# [Pw_forum] Electron-phonon coupling

Eyvaz Isaev eyvaz_isaev at yahoo.com
Tue Apr 1 17:35:42 CEST 2003

Dear Gosia and Paolo,

delayed reply. Unfortunately, there are a lot of
useless  things I have to do.

I would like to clarify what I am doing. According to
7-th example,  the code is able to calculate
\lambda_{nk} (in the example k-point is X).
I am calculating it for a number of k-points in the
1/48 part of the BZ for FCC lattice. The origin of the
k-points I am using is slightly shifted (so, it is
not k=(000)).  I supposed that later \lambda_{nk}
could be  integrated using the tetrahedron method.

So, my question was  about correctness of this
procedure and as I understood there is no problem,
isn't it?

I am not going to calculate \lambda integrating of
functions containing double delta functions by means
of the tetrahedron method. It is well known that it is
not
easy to integrate this kind of functions using
tetrahedra.

Finally, I will be happy, if the procedure is correct
and I can evaluate estimated \lambda.

Regards,
Eyvaz.
--- Paolo Giannozzi <giannozz at nest.sns.it> wrote:
> Hi Gosia
>
> > No, it is not not correct. Look to the definition
> of el-ph
> > in one of Savrasov's papers and you will see that
> that there is
> > double delta on Fermi surface. You can split the
> integration over
> > phonon vectors (q-points) and over electron
> momentum (k-points)
> > if you first  integrate over phonons and later
> over electrons.
> > Not the other way around. Just because there is
> delta_k+q delta_k .
>
> the el-ph coefficients in PWscf are presently
> calculated by performing
> the sum over k at a given q, then summing the
> results over q. Maybe
> I haven't understood your point: are you implying
> that this is not correct?
> While I agree that the present implementation is
> dumb and ineffective,
> I don't see anything wrong with it.
>
> > You try to integrate delta_k * delta_q  or
> delta_k+q * delta_q
> > if I understand correctly your e-mail.
> > If you start from the integration over k first
> then at q=0 you meet
> > the problem of delta_k*delta_k+0 which is
> mathematically not defined.
>
> A gaussian broadening scheme is used to deal with
> the double delta.
> In this scheme, the double delta should be defined
> also for q=0.  Maybe
> what bothers you is that in the q=0 limit the
> function to be summed
> contains a 1/\omega^2 term. I "solved" the problem
> by averaging over
> translated grids (that do not include q=0). For an
> estimate of \lambda -
> that is what most people want - this should be good
> enough. For an
> accurate value of \lambda, I don't know, but getting
> an accurate value
> of \lambda is difficult anyway
>
> Paolo
>
> --
> Paolo Giannozzi             e-mail:
> giannozz at nest.sns.it
> Scuola Normale Superiore    Phone:   +39/050509412
> Piazza dei Cavalieri 7      Fax:     +39/050509417,
> 050563513
> I-56126 Pisa, Italy         Office:  Lab. NEST, Via
> della Faggiola 19
>
>
>
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