[Pw_forum] Question about charged supercell

[Mahmoud Payami Shabestari]

Dear Stefano, Nicola,

Thank you very much Stefano 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.  
Nicola, where do you use the linear property (for particle number between 
integer values) of the energy functional? 
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.
To summarize my need, I would like to control (by hand) the occupation 
numbers of KS orbitals. How is it possible?

Bests,
         mahmoud





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-----Original Message-----
From: Stefano de Gironcoli <degironc at sissa.it>
To: mpayami at aeoi.org.ir, PWSCF Forum <pw_forum at pwscf.org>
Date: Mon, 25 Feb 2013 14:19:37 +0100
Subject: Re: [Pw_forum] Question about charged supercell


dear   Mahmoud

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.

This is wrong and is due to the self interaction error present in 
approximate DFT functionals.

Actually this problem (partial charges on the fragments) may arise even for 
neutral case and is a very important failure of approximate DFT

let's examine this latter case and let's take NaCl dimer as an example...

In nature, in vacuum, NaCl dissociates in neutral fragments

This is because the Na Ionization Potential  (I_Na, energy required to 
extract one electron from Na
is higher than Cl Electron Affinity (A_Cl, energy gained by adding one 
electron to Cl).

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

As occupations are bound between 0 and 1 this fixes the GS to be given by 
neutral fragments.

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...
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 ...
but this means that Na has (1-xc) positive charge and Cl has (1-xc) negative 
charge with xc not integer.

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....

Hybrids functional can serve that purpose. 
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.

HTH

stefano

On 02/23/2013 04:36 PM, Mahmoud Payami Shabestari wrote:

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: mpayami at aeoi.org.ir
Phone: +98 (0) 21 82064393
Fax:     +98 (0) 21 88221105
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