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<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">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<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>
</div>
<blockquote type="cite"
cite="mid:CAPMgbCu_Shz_vp+E+7Vn0cSsayi0OTZwDV6Qamn31AB8YicS-w@mail.gmail.com">
<div dir="ltr">
<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>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
<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>
</div>
<blockquote type="cite">
<div dir="ltr">
<div class="gmail_quote">
<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>
</div>
<blockquote class="gmail_quote" style="margin:0px
0px 0px 0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
<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>
</div>
</blockquote>
<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>
</div>
<blockquote class="gmail_quote" style="margin:0px
0px 0px 0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
<div
class="gmail-m_-2127499003259828511gmail-m_7390029215997806863moz-cite-prefix">On
9/26/19 10:57 AM, Paolo Giannozzi wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">
<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>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
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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<div>Paolo Giannozzi, Dip. Scienze
Matematiche Informatiche e Fisiche,<br>
Univ. Udine, via delle Scienze 208,
33100 Udine, Italy<br>
Phone +39-0432-558216, fax
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<div>
<div dir="ltr">
<div>Paolo Giannozzi, Dip. Scienze Matematiche
Informatiche e Fisiche,<br>
Univ. Udine, via delle Scienze 208, 33100
Udine, Italy<br>
Phone +39-0432-558216, fax +39-0432-558222<br>
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<pre class="gmail-m_-2127499003259828511moz-quote-pre">_______________________________________________
Quantum ESPRESSO is supported by MaX (<a class="gmail-m_-2127499003259828511moz-txt-link-abbreviated" href="http://www.max-centre.eu/quantum-espresso" target="_blank" moz-do-not-send="true">www.max-centre.eu/quantum-espresso</a>)
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<div>Paolo Giannozzi, Dip. Scienze Matematiche
Informatiche e Fisiche,<br>
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy<br>
Phone +39-0432-558216, fax +39-0432-558222<br>
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<pre class="moz-quote-pre" wrap="">_______________________________________________
Quantum ESPRESSO is supported by MaX (<a class="moz-txt-link-abbreviated" href="http://www.max-centre.eu/quantum-espresso">www.max-centre.eu/quantum-espresso</a>)
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