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<p><tt>Dear Ben,</tt></p>
<p><tt>what is the E - E' difference you are referring to ? <br>
</tt></p>
<p><tt>Is it the difference between the two estimates of the energy
("total energy" and "Harris-Foulkes estimate") ?</tt></p>
<p><tt>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...</tt></p>
<p><tt>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.</tt></p>
<p><tt>stefano<br>
</tt></p>
<div class="moz-cite-prefix">On 11/10/19 19:01, Ben Comer wrote:<br>
</div>
<blockquote type="cite"
cite="mid:57380fdd-bcf1-3fb0-ebeb-a60d394249c8@gatech.edu">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<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>
</div>
<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>
</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>
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208, 33100 Udine, Italy<br>
Phone +39-0432-558216, fax
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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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