Dear Ben,
I think you are right on both accounts... thanks for pointing out the
problem in eq A7
the equation in reciprocal space equivalent to A6 and correctly coded
in PW/src/scf_mod.f90 in function rho_ddot (lines ~450 - 490 )
0.5 4pi e^2 Omega \sum |Delta_rho|^2/|G|^2
it has the correct dimensions of e^2 x [length^-1]
so A7 should be multiplied by Omega^2/2 to make it correct.
The root of the equivalence between A6 and the (corected) A7 is that
\int exp(+iGr) 1/|r| d3r = 4pi/|G|^2; rho(r) = \sum_G exp(+iGr) rho(G); and
\int exp(+i(G-G')r) d3r = Omega delta(G,G')
where in the last term the integral is done over the unit cell because
we are looking for a "per cell" quantity.
best regards
stefano
On 27/09/19 21:04, Ben Comer wrote:
I figured the code had to be correct, and are equations A.6 and A.7
equivalent? It's not trivially obvious that they would be equal as one
is an integral in real space whereas the other is an integral in
reciprocal space. If they are the same it looks like A.7 might be
missing the volume factor and a factor of 1/2.
On 9/27/19 2:28 AM, Paolo Giannozzi wrote:
The code is correct. Eq.A7 likely assumes that rho(G)=\int rho(r)
exp(-iGr)dr, instead of the more usual definition rho(G)=(1/Omega)
\int rho(r) exp(-iGr)dr
Paolo
On Thu, Sep 26, 2019 at 11:53 PM Ben Comer <bcom...@gatech.edu
<mailto:bcom...@gatech.edu>> wrote:
Dr. Giannozzi,
Per the conversation, I read through the rho_ddot function. In
line 490 of scf_mod.f90 it appears that the volume, omega, is
being multiplied rather than divided as it is in equation A.7 I'm
concerned that one of the versions of these equations may be
incorrect. please let me know if I am under a misapprehension.
https://github.com/QEF/q-e/blob/master/PW/src/scf_mod.f90#L490
On 9/26/19 3:57 PM, Paolo Giannozzi wrote:
On Thu, Sep 26, 2019 at 9:44 PM Ben Comer <bcom...@gatech.edu
<mailto:bcom...@gatech.edu>> wrote:
Just a quick follow up, the text seems to imply that A7 is
used rather than A6. do you know where this is defined in
the source code?
Variable dr2 in PW/src/mix_tho.f90, routine rho_ddot in
PW/src/scf_mix.f90
Paolo
On 9/26/19 10:57 AM, Paolo Giannozzi wrote:
If I remember correctly: Eq.A6 of J.Phys.: Condens. Matter
21, 395502 (2009)
Paolo
On Thu, Sep 26, 2019 at 4:52 PM Ben Comer
<bcom...@gatech.edu <mailto:bcom...@gatech.edu>> wrote:
Hello,
I'm trying to understand what exactly estimated SCF
accuracy is. Does
anyone know where I can find a formal definition of
what it is and how
it is being calculated? The structure of the output
file implies that it
is related to the Harris-Foulkes and the total energy,
but it is clearly
not the trivial difference between these two quantities.
Thanks in advance,
Ben Comer
Georgia Tech
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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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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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