[Pw_forum] Question about charged supercell

[Stefano de Gironcoli]

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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