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.cannuc...@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 > > > > > _______________________________________________ > Quantum ESPRESSO is supported by MaX (www.max-centre.eu) > users mailing list users@lists.quantum-espresso.org > https://lists.quantum-espresso.org/mailman/listinfo/users -- 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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