## Difference between vme = dipole and vme = wannier

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fgoudreault
Posts: 5
Joined: Fri Jun 14, 2019 11:22 am
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### Difference between vme = dipole and vme = wannier

Dear EPW community,

I am having trouble understanding the difference between the vme = dipole and vme = wannier options. According to the docs, vme = dipole includes the commutator with the non-local part of the potential while it is another formula dH_nmk/dk - i(e_nk-e_mk)A_nmk for vme = wannier. However, in the following paper https://journals.aps.org/prresearch/pdf ... h.3.043022, the same formula as the one for vme = wannier is used for the velocity matrix element and it is stated that it contains the aforementioned commutator. So my question is, what is the difference between these two options? Should they converge to the same values w.r.t. the coarse grid k-mesh? Is there a formula for vme = dipole?

Thanks
Felix

sponce
Posts: 616
Joined: Wed Jan 13, 2016 7:25 pm
Affiliation: EPFL

### Re: Difference between vme = dipole and vme = wannier

Dear Félix,

vme = 'dipole' corresponds to Eq. 24 from the paper that you mention.
vme = 'wannier' corresponds to Eq. 27 from the PRR paper.

Both are equivalent when Wannier functions are well converged.
In case where the Wannier function are not perfect, vme = 'dipole' is expected to be more accurate, see Fig. 17 from the PRR for an illustration of that point.

Both options now include the non-local part and the vme = .false. option has been removed.

Best wishes,
Samuel
Prof. Samuel Poncé
Chercheur qualifié F.R.S.-FNRS / Professeur UCLouvain
Institute of Condensed Matter and Nanosciences
UCLouvain, Belgium
Web: https://www.samuelponce.com