[Pw_forum] Electron-phonon coupling

[Malgorzata Wierzbowska]

Hi Paolo,

Everything what you write is correct for "smearing" kind
of summation which is implemented know. Except that
probably you mistyped summation over k and q with
what should be k and k+q (which is done in the present version of the code).

But my reply was to the question about using tetrahedron method  on top
of the result of summation over k. It wouldn't be correct because in that
case we would sum k and q not k and k+q.

So once again if the method for both summations is consistent it works.
But we can't mix it. And summation over q only in the definition of el-ph
does not exist. We always have k together with q. But we can find weghts
for all k and fixed q with broadenning technique and later use them
for summation in total lambda. So there is no need at present to mix it with
tetrahedrons. If we want tetrahedrons we should use them for both deltas 
not only
at the end.

About double delta problem: yes, you are write with broadenning it is 
not a problem.
But again a question by Eyvaz was about tetrahedrons.

Gosia



Paolo Giannozzi 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
>