[QE-developers] Gygi-Baldereschi in exx_divergence

[Colonna Nicola (PSI)]

Dear QE developers,

 I would like to better understanding the details of the "exx_divergence" routine and in particular the
 implementation of the Gygi-Baldereschi scheme.
 Following the paper by Nguyen and de Gironcoli (Phys. Rev. B 79, 205114) I understand the first part
 of the routine where the reciprocal-space part of the Ewald sum for a single point charge in the
 supercell is computed. As far as I understand this first part is the implementation of Eq. (17) in their paper.

 What I do not understand is the last part of the routine (I paste it below for clarity) which as far as I understand
 is not discussed in the paper (or at least it is not obvious to me).
 Any hint and/or reference to help me understand it would be greately appreciated!

Thank you for your help and best regards,

Nicola Colonna

........
     !
     alpha = alpha / tpiba2
     !
     nqq = 100000
     dq = 5.0d0 / SQRT(alpha) / nqq
     aa = 0._dp
     !
     DO iq = 0, nqq
        q_ = dq * (iq+0.5d0)
        qq = q_ * q_
        IF ( erfc_scrlen > 0 ) THEN
           aa = aa  -EXP( -alpha * qq) * EXP(-qq/4.d0/erfc_scrlen**2)*dq
        ELSEIF ( erf_scrlen > 0 ) THEN
           aa = 0._dp
        ELSE
           aa = aa - EXP( -alpha * qq) * yukawa / (qq + yukawa)*dq
        ENDIF
     ENDDO
     !
     aa = aa * 8.d0/fpi
     aa = aa + 1._dp/SQRT(alpha*0.25d0*fpi)
     IF ( erf_scrlen > 0) aa = 1._dp/SQRT((alpha+1._dp/4.d0/erf_scrlen**2)*0.25d0*fpi)
     div = div - e2*omega * aa
     !
     exx_divergence = div * nqs
     !
     CALL stop_clock( 'exx_div' )
     !
     RETURN



-----------------------------------------------------
PAUL SCHERRER INSTITUT
Nicola S. Colonna
WHGA/150
CH-5232 Villigen-PSI
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/developers/attachments/20210820/856bb625/attachment.html>