Dear Ben,
what is the E - E' difference you are referring to ?
Is it the difference between the two estimates of the energy ("total
energy" and "Harris-Foulkes estimate") ?
If so, the first is the expression of the TE from the variational
principle and is an upper bound to the scf result (not exactly but it
approaches to it as self consistency gets better), the second is a
different expression proposed by Harris & Foulkes which is also
stationary at scf... I don't remember if it is also variational from
above or just stationary...
anyhow they converge to the same value but are different and their
difference can give an idea of how far one is from the scf results but
is not a precise measure of it.
stefano
On 11/10/19 19:01, Ben Comer wrote:
Stefano,
Thanks for the details, I think we have the definitions sorted out.
But why is the E - E' from the output file not approximately equal to
the estimated SCF accuracy? It seemed there is always some
multiplicative factor difference between 1-20.
On 9/28/19 12:51 PM, Stefano de Gironcoli wrote:
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 <[email protected]
<mailto:[email protected]>> 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 <[email protected]
<mailto:[email protected]>> 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
<[email protected] <mailto:[email protected]>> 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
_______________________________________________
Quantum ESPRESSO is supported by MaX
(www.max-centre.eu/quantum-espresso
<http://www.max-centre.eu/quantum-espresso>)
users mailing list [email protected]
<mailto:[email protected]>
https://lists.quantum-espresso.org/mailman/listinfo/users
--
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
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu/quantum-espresso
<http://www.max-centre.eu/quantum-espresso>)
users mailing [email protected]
<mailto:[email protected]>
https://lists.quantum-espresso.org/mailman/listinfo/users
_______________________________________________
Quantum ESPRESSO is supported by MaX
(www.max-centre.eu/quantum-espresso
<http://www.max-centre.eu/quantum-espresso>)
users mailing list [email protected]
<mailto:[email protected]>
https://lists.quantum-espresso.org/mailman/listinfo/users
--
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
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu/quantum-espresso
<http://www.max-centre.eu/quantum-espresso>)
users mailing [email protected]
<mailto:[email protected]>
https://lists.quantum-espresso.org/mailman/listinfo/users
--
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
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu/quantum-espresso)
users mailing [email protected]
https://lists.quantum-espresso.org/mailman/listinfo/users
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu/quantum-espresso)
users mailing [email protected]
https://lists.quantum-espresso.org/mailman/listinfo/users
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu/quantum-espresso)
users mailing list [email protected]
https://lists.quantum-espresso.org/mailman/listinfo/users
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu/quantum-espresso)
users mailing list [email protected]
https://lists.quantum-espresso.org/mailman/listinfo/users
