[QE-users] What Is Estimated SCF Accuracy

Sat Sep 28 18:51:32 CEST 2019

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 <bcomer3 at gatech.edu 
>> <mailto:bcomer3 at 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 <bcomer3 at gatech.edu
>>>     <mailto:bcomer3 at 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
>>>>         <bcomer3 at gatech.edu <mailto:bcomer3 at 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
>>>>
>>>>             _______________________________________________
>>>>             Quantum ESPRESSO is supported by MaX
>>>>             (www.max-centre.eu/quantum-espresso
>>>>             <http://www.max-centre.eu/quantum-espresso>)
>>>>             users mailing list users at lists.quantum-espresso.org
>>>>             <mailto:users at 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 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 listusers at lists.quantum-espresso.org  <mailto:users at lists.quantum-espresso.org>
>>>>         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 users at lists.quantum-espresso.org
>>>         <mailto:users at 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 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 listusers at lists.quantum-espresso.org  <mailto:users at 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 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 list users at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20190928/e7ca916a/attachment.html>