[Pw_forum] correspondence between diagonal elements of the occupation matrix and atomic d-orbitals

[Matteo Cococcioni]

Dear Ricardo,

On Thu, Jan 13, 2011 at 8:16 AM, Ricardo Faccio <rfaccio at fq.edu.uy> wrote:

> Dear QE users
>
> I'm trying to understand what is the correspondence between the d-orbital
> diagonal elements of the occupation matrix and the atomic d-orbitals used
> as
> projectors. I found two responses in the mailing list, but they have
> different orbital ordering. I would like to know if the following is
> correct:
>
>
> $$$$$$
> atom  4  spin  1
> eigenvalues:  0.7294836 0.7306191 0.7326025 0.7629065 0.8283887
>  eigenvectors
>  1   0.0000000  0.0000000 -1.0000000  0.0000000  0.0000000
>  2   0.0000000 -1.0000000  0.0000000  0.0000000  0.0000000
>  3  -0.0087135  0.0000000  0.0000000  0.9999620  0.0000000
>  4   0.0000000  0.0000000  0.0000000  0.0000000 -1.0000000
>  5  -0.9999620  0.0000000  0.0000000 -0.0087135  0.0000000
>  occupations
>  0.828  0.000  0.000  0.001  0.000
>  0.000  0.731  0.000  0.000  0.000
>  0.000  0.000  0.729  0.000  0.000
>  0.001  0.000  0.000  0.733  0.000
>  0.000  0.000  0.000  0.000  0.763
> $$$$
>
> .....Do we have this?
>  z2-r2  / xz /  yz / x2-y2 / xy
>

this is how the basis of d states is ordered (growing |m| from 0 to 2).


> n 0.8283887  0.7306191 0.7294836  0.7326025  0.7629065
>

In this particular case the matrix is diagonal so the eigenvectors coincide
with the basis vectors.
Yes, 0.7294 is the occupation of yz, 0.7306 of xz, 0.7326 of x2-y2, etc.
as can be read from the composition of the eigenvectors.

Matteo



> Thanks
> Ricardo
> -------------------------------------------------------------------------
>  Dr. Ricardo Faccio
>  Prof. Adjunto de Física
>  Mail: Cryssmat-Lab., Cátedra de Física, DETEMA
>  Facultad de Química, Universidad de la República
>       Av. Gral. Flores 2124, C.C. 1157
>       C.P. 11800, Montevideo, Uruguay.
>  E-mail: rfaccio at fq.edu.uy
>  Phone: (+598) 2924 9859
>              (+598) 2929 0648
>  Fax:      (+598) 2924 1906
>  Web:  http://cryssmat.fq.edu.uy/ricardo/ricardo.htm
>
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>
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-- 
Matteo Cococcioni
Department of Chemical Engineering and Materials Science,
University of Minnesota
421 Washington Av. SE
Minneapolis, MN 55455
Tel. +1 612 624 9056    Fax +1 612 626 7246
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