[Pw_forum] The electron affinities of defect in bulk crystal

Tima Perevalov timmka at gmail.com
Fri Oct 5 06:05:10 CEST 2012

Dear all,

I am trying to define the value of the electron affinities of oxygen
vacancy (i.e., the energy gain when the electron from the bottom of the
conduction band is trapped at the defect) in bulk crystal of transition
metal oxides, as follows:

E_tot(perfect, q=-1) + E_tot(defect, q= 0) - E_tot(perfect, 0) -
E_tot(defect, q=-1)

Whether this approach is valid for direct using in ESPRESSO? I know the
total energy of charged systems have no physical meaning in ESPRESSO
because of the interaction with the balancing background of charge. However
in such approach there is difference: E(perfect, q=-1)-E(defect, q=-1), and
I suppose that errors are cancelled. Is it true supposition? I am
exploiting B3LYP functional and have no problem with band gap value.

For preliminary results, I obtained electron affinities for  oxygen vacancy
in HfO2 and Ta2O5 polymorphs are close to zero. Moreover, the results are
sensitive to supercell size.

My second question is follows. Is it possible to define the value of the
electron affinities using the above equation adapted with Janak’s theorem?
The simplified according to the mean value theorem for integrals Janak’s
theorem stating that:

E_tot(q=-1) - E_tot(q= 0) ~= [e(h+1,N) + e(h+1,N+1)]/2,

where e(h+1,N) is the Kohn-Sham eigenvalue of the lowest unoccupied state
for the neutral system

e(h+1,N+1) is the Kohn-Sham eigenvalue of the highest occupied state for
the -1 charged system.

Best Regards, Timofey Perevalov,

Rzhanov Institute of Semiconductor Physics SB RAS
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