[QE-users] vloc_of_g , a deep understanding

[Elena Cannuccia]

Thanks Paolo,

I understand now where the sinus comes from.

Elena

On Wed, 8 Sept 2021 at 08:46, Paolo Giannozzi <p.giannozzi at gmail.com> wrote:

> 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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