Symmetry for EXX

[maki49]

Background

Currently, EXX calculation does not support symmetry=0 and 1, due to wrong DM(R) (for all the functionals) and wrong Vs (for HF and PBE0). If symmetry is supported, the PBE part calculation can be reduced to a rate of nks_ibz/nks_tot.

To Implement

• symmetry=0, DM(R) and Vs (Feature: support symmetry=0 for exx #2868)
• symmetry=1, DM(R)

[hongriTianqi]

@maki49 Has the PR fully solved this issue?

[maki49]

@maki49 Has the PR fully solved this issue?

Not yet.

[maki49]

Our current conclusion is that "symmetry=1" cannot be supported for EXX, because in LCAO $\ket{\phi_{\mu,k}}=\sum_R\phi_\mu(r-\tau_\mu-R)e^{ik\cdot R}$ is orthogonal with $\ket{\phi_{\mu,gk}}$ where g is a group operation, so I failed to use the relation $c_k=S^{-1}(gk,k)S(gk)c_{gk}$ ( where $S_{\mu\nu}(k_1,k_2)\equiv\braket{\phi_{k_1}|\phi_ {k_2}}$ ) derived from group theory to restore dm(k) from dm(gk): I implemented $S(gk,k)$ and found it a non-invertible zero-matrix ...
In other words, the dm(k) of every k-point is indispensable for constructing dm(R) for EXX.

I close this issue with the conclusion above. If someday I find any solution to this problem, I will reopen it.