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<p><tt>Dear Phani,</tt></p>
<p><tt> there is no Journal reference for the local-TF scheme. <br>
</tt></p>
<p><tt> if one assumes that the error in self-consistency is small
enough that the linear regime applies then</tt></p>
<p><tt> \delta n_inp = \chi \chi_0^-1 \Delta n_I/O or
chi^-1 \delta n_inp = chi_0^-1 \Delta n_I/O<br>
</tt></p>
<p><tt> where \delta n_inp is the error in the input density (the
error that you want to correct) and \Delta n_I/O = n_inp - n_out
is the difference between input and output densities (that one
has access to in the calculation).</tt></p>
<p><tt> chi_0 is the non-interacting electron density response
function of the system and chi the interacting electron one,
linked to the previous by the Dyson equation \chi = \chi_0 +
\chi_0 ( v_c + f_xc ) \chi or, equivalently, </tt><tt><tt>\chi^-1
= \chi_0^-1 - (v_c + f_xc) </tt>where v_c is the Coulomb
kernel and f_xc the exchange-correlation one (neglected in the
following).<br>
</tt></p>
<p><tt> in the TF context chi_0^-1 = \partial V_KS/ \partial n = -
\partial^2 T[n]_TF / \partial n^2 \propto n(r)^(-1/3)</tt></p>
<p><tt> so using this approximation for \chi_0^-1 and iteratively
solving (with some not too strict threshold) the linear system
one gets an estimate for \delta n_inp from \Delta n_I/O</tt></p>
<p><tt> best</tt></p>
<p><tt>stefano</tt><br>
</p>
<div class="moz-cite-prefix">On 03/04/19 09:04, Phani Motamarri
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CALJ=y3-XYijXb31__wYRwq1W0HvZfEu9ZEcLb2V2j1K56UZcLw@mail.gmail.com">
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<div dir="ltr">
<div>Hi,</div>
<div><br>
</div>
<div>Many thanks for the reply. I already saw the reference, but
I am talking of the reference for the mixing scheme which
applies local-density dependent TF preconditioning. (Key word:
'<span
style="color:rgb(0,128,0);font-family:monospace;font-size:14px;font-weight:700">local-TF').</span></div>
<div><span style="font-family:monospace;font-size:14px"><font
style="" color="#000000">The reference</font></span> D.D.
Johnson PRB 38, 12807 (1988) does not talk about this local
T-F.</div>
<div><br>
</div>
<div>Regards</div>
<div>Phani</div>
<div><br>
</div>
<br>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Apr 3, 2019 at 2:54 AM
Paolo Giannozzi <<a href="mailto:p.giannozzi@gmail.com"
moz-do-not-send="true">p.giannozzi@gmail.com</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 dir="ltr">
<div dir="ltr">
<div>The reference is in the header of file
PW/src/mix_rho.f90:</div>
<div> ! ... Modified Broyden's method for charge density
mixing<br>
! ... D.D. Johnson PRB 38, 12807 (1988)<br>
</div>
<div>Paolo<br>
</div>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Apr 3, 2019 at
7:36 AM Phani Motamarri <<a
href="mailto:phanim@umich.edu" target="_blank"
moz-do-not-send="true">phanim@umich.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 dir="ltr">
<div dir="ltr">Hello Quantum Espresso Developers,
<div><br>
</div>
<div>We are developing an in-house real-space DFT code
and looking to implement better mixing schemes
beyond Anderson and Broyden specifically for
in-homogeneous systems. To this end, I came across
local-density-dependent Thomas Fermi screening
mixing implemented in Quantum expresso which is
performing really well for in-homogeneous systems.
I would like to know if you have any suitable
journal article reference for understanding the
mixing method implemented in Quantum espresso.</div>
<div><br>
</div>
<div>Looking forward to hearing from you</div>
<div><br>
</div>
<div>Thanks</div>
<div>Phani</div>
</div>
</div>
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</blockquote>
</div>
<br clear="all">
<br>
-- <br>
<div dir="ltr"
class="gmail-m_-7903780632649496780gmail_signature">
<div dir="ltr">
<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>
<br>
</div>
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