[Pw_forum] Overlap integral for periodic part of eigenfunction

[Lorenzo Paulatto]

On Wednesday, March 15, 2017 11:11:54 PM CET Vahid Askarpour wrote:
> I would like to calculate the overlap integral  u*_k’(r)u_k(r)d^3r. 

Dear Vahid,
if you want to do it for excercize, go on and do it.

But, you may be happy to know that this integral is already computed in 
several places in the pw code. One in particular is the pw2wannier90.x code in 
particular in  PP/src/pw2wannier90.f90 from line 2120 to line 2187

 (and in general all the compute_mmn subroutine, but it does also a few more 
operations and some parts related to ultrasoft pseudopotentials are a bit 
difficult to understand)

> 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? 

No, i I remember correctly the wfcs on files are in G-space. Doing the product 
in G-space is equivalent to doing a convolution in real space.

>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?

No, because the order is not necessarily the same. Also, because you wouldn't 
be doing the product of the two functions but their convolution.

hth


-- 
Dr. Lorenzo Paulatto 
IdR @ IMPMC -- CNRS & Université Paris 6
phone: +33 (0)1 442 79822 / skype: paulatz
www:   http://www-int.impmc.upmc.fr/~paulatto/
mail:  23-24/423 Boîte courrier 115, 4 place Jussieu 75252 Paris Cédex 05