[QE-users] What Is Estimated SCF Accuracy

Sat Oct 12 23:24:20 CEST 2019

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 <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
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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
>>>>>>
>>>>>>
>>>>>>         _______________________________________________
>>>>>>         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>
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>>>>>         _______________________________________________
>>>>>         Quantum ESPRESSO is supported by MaX
>>>>>         (www.max-centre.eu/quantum-espresso
>>>>>         <http://www.max-centre.eu/quantum-espresso>)
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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
>>>>>
>>>>>
>>>>>     _______________________________________________
>>>>>     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 listusers at lists.quantum-espresso.org
>>> https://lists.quantum-espresso.org/mailman/listinfo/users
>>
>> _______________________________________________
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>
> _______________________________________________
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