[QE-users] vloc_of_g , a deep understanding

[Paolo Giannozzi]

What we want to compute is V(\vec q) = (1/\Omega) \int V(r) e^{i\vec q
\cdot \vec r}dr^3. V(r) contains an atomic part plus a term Ze^2 erf(r)/r
removing the long-range term and is a function of |\vec r| only. The
integral can be written in radial coordinates and integrated wrt \theta and
\phi. FInally: V(q) = 4\pi/\Omega \int V(r) (sin(qr)/qr)r^2 dr =
4\pi/\Omega \int (r V(r)) (sin(qr)/q) dr.

Paolo

On Tue, Sep 7, 2021 at 5:15 PM Elena Cannuccia <elena.cannuccia at univ-amu.fr>
wrote:

> Dear all,
>
> I am interested in understanding the calculation of pseudopotential in
> plane waves. I have started from the subroutine vloc_of_g.f90.
>
> I am aware of the fact that a separation of the short and long range part
> of the Coulomb potential is obtained by means of the error function, and
> the subsequent treatment of the two parts in order to get the Fourier
> transform of the Coulomb potential.
>
> I do not understand the multiplication by r(ir) at line 103
> aux1 (ir) =r (ir) * vloc_at (ir) + zp * e2 * erf (r (ir))
> and why, a few lines below, the Fourier transform is obtained by
> sin (gx * r (ir) ) / gx .  Is it because the function to be transformed is
> odd?
>
> Some references will be really appreciated.
> Thank you very much
>
> Elena Cannuccia
> Aix Marseille Université
>
>
>
>
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-- 
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 206, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
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