[Pw_forum] calculating atoms oxidation states

[pboulet]

Dear all,

Does anyone have tried to used Jiang, Levchenko and Rappe’s method to calculate oxidation state of atoms?  (Phys. Rev Letters, 108, 2012, 166403.

In brief, the formula is N=V/e \Delta(P) x R /R^2,
where N, V, e, \Delta(P) and R are the oxidation state, cell volume, electron charge, change in polarisation and lattice vector, respectively. \Delta(P) x R corresponds to the dot product.
The idea is just to displace an atom along a path traversing the cell in a way that the atom goes from its location to that in the next cell.

 I have tried with the PbTiO3 example of QE for the calculation of polarization via the Berry phase. If I am right I should obtain +2 as an oxidation state. 

I have displaced the Pb atom (crystal position at 0. 0. 0.) along the z axis from 0 to 1. 

The enclosed picture depicts N versus z for z=0..1. I used the polarization P given by QE in units of (e/Omega).bohr, since it is similar to the formula above.
I have just divided P by z since Delta(P) and R are collinear… and I guess V/e of the formula cancels with e/Omega… I am not sure of these assumptions, however…

First the variation is -2 instead of +2. In addition the evolution is not smooth and the missing points on the curve are calculated to be negative. I have removed them but it is nonsense to me. 

Does anyone know what is wrong?

Thank you for your suggestions,

Pascal









Pascal Boulet
—
Professor in computational chemistry - DEPARTMENT OF CHEMISTRY
Director of the Madirel laboratory
Aix-Marseille University - Avenue Escadrille Normandie Niemen - F-13013 Marseille - FRANCE
Tél: +33(0)4 13 55 18 10 et +33(0)4 13 55 18 19 - Fax : +33(0)4 13 55 18 50
Email : pascal.boulet at univ-amu.fr <mailto:pascal.boulet at univ-amu.fr>








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