velocity operator

[xiaoming_wang]

Hello,

I'd like to evaluate the velocity operator acting on the wave function v|phi>. In general, v = i[H, r], so v|phi> = i[H, r] |phi>. From elinear_response.F line 1157,
|xi> = [H, r]|phi>, which is calculated by LRF_COMMUTATOR subroutine. However, after looking at the subroutine, extra terms related to the overlap S are also
calculated, i.e., |xi> = ([H, r] - e [S, r] - de/dk S)|phi>. Then I'm confused. Which is the correct formula for the velocity operator for the VASP implementations?

Best,
Xiaoming

[henrique_miranda]

Have a look at the relevant literature:
https://journals.aps.org/prb/abstract/1 ... .73.045112
in particular Eq. 31 and comments therein.
Let me know if this answers your question.