[QE-users] What Is Estimated SCF Accuracy

[Ben Comer]

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

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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>)
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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>)
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