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<p>Stefano,</p>
<p>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.<br>
</p>
<div class="moz-cite-prefix">On 9/28/19 12:51 PM, Stefano de Gironcoli wrote:<br>
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<blockquote type="cite" cite="mid:36cddd05-65c2-b89f-bcd3-bc69ff0063d5@sissa.it">
<p>Dear Ben,</p>
<p>I think you are right on both accounts... thanks for pointing out the problem in eq A7<br>
</p>
<p>the equation in reciprocal space equivalent to A6 and correctly coded in PW/src/scf_mod.f90 in function rho_ddot (lines ~450 - 490 )<br>
</p>
<p>0.5 4pi e^2 Omega \sum |Delta_rho|^2/|G|^2<br>
</p>
<p>it has the correct dimensions of e^2 x [length^-1] <br>
</p>
<p>so A7 should be multiplied by Omega^2/2 to make it correct.</p>
<p><br>
</p>
<p>The root of the equivalence between A6 and the (corected) A7 is that <br>
</p>
<p>\int exp(+iGr) 1/|r| d3r = 4pi/|G|^2; rho(r) = \sum_G exp(+iGr) rho(G); and<br>
</p>
<p>\int exp(+i(G-G')r) d3r = Omega delta(G,G')</p>
<p>where in the last term the integral is done over the unit cell because we are looking for a "per cell" quantity.</p>
<p><br>
</p>
<p>best regards</p>
<p>stefano</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 27/09/19 21:04, Ben Comer wrote:<br>
</div>
<blockquote type="cite" cite="mid:5c94b289-d7a4-7bd1-5970-f6ff97df7582@gatech.edu">
<p>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.<br>
</p>
<div class="moz-cite-prefix">On 9/27/19 2:28 AM, Paolo Giannozzi wrote:<br>
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<blockquote type="cite" cite="mid:CAPMgbCu_Shz_vp+E+7Vn0cSsayi0OTZwDV6Qamn31AB8YicS-w@mail.gmail.com">
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<div>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
<br>
</div>
<div><br>
</div>
<div>Paolo<br>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Thu, Sep 26, 2019 at 11:53 PM Ben Comer <<a href="mailto:bcomer3@gatech.edu" moz-do-not-send="true">bcomer3@gatech.edu</a>> wrote:<br>
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<p>Dr. Giannozzi,</p>
<p>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.</p>
<p><a href="https://github.com/QEF/q-e/blob/master/PW/src/scf_mod.f90#L490" target="_blank" moz-do-not-send="true">https://github.com/QEF/q-e/blob/master/PW/src/scf_mod.f90#L490</a></p>
<div class="gmail-m_-2127499003259828511moz-cite-prefix">On 9/26/19 3:57 PM, Paolo Giannozzi wrote:<br>
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<div dir="ltr" class="gmail_attr">On Thu, Sep 26, 2019 at 9:44 PM Ben Comer <<a href="mailto:bcomer3@gatech.edu" target="_blank" moz-do-not-send="true">bcomer3@gatech.edu</a>> wrote:<br>
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<p>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?<br>
</p>
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<div>
<div dir="ltr">Variable dr2 in PW/src/mix_tho.f90, routine rho_ddot in PW/src/scf_mix.f90
</div>
<br>
</div>
<div>Paolo<br>
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On 9/26/19 10:57 AM, Paolo Giannozzi wrote:<br>
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<div>If I remember correctly: Eq.A6 of J.Phys.: Condens. Matter 21, 395502 (2009)</div>
<div><br>
</div>
<div>Paolo<br>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Thu, Sep 26, 2019 at 4:52 PM Ben Comer <<a href="mailto:bcomer3@gatech.edu" target="_blank" moz-do-not-send="true">bcomer3@gatech.edu</a>> wrote:<br>
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Hello,<br>
<br>
I'm trying to understand what exactly estimated SCF accuracy is. Does <br>
anyone know where I can find a formal definition of what it is and how <br>
it is being calculated? The structure of the output file implies that it <br>
is related to the Harris-Foulkes and the total energy, but it is clearly <br>
not the trivial difference between these two quantities.<br>
<br>
Thanks in advance,<br>
Ben Comer<br>
Georgia Tech<br>
<br>
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