[Pw_forum] electron-phonon matrix elements for molecules

[Marci]

Dear Users and Developers,

I would like to calculate electron-phonon matrix elements for
molecular systems.
As stated in the FAQ/12.8.0.6, electron-phonon calculations are presently
implemented for metals only. I think this constraint is due to the
integration over
the Fermi surface to obtain the electron-phonon coefficients
(\lambda). However,
I'm not interested in such integration and only the electron-phonon
matrix elements
are needed. Thus, instead of commenting out the corresponding part of
the code I
decided to use an artifical small gaussian smearing so that there are
no fractional
occupations, but still, the code does not complain and calculates
everything I need.

In order to test whether I get meaningful numbers for a system with only one
k-point (gamma) I decided to set up the following test: I compared the
electron-phonon
matrix elements of a 2x2x2 supercell of silicon (16 atoms), where the BZ is
sampled only by the gamma point and primitive cell of silicon (2
atoms), where the
BZ is sampled by a 2x2x2 unshifted MP scheme. If all numerical details (cutoff,
convergence criteria) are the same then in principle these two
calculations should
yield exactly the same results within numerical noise. Indeed, total
energies/atom
are the same, single particle energies can be easily mapped to each other, and
also phonon modes are the same, though there are little bit larger
than expected
deviations (in order of 0.1-1 cm^{-1}) especially for modes whose energy should
be zero. Interestingly, when I printed the electron-phonon matrix elements
(el_ph_mat in PH/elphon.f90) and compared matrix elements of corresponding
non-degenerate bands (so that arbitrary rotations within a degenerate subspace
do not matter) I found orders of magnitude differences in some cases.
Also, there
were non-zero matrix elements even when they should have been zero by symmetry.
I expected that by doing the mapping between phonon modes and electronic bands,
electron-phonon matrix elements would have been the same.

Am I missing something in the comparison? Is there any normalization
or any other
fundamental/numerical issue of calculating electron-phonon matrix elements for
insulators / molecules using only one k-point (gamma)?

The espresso version is 4.0.5, since this is the one which is
interfaced to a code we
are using for post processing.

Thanks in advance.

Yours sincerely,
Marton Voros

--
PhD student
Department of Atomic Physics
Budapest University of Technology and Economics
Budafoki út 8., H-1111, Budapest, Hungary
www.fat.bme.hu/MartonVoros