[Pw_forum] Electron-phonon coupling

[Paolo Giannozzi]

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

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Paolo Giannozzi             e-mail:  giannozz at nest.sns.it
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