[Pw_forum] Fwd: Fwd: shape of real space wave functions in wfc2kr

[Jacopo Simoni]

Ok, still many thanks for the reply.

Indeed, the wave functions look normalized, I realized only later that you
have to divide by the number of points on the grid.

Unfortunately I do not think that the type of calculation that I have to do
is already implemented, the reason is that I need to compute matrix
elements of the form
\int d^3r \Psi_nk(r)* F(r) \Psi_n'k'(r)
where F(r) is the gradient of the ionic potential localized on a particular
atom. So, it is very similar to the el-phon matrix element but it is not
exactly the same. In addition I need some
freedom in handling these matrix elements because I want to do a further
calculations involving occupations and eigenvalues and I want to see which
transitions are important and which are not.

In practice my issue at the moment is that I need to know what is exactly
the grid in real space where the wave functions are reconstructed. And the
second thing I would like to know is if you supplemented the wave functions
with other points in real space when you do integrals like the previous one
for the el-phonon coupling or you simply use the smooth grid coming out
from the invfft('Wave') routine. I understand that dffts is the smooth grid
for the wave functions and dfftp is the finer one for the density but I am
not sure about the ordering of the evc_r array in real space with respect
to the smooth real space grid.

Is the ordering given by this expression
r_ijk(:) = (i-1)/dffts%nr1x * a_1(:) + (j-1)/dffts%nr2x * a_2(:) +
(k-1)/dffts%nr3x * a_3(:) ?
with a_1, a_2, a_3 lattice parameters (I have a simple cubic cell), this is
what I have found looking around in the documentation. In particular this
is what it is written in the developer manual. The issue is that in the
wfck2r program the real space grid does not appear explicitly so I am
wondering if the previous expression for the wave function index is still
usable.

Many thanks in advance for the help
Jacopo Simoni
Los Alamos National Laboratory, Theoretical division.

---------- Forwarded message ----------
From: Lorenzo Paulatto <paulatz at gmail.com>
Date: 28 September 2017 at 02:28
Subject: Re: [Pw_forum] Fwd: shape of real space wave functions in wfc2kr
To: pw_forum at pwscf.org


On 27/09/17 19:33, Jacopo Simoni wrote:
> Ok many thanks for the reply, and sorry for the delay.
> 2- So you are saying that the wave functions I get are the coefficients
> u_nk(r) in Psi_nk(r) = u_nk(r) e^ikr . These cannot be used to
> reconstruct the density in real space because they are on the smooth
> grid . This smooth grid is always given by the expression
> r_ijk(:) = (i-1)/nr1x * a_1(:) + (j-1)/nr2x * a_2(:) + (k-1)/nr3x *
a_3(:) ?

There are several grid, dfftp is the charge density grid (ecutrho) dffts
is the smooth grid (4*ecutwfc). There is no specific grid for the
wavefunctions, as they are always put on the smooth grid (in g-space)
before being fourier transformed.

Also keep in mind that when things are in G-space, their plane-waves
could be in order of the Fourier transform grid, or in order of
increasing |G|. There are two integer arrays, nl and nls from modules
gvect and gvecs that map between these two representations


> This function u_nk(r) does not seem to be normalized, what is the
> normalization factor ? are these the same wave functions used in the
> routine hpsi to compute the product with the local part of the potential ?

As far as I know they are normalized, did you include the volume
element? Volume/nnr

>
> I am sorry for all these questions, but before using this object I want
> to be sure what it is exactly. So I really appreciate your effort in
> answering these question.

No problem, but you may want to tell us what you are trying to do,
because there is a good chance that is has been done already.

cheers


--
Lorenzo Paulatto - Paris
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