[Pw_forum] Overlap integral for periodic part of eigenfunction

[Vahid Askarpour]

Dear QE Community,

We know that |psi(k,r)> =u(r)exp(ik.r), where u(r) has the periodicity of the lattice. The index k includes band index as well.

I would like to calculate the overlap integral  u*_k’(r)u_k(r)d^3r. To this end, I have extracted the real and imaginary parts of
wave function coefficients from evc.dat for all the k-points and bands by setting wf_collect=.true..

I have two questions:

1. Am I correct in assuming that the above integral is equivalent to the sum(C*_k C_k’), where C’s are the coefficients from evc.dat and the sum is
over igwx (maximum G-vector index) specified in eve.dat?

2. igwx is different for different k-points. One k-point may have igwx=1459 while another k-point has igwx=1468. In the above sum, is it correct to
to use the top 1468 coefficients of the first k-point to calculate the overlap integral between the two k-points?


An earlier post (http://qe-forge.org/pipermail/pw_forum/2015-April/106663.html) suggests a similar concept for <psi_i|psi_j>  but not for <u_i|u_j>.

Thank you,

Vahid

Vahid Askarpour
Department of Physics and Atmospheric Science
Dalhousie University,
Halifax, NS, Canada

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