR) (Project No. 2019-05551) and the ERC (synergy grant FASTCORR project 854843). F.K. acknowledges Christian Carbogno for introducing him to Olle. # References From 42439c53196362e2c67b76030c3a758eb2a58310 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Thu, 25 Jan 2024 15:06:52 +0100 Subject: [PATCH 47/48] paper | final comment David --- paper/paper.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 917bdc40..5f6a5dcc 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -86,7 +86,7 @@ An alternative strategy is to construct approximate model Hamiltonians for the n The chemical bonding in the lattice dynamics Hamiltonian is represented through force constants. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically-arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem, in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in [@Klein.1972]. -While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_-self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. This idea was extended in the TDEP method to describe phonons in systems like Zirconium in the high-temperature body-centered cubic (bcc) phase, which is dynamically unstable at low temperatures [@Hellman.2011; @Hellman.2013]. While the initial TDEP method was based on _ab initio_ MD, a self-consistent extension was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself and the force constants are optimized iteratively until self-consistency [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. +While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_-self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. This idea was extended in the TDEP method to describe phonons in systems like Zirconium in the high-temperature body-centered cubic (bcc) phase, which is dynamically unstable at low temperatures [@Hellman.2011; @Hellman.2013]. While the initial TDEP method was based on _ab initio_ MD, a self-consistent extension was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself and the force constants are optimized iteratively until self-consistency is achieved [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Klarbring.2020vk; @Dangic.2021; @Reig.2022], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in [@Castellano.2023]. Explicitly incorporating dielectric response properties for light-scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. @@ -122,6 +122,6 @@ We note that parts of the TDEP method have been implemented in other code packag # Acknowledgements -F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). S.I.S. acknowledges the support from Swedish Research Council (VR) (Project No. 2019-05551) and the ERC (synergy grant FASTCORR project 854843). F.K. acknowledges Christian Carbogno for introducing him to Olle. +F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). S.I.S. acknowledges the support from Swedish Research Council (VR) (Project No. 2019-05551) and the ERC (synergy grant FASTCORR project 854843). F.K. thanks Christian Carbogno for introducing him to Olle. # References From 5c7c95de66dc75ca55c6ea201295f2ba77c0d434 Mon Sep 17 00:00:00 2001 From: Florian Knoop Date: Fri, 26 Jan 2024 10:05:45 +0100 Subject: [PATCH 48/48] paper | final comment Sergei --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 5f6a5dcc..3cf62c18 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -122,6 +122,6 @@ We note that parts of the TDEP method have been implemented in other code packag # Acknowledgements -F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). S.I.S. acknowledges the support from Swedish Research Council (VR) (Project No. 2019-05551) and the ERC (synergy grant FASTCORR project 854843). F.K. thanks Christian Carbogno for introducing him to Olle. +F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). S.I.S. acknowledges the support from Swedish Research Council (VR) (Project No. 2023-05247) and the ERC (synergy grant FASTCORR project 854843). F.K. thanks Christian Carbogno for introducing him to Olle. # References