deepmodeling · dyzheng · Oct 9, 2023 · Aug 27, 2023 · Sep 12, 2023 · Sep 16, 2023
diff --git a/docs/advanced/elec_properties/potential.md b/docs/advanced/elec_properties/potential.md
@@ -24,7 +24,7 @@ smearing_method gaussian
 smearing_sigma 0.01
 
 #Parameters (5.Mixing)
-mixing_type pulay
+mixing_type broyden
 mixing_beta 0.4
 out_pot 2
 ```

diff --git a/docs/advanced/input_files/input-main.md b/docs/advanced/input_files/input-main.md
@@ -907,9 +907,9 @@ calculations.
 - **Availability**: `smearing_method` is not `fixed`.
 - **Description**: Charge mixing methods.
   - **plain**: Just simple mixing.
-  - **pulay**: Standard Pulay method.
-  - **broyden**: Broyden method.
-- **Default**: pulay
+  - **pulay**: Standard Pulay method. [P. Pulay Chemical Physics Letters, (1980)](https://www.sciencedirect.com/science/article/abs/pii/0009261480803964)
+  - **broyden**: Simplified modified Broyden method. [D.D. Johnson Physical Review B (1988)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.38.12807)
+- **Default**: broyden
 
 ### mixing_beta
 
@@ -929,7 +929,7 @@ calculations.
 ### mixing_ndim
 
 - **Type**: Integer
-- **Description**: It indicates the mixing dimensions in Pulay, Pulay method uses the density from previous mixing_ndim steps and do a charge mixing based on this density.
+- **Description**: It indicates the mixing dimensions in Pulay or Broyden. Pulay and Broyden method use the density from previous mixing_ndim steps and do a charge mixing based on this density.
 - **Default**: 8
 
 ### mixing_gg0

diff --git a/docs/advanced/interface/dpgen.md b/docs/advanced/interface/dpgen.md
@@ -168,7 +168,7 @@ Next, for the "dpgen run" step, the following `run_param.json` should be provide
     "user_fp_params":{  # All the ABACUS input paramters are defined here
     "ntype": 1,         # defining input parameters from INPUT files is not supported yet.
     "ecutwfc": 80,      
-    "mixing_type": "pulay",
+    "mixing_type": "broyden",
     "mixing_beta": 0.8,
     "symmetry": 1,
     "nspin": 1,

diff --git a/docs/advanced/interface/pyatb.md b/docs/advanced/interface/pyatb.md
@@ -42,7 +42,7 @@ ks_solver             genelpa
 nspin                 4
 smearing_method       gauss
 smearing_sigma        0.02
-mixing_type           pulay
+mixing_type           broyden
 mixing_beta           0.7
 scf_nmax              200
 scf_thr               1e-8

diff --git a/docs/advanced/scf/converge.md b/docs/advanced/scf/converge.md
@@ -8,7 +8,7 @@ By mixing the electron density with that obtained from previous steps, numerical
 
 For each of the mixing types, we also provide variables for controlling relevant parameters, including `mixing_beta`, `mixing_ndim`, and `mixing_gg0`.
 
-The default choice is `pulay`, which should work fine in most cases. If convergence issue arises in metallic systems, inclusion of Kerker preconditioning may be helpful, which can be achieved by setting [mixing_gg0](../input_files/input-main.md#mixing_gg0) to be a positive number. For the default pulay method, a choice of 1.5 might be a good start.
+The default choice is `broyden`, which should work fine in most cases. If convergence issue arises in metallic systems, inclusion of Kerker preconditioning may be helpful, which can be achieved by setting [mixing_gg0](../input_files/input-main.md#mixing_gg0) to be a positive number. For the default broyden method, a choice of 1.5 might be a good start.
 
 A large `mixing_beta` means a larger change in electron density for each SCF step. For well-behaved systems, a larger `mixing_beta` leads to faster convergence. However, for some difficult cases, a smaller `mixing_beta` is preferred to avoid numerical instabilities.
 

diff --git a/examples/charge_density/pw_nspin2_Fe/INPUT b/examples/charge_density/pw_nspin2_Fe/INPUT
@@ -15,6 +15,6 @@ ks_solver     cg
 smearing_method    gaussian
 smearing_sigma       0.07
 
-mixing_type    pulay 
+mixing_type    broyden 
 mixing_beta    0.5
 
diff --git a/examples/charge_mixing/pw_Al/INPUT_1 b/examples/charge_mixing/pw_Al/INPUT_1
@@ -20,5 +20,5 @@ smearing_method		gauss
 smearing_sigma			0.002
 
 #Parameters (5.Mixing)
-mixing_type		pulay
+mixing_type		broyden
 mixing_beta		0.7
diff --git a/examples/charge_mixing/pw_Al/INPUT_3 b/examples/charge_mixing/pw_Al/INPUT_3
@@ -20,5 +20,5 @@ smearing_method		gauss
 smearing_sigma			0.002
 
 #Parameters (5.Mixing)
-mixing_type		pulay
+mixing_type		broyden
 mixing_beta		0.2
diff --git a/examples/charge_mixing/pw_Al/README b/examples/charge_mixing/pw_Al/README
@@ -1,5 +1,5 @@
 Showcasing different charge mixing methods
-- INPUT_1 : pulay mixing with beta=0.7, takes 5 steps to converge
+- INPUT_1 : broyden mixing with beta=0.7, takes 5 steps to converge
 - INPUT_2 : plain mixing with beta=0.7, takes 8 steps to converge
-- INPUT_3 : pulay mixing with beta=0.2, takes 6 steps to converge
+- INPUT_3 : broyden mixing with beta=0.2, takes 6 steps to converge
 - INPUT_4 : plain mixing with beta=0.2, takes 37 steps to converge
diff --git a/examples/compensating_charge/Pt-slab/INPUT b/examples/compensating_charge/Pt-slab/INPUT
@@ -11,7 +11,7 @@ basis_type	  pw
 gamma_only        1
 smearing_method	  gauss
 smearing_sigma	  0.02
-mixing_type       pulay
+mixing_type       broyden
 mixing_beta       0.1
 
 #Parameters (compensating charge)

diff --git a/examples/deepks/lcao_CsPbI3/INPUT b/examples/deepks/lcao_CsPbI3/INPUT
@@ -20,7 +20,7 @@ smearing_method                gaussian
 smearing_sigma                   0.0015
 
 #Parameters (5.Mixing)
-mixing_type             pulay
+mixing_type             broyden
 mixing_beta             0.4
 
 #Parameters (6.Deepks)

diff --git a/examples/deepks/lcao_H2O/INPUT b/examples/deepks/lcao_H2O/INPUT
@@ -21,7 +21,7 @@ smearing_method                gaussian
 smearing_sigma                   0.02
 
 #Parameters (5.Mixing)
-mixing_type             pulay
+mixing_type             broyden
 mixing_beta             0.4
 
 #Parameters (6.Deepks)

diff --git a/examples/deepks/pw_H2O/INPUT b/examples/deepks/pw_H2O/INPUT
@@ -21,7 +21,7 @@ smearing_method                gaussian
 smearing_sigma                   0.1
 
 #Parameters (5.Mixing)
-mixing_type             pulay
+mixing_type             broyden
 mixing_beta             0.4
 
 #Parameters (6. Bessel function)

diff --git a/examples/dft_plus_u/NiO/INPUT b/examples/dft_plus_u/NiO/INPUT
@@ -21,7 +21,7 @@ smearing_method    gaussian
 smearing_sigma    0.05
 
 
-mixing_type    pulay
+mixing_type    broyden
 mixing_beta    0.4
 #mixing_gg0    1.5
 

diff --git a/examples/dipole_correction/Pt-slab/INPUT1 b/examples/dipole_correction/Pt-slab/INPUT1
@@ -12,7 +12,7 @@ basis_type	  pw
 gamma_only        1
 smearing_method	  gauss
 smearing_sigma	  0.02
-mixing_type       pulay
+mixing_type       broyden
 mixing_beta       0.1
 
 #Parameters (dipole correction)

diff --git a/examples/dipole_correction/Pt-slab/INPUT2 b/examples/dipole_correction/Pt-slab/INPUT2
@@ -12,7 +12,7 @@ basis_type	  pw
 gamma_only        1
 smearing_method	  gauss
 smearing_sigma	  0.02
-mixing_type       pulay
+mixing_type       broyden
 mixing_beta       0.1
 
 #Parameters (electric field and dipole correction)

diff --git a/examples/electric_field/Pt-slab/INPUT b/examples/electric_field/Pt-slab/INPUT
@@ -11,7 +11,7 @@ basis_type	  pw
 gamma_only        1
 smearing_method	  gauss
 smearing_sigma	  0.02
-mixing_type       pulay
+mixing_type       broyden
 mixing_beta       0.1
 
 #Parameters (electric field)

diff --git a/examples/electrostatic_potential/lcao_Si/INPUT b/examples/electrostatic_potential/lcao_Si/INPUT
@@ -10,7 +10,7 @@ basis_type		lcao
 
 smearing_method gaussian
 smearing_sigma 0.01
-mixing_type pulay
+mixing_type broyden
 mixing_beta 0.4
 
 out_pot 		2
diff --git a/examples/fixed_occupations/INPUT b/examples/fixed_occupations/INPUT
@@ -5,7 +5,7 @@ scf_nmax                      400
 scf_thr                       1e-08
 basis_type                    lcao
 ks_solver                     genelpa
-mixing_type                   pulay
+mixing_type                   broyden
 mixing_beta                   0.4
 mixing_gg0                    1.5
 pseudo_dir                    ../../tests/PP_ORB

diff --git a/examples/gpu/si16_pw/INPUT b/examples/gpu/si16_pw/INPUT
@@ -20,5 +20,5 @@ smearing_method		gauss
 smearing_sigma		0.002
 
 #Parameters (5.Mixing)
-mixing_type		pulay
+mixing_type		broyden
 mixing_beta		0.3
diff --git a/examples/hefei-namd/INPUT b/examples/hefei-namd/INPUT
@@ -19,7 +19,7 @@ INPUT_PARAMETERS
  force_thr_ev    1.0e-3
 
  ks_solver       genelpa
- mixing_type     pulay
+ mixing_type     broyden
  mixing_beta     0.7
 
  md_type          nve

diff --git a/examples/hse/lcao_Si2/INPUT b/examples/hse/lcao_Si2/INPUT
@@ -12,7 +12,7 @@ scf_nmax                100
 gamma_only              0
 symmetry                -1
 smearing_method         gauss
-mixing_type             pulay
+mixing_type             broyden
 mixing_beta             0.4
 
 dft_functional          hse
diff --git a/examples/implicit_solvation_model/Pt-slab/INPUT b/examples/implicit_solvation_model/Pt-slab/INPUT
@@ -11,7 +11,7 @@ basis_type	  pw
 gamma_only        1
 smearing_method	  gauss
 smearing_sigma	  0.02
-mixing_type       pulay
+mixing_type       broyden
 mixing_beta       0.1
 
 #Parameters (Solvation Model)

diff --git a/examples/interface_ShengBTE/LCAO/2nd/INPUT b/examples/interface_ShengBTE/LCAO/2nd/INPUT
@@ -20,7 +20,7 @@ ks_solver       genelpa
 gamma_only      0
 smearing_method gauss
 smearing_sigma  0.01
-mixing_type     pulay
+mixing_type     broyden
 mixing_beta     0.7
 
 stru_file       STRU-001
diff --git a/examples/interface_ShengBTE/LCAO/3rd/run_stru.sh b/examples/interface_ShengBTE/LCAO/3rd/run_stru.sh
@@ -29,7 +29,7 @@ ks_solver       genelpa
 gamma_only      0
 smearing_method gauss
 smearing_sigma  0.01
-mixing_type     pulay
+mixing_type     broyden
 mixing_beta     0.7
 
 stru_file       STRU_$stru

diff --git a/examples/interface_ShengBTE/PW/2nd/INPUT b/examples/interface_ShengBTE/PW/2nd/INPUT
@@ -19,7 +19,7 @@ basis_type      pw
 ks_solver       cg
 smearing_method gauss
 smearing_sigma  0.01
-mixing_type     pulay
+mixing_type     broyden
 mixing_beta     0.7
 
 stru_file       STRU-001
diff --git a/examples/interface_ShengBTE/PW/3rd/run_stru.sh b/examples/interface_ShengBTE/PW/3rd/run_stru.sh
@@ -28,7 +28,7 @@ basis_type      pw
 ks_solver       cg
 smearing_method gauss
 smearing_sigma  0.01
-mixing_type     pulay
+mixing_type     broyden
 mixing_beta     0.7
 
 stru_file       STRU_$stru

diff --git a/examples/interface_dpgen/autotest/INPUT b/examples/interface_dpgen/autotest/INPUT
@@ -8,7 +8,7 @@ basis_type          lcao
 ks_solver           genelpa
 smearing_method     gaussian
 smearing_sigma      0.01
-mixing_type         pulay
+mixing_type         broyden
 mixing_beta         0.7
 scf_nmax            100
 scf_thr             1e-08

diff --git a/examples/interface_dpgen/autotest/INPUT.rlx b/examples/interface_dpgen/autotest/INPUT.rlx
@@ -13,7 +13,7 @@ basis_type          lcao
 ks_solver           genelpa
 smearing_method     gaussian
 smearing_sigma      0.01
-mixing_type         pulay
+mixing_type         broyden
 mixing_beta         0.7
 scf_nmax            100
 scf_thr             1e-08

diff --git a/examples/interface_dpgen/init_and_run/run_param.json b/examples/interface_dpgen/init_and_run/run_param.json
@@ -128,7 +128,7 @@
     "user_fp_params":{
     "ntype": 1,
     "ecutwfc": 40,
-        "mixing_type": "pulay",
+        "mixing_type": "broyden",
     "mixing_beta": 0.8,
     "symmetry": 1,
     "nspin": 1,

diff --git a/examples/interface_phonopy/INPUT b/examples/interface_phonopy/INPUT
@@ -18,7 +18,7 @@ smearing_method         gauss
 smearing_sigma          0.01
 
 #Parameters (5.Mixing)
-mixing_type             pulay
+mixing_type             broyden
 mixing_beta             0.7
 
 pseudo_mesh     	1

diff --git a/examples/matrix_hs/out_hs2_multik/INPUT b/examples/matrix_hs/out_hs2_multik/INPUT
@@ -21,7 +21,7 @@ smearing_method		gauss
 smearing_sigma			0.002
 
 #Parameters (5.Mixing)
-mixing_type		pulay
+mixing_type		broyden
 mixing_beta		0.7
 
 out_mat_hs2  1

diff --git a/examples/matrix_hs/out_hs_gammaonly/INPUT b/examples/matrix_hs/out_hs_gammaonly/INPUT
@@ -24,7 +24,7 @@ smearing_sigma			0.002
 out_mat_hs                  1
 
 #Parameters (5.Mixing)
-mixing_type		pulay
+mixing_type		broyden
 mixing_beta		0.7
 mixing_gg0      1.5
 

diff --git a/examples/matrix_hs/out_hs_multik/INPUT b/examples/matrix_hs/out_hs_multik/INPUT
@@ -21,7 +21,7 @@ smearing_method		gauss
 smearing_sigma			0.002
 
 #Parameters (5.Mixing)
-mixing_type		pulay
+mixing_type		broyden
 mixing_beta		0.7
 
 out_mat_hs  1

diff --git a/examples/matrix_hs/out_s_multik/INPUT b/examples/matrix_hs/out_s_multik/INPUT
@@ -21,7 +21,7 @@ smearing_method		gauss
 smearing_sigma			0.002
 
 #Parameters (5.Mixing)
-mixing_type		pulay
+mixing_type		broyden
 mixing_beta		0.7
 
 out_mat_hs  1

diff --git a/examples/md/lcao_gammaonly_Si8/INPUT_0 b/examples/md/lcao_gammaonly_Si8/INPUT_0
@@ -22,7 +22,7 @@ smearing_method        gaussian
 smearing_sigma         0.001
 
 #Parameters (5.Mixing)
-mixing_type            pulay
+mixing_type            broyden
 mixing_beta            0.3
 chg_extrap             second-order
 

diff --git a/examples/md/lcao_gammaonly_Si8/INPUT_1 b/examples/md/lcao_gammaonly_Si8/INPUT_1
@@ -22,7 +22,7 @@ smearing_method        gaussian
 smearing_sigma         0.001
 
 #Parameters (5.Mixing)
-mixing_type            pulay
+mixing_type            broyden
 mixing_beta            0.3
 chg_extrap             second-order
 

diff --git a/examples/md/lcao_gammaonly_Si8/INPUT_2 b/examples/md/lcao_gammaonly_Si8/INPUT_2
@@ -22,7 +22,7 @@ smearing_method        gaussian
 smearing_sigma         0.001
 
 #Parameters (5.Mixing)
-mixing_type            pulay
+mixing_type            broyden
 mixing_beta            0.3
 chg_extrap             second-order
 

diff --git a/examples/md/lcao_gammaonly_Si8/INPUT_3 b/examples/md/lcao_gammaonly_Si8/INPUT_3
@@ -22,7 +22,7 @@ smearing_method        gaussian
 smearing_sigma         0.001
 
 #Parameters (5.Mixing)
-mixing_type            pulay
+mixing_type            broyden
 mixing_beta            0.3
 chg_extrap             second-order
 

diff --git a/examples/md/lcao_gammaonly_Si8/INPUT_4 b/examples/md/lcao_gammaonly_Si8/INPUT_4
@@ -22,7 +22,7 @@ smearing_method        gaussian
 smearing_sigma         0.001
 
 #Parameters (5.Mixing)
-mixing_type            pulay
+mixing_type            broyden
 mixing_beta            0.3
 chg_extrap             second-order
 

diff --git a/examples/md/lcao_gammaonly_Si8/INPUT_5 b/examples/md/lcao_gammaonly_Si8/INPUT_5
@@ -22,7 +22,7 @@ smearing_method        gaussian
 smearing_sigma         0.001
 
 #Parameters (5.Mixing)
-mixing_type            pulay
+mixing_type            broyden
 mixing_beta            0.3
 chg_extrap             second-order
 

diff --git a/examples/md/lcao_gammaonly_Si8/INPUT_6 b/examples/md/lcao_gammaonly_Si8/INPUT_6
@@ -22,7 +22,7 @@ smearing_method        gaussian
 smearing_sigma         0.001
 
 #Parameters (5.Mixing)
-mixing_type            pulay
+mixing_type            broyden
 mixing_beta            0.3
 chg_extrap             second-order
 

diff --git a/examples/md/lcao_gammaonly_Si8/INPUT_7 b/examples/md/lcao_gammaonly_Si8/INPUT_7
@@ -22,7 +22,7 @@ smearing_method        gaussian
 smearing_sigma         0.001
 
 #Parameters (5.Mixing)
-mixing_type            pulay
+mixing_type            broyden
 mixing_beta            0.3
 chg_extrap             second-order