[QE-developers] Constants in reciprocal space Hartree calculation

[Paolo Giannozzi]

tpiba2=2\pi/a^2 comes from G^2 (in the code it is in units of tpiba2)
4\pi comes from the Fourier transform of 1/r => 4\pi/G^2
e2=e^2=2 is the electron charge in Ry a.u. (note that the charge is in
units of e and integrates to then number of electrons)
there is a factor 1/2 that multiplies the electrostatic energy. In the
"gamma only" case, we sum over half G-components and multiply by 2.

Paolo

On Thu, Jun 28, 2018 at 2:07 AM, Aaron Mahler <m.tesseracted at gmail.com>
wrote:

> Dear all,
> I'm working on implementing this scheme: https://arxiv.org/pdf/
> 1707.00856.pdf in QE and need to evaluate Hartree energy integrals for
> individual orbital densities. As such I have a question regarding
> evaluating the Hartree energy in reciprocal space. At the of the
> calculation in v_h in the PW/src/v_of_rho.f90 file, ehart is multiplied by
> e2 * fpi / tpiba2.
> https://gitlab.com/QEF/q-e/blob/develop/PW/src/v_of_rho.f90#L623
> I assume the 1/tpiba2 term is to scale the G^2 terms in the calculation.
> I'm unsure what the e2 * fpi is for though. I'm also unsure about right
> after that if it's gamma_only there's no factor of 0.5. Lastly I don't
> understand why does e2 = 2 if it's the elementary charge squared in a.u.?
> https://gitlab.com/QEF/q-e/blob/develop/Modules/constants.f90#L105
> Any insights would be very helpful.
>
> Cheers,
> Aaron Mahler
> Duke University
>
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-- 
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
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