Re: [QE-users] What Is Estimated SCF Accuracy

[Stefano de Gironcoli]

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 > 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 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
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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Re: [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 
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 
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 
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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--
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Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222




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users 

Re: [QE-users] What Is Estimated SCF Accuracy

[Stefano de Gironcoli]

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 > 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 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
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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users mailing list users@lists.quantum-espresso.org

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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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Univ. Udine, via delle Scienze 208, 33100 Udine, 

Re: [QE-users] What Is Estimated SCF Accuracy

[Ben Comer]

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 
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 
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 
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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--
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Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222




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--
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Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222




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--
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Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222

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Re: [QE-users] What Is Estimated SCF Accuracy

[Paolo Giannozzi]

On Thu, Sep 26, 2019 at 9:44 PM Ben Comer  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  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)
>> users mailing list users@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@lists.quantum-espresso.orghttps://lists.quantum-espresso.org/mailman/listinfo/users
>
> ___
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> https://lists.quantum-espresso.org/mailman/listinfo/users



-- 
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Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
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Re: [QE-users] What Is Estimated SCF Accuracy

[Ben Comer]

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?

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 
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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--
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Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222




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Re: [QE-users] What Is Estimated SCF Accuracy

[Ben Comer]

Thanks this answered my question, the responses are much appreciated!

On 9/26/19 10:58 AM, Stefano de Gironcoli wrote:
> In the simplest case it is the electrostatic self energy of the 
> difference between rho_in and rho_out and as such it is an estimate of 
> the energy error. in more complex cases (magnetic systems, lda+u, ...) 
> it is modified in the same spirit.
>
> stefano
>
> On 26/09/19 16:51, Ben Comer 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)
>> users mailing list users@lists.quantum-espresso.org
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Re: [QE-users] What Is Estimated SCF Accuracy

[Paolo Giannozzi]

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  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)
> users mailing list users@lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
>


-- 
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Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
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