ADMM is indeed a method to speed up the calculations, but in theory should not really influence the results. It might be a random effect in the numerics, but no bandgap vs a bandgap is not a small effect. I wonder if we can solve the time-reversal issue and combine if with HSE06 (no ADMM) to see a band gap there, and then just use ADMM as intended to speed it up.
Can you share a few more details about how you determine the time-reversal didn't work?
Yes, I believe it is numeric random effect, right now I can't reproduce the band gap opening's results (with ADMM is on). I initially ran a calculation (with ADMM on) and able to open the band gap, I later rewrite the script with some minor changes in parameters and using the previous calculation (with band gap) as initial state, this indeed reproduce band gap solution as expected. However, I had forgotten what parameters had been used in the initial run and cant reproduce the band gap result without reading the "right" initial state, so the band gap opening is probably unrelated to ADMM. May I know if there is a way to initialize different density matrix during beginning of calculation (without using pre-converged calculation)? Or is there a way to fix selective occupation state throughout the calculation?
I also tried a dozen of calculation with and without ADMM, in some cases (e.g. MnO), I do notice significant difference (band gap differ by about 10%), not sure if such a difference is within reasonable range.
Regarding the time-reversal symmetry, in the bulkscf.log file, the "Diagonalization solver parallelization report" states there are 260 kpoints in 8x8x8 MK grids, so I assumed the time reversal symmetry is on (please correct me if I am wrong).