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<div>Dear Stefano, Nicola,<br />
</div>
<div>Thank you very much <strong><u>Stefano</u></strong> for your clear
explanation of derivative discontinuities of the ground-state energy
functional (at integer values of the particle number) which leads to
discontinuity in the chemical potential. The NaCl example you explained is
what that is used to resovle the famous paradox, leading to the formulation
of the ensemble-DFT (Perdew et al, 1982, if I remember correctly). However,
what mechanism brings the small fraction of charge from "A"
fragment to "B"? There is no overlap between the occupied
Kohn-Sham orbitals of "A" and "B", irrespective of the
approximation chosen for the XC-functional. </div>
<div><strong><u>Nicola</u></strong>, where do you use the linear property
(for particle number between integer values) of the energy functional?</div>
<div>I use the Janack's theorem and half occupation numbers in HOMO or in
LUMO to find the ionization energy or electron affinity of a system
irrespective of the approximation in XC-functional.</div>
<div>To summarize my need, I would like to control (by hand) the occupation
numbers of KS orbitals. How is it possible?</div>
<div> </div>
<div>Bests,</div>
<div> mahmoud</div>
<div> </div>
<div> </div>
<div> </div>
<div> </div>
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<blockquote style="border-left: #000000 2px solid; padding-left: 5px;
padding-right: 0px; margin-left: 5px; margin-right: 0px">-----Original
Message-----<br />
From: Stefano de Gironcoli <degironc@sissa.it><br />
To: mpayami@aeoi.org.ir, PWSCF Forum <pw_forum@pwscf.org><br />
Date: Mon, 25 Feb 2013 14:19:37 +0100<br />
Subject: Re: [Pw_forum] Question about charged supercell<br />
<br />
<div class="moz-cite-prefix">dear Mahmoud<br />
<br />
As Prasenjit wrote you, most probably the system will not remove the
electron from one of the two fragments only but will split it among
the two fragments.<br />
<br />
This is wrong and is due to the self interaction error present in
approximate DFT functionals.<br />
<br />
Actually this problem (partial charges on the fragments) may arise even for
neutral case and is a very important failure of approximate DFT<br />
<br />
let's examine this latter case and let's take NaCl dimer as an example...<br
/>
<br />
In nature, in vacuum, NaCl dissociates in neutral fragments<br />
<br />
This is because the Na Ionization Potential (I_Na, energy required to
extract one electron from Na<br />
is higher than Cl Electron Affinity (A_Cl, energy gained by adding one
electron to Cl).<br />
<br />
A property of Isolated systems (as the fragments are assumed to be) is that
the energy as a function of fractional occupation is piece-wise linear
w.r.t. the occupation of the last eigenvalue and the linear slope in the
total energy is the eigenvalue itself (equal to -I_Na and -A_Cl for the two
isolated fragments in our case). I_Na > A_Cl<br />
<br />
As occupations are bound between 0 and 1 this fixes the GS to be given by
neutral fragments.<br />
<br />
However due to self-interaction error the energy vs occupation function is
not linear for approximate functionals which in turn implies that the
partially occupied eigenvalue of the fragments depends on the occupation and
it may and does happen that HOMO_Na(x=1) > LUMO_Cl(1-x=0) ...
that is there is an initial gain in energy coming from transferring a
fraction of electron from Na to Cl...<br />
as the transfer progresses the HOMO_Na eigengalue goes down and LUMO_Cl goes
up until for a certain critical value of x (call it xc)
HOMO_Na(xc)=LUMO_Cl(1-xc) and the transfer stops ...<br />
but this means that Na has (1-xc) positive charge and Cl has (1-xc) negative
charge with xc not integer.<br />
<br />
Way to fix this requires the use of a better functional for which the piece
wise linearity is restored (with an accurate value for the slope of course)
or at least such that the HOMO_Na(x=1) > LUMO_Cl(1-x=0) condition does
not occurs and the average slope has an accurate vale for -I_Na and
-A_Cl....<br />
<br />
Hybrids functional can serve that purpose. <br />
DFT+U corrections can also address this issue if the U parameter and the
molecular orbital manifold of the fragments on which it is applied is chosen
properly.<br />
<br />
HTH<br />
<br />
stefano<br />
<br />
On 02/23/2013 04:36 PM, Mahmoud Payami Shabestari wrote:<br />
</div>
<blockquote cite="mid:WC20130223153628.501042@aeoi.org.ir" type="cite">
<pre wrap="">
Dear QE Developers and Users,
I have constructed a supercell containing two molecules "A" and
"B" well
separated by, say, 15 Bohrs distance. Now I give a total charge +1 for the
cell. How the code decides to assign the charge +1 to molecule "A"
or "B"?
Any comments is highly appreciated.
Best regards,
Mahmoud Payami
Condensed Matter Section
Physics Group, AEOI, Tehran-Iran
Email: <a class="moz-txt-link-abbreviated" href="mailto:mpayami@aeoi.org.ir">
mpayami@aeoi.org.ir</a>
Phone: +98 (0) 21 82064393
Fax: +98 (0) 21 88221105
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