[Pw_forum] [LDA+U] elements in occupation matrix are real number?

[Alex Smogunov]

Dear Chan-Woo.
The n matrix is always hermitian, it is clear from definition. In the case
of
collinear LSDA there is always psi_sigma --> psi_sigma* symmetry, due
to hermicity of Hamiltonians for each spin, which can be considered as the
time-reversal operation. This is why you always have k --> -k symmetry
even if you do not have inversion operation. Because of this time-reversal
symmetry one can readily see that the n matrix should be real.
It is not anymore the case in general noncollinear calculation where the
occupation matrix is in general complex (and hermitian).

Concerning negative eigenvalues, I think they are just small numbers,
probably due to computational errors, which should be thought of as 0.

regards,
Alexander


Le 1 mars 2012 20:56, Chan-Woo Lee <cwandtj at gmail.com> a écrit :

> Dear QE developers and users,****
>
> ** **
>
> I have a question in understanding occupation matrix from LDA+U output
> file.****
>
> ** **
>
> 1) Definition of occupation matrix, n is:****
>
> ** **
>
> n= \sum{f<psi|phi_i><phi_j><psi>}, where psi is KS eigenstates, phi_i is
> atomic orbital of i orbital, f is scaling factor. As i and j from phi_i and
> phi_j don’t have to be identical, I think it’s not guaranteed that elements
> in n matrix are always real… However, in the QE output, they are all shown
> as real numbers. In new_ns.f90, I can find that n (nr and ns) are defined
> as real numbers but I can’t find any restrictions other than this. ****
>
> ** **
>
> 2) While elements in the matrix are real, some of them are “negative”. How
> can I understand this? I found one paper about multiconfigurational
> character of wave functions (
> http://jcp.aip.org/resource/1/jcpsa6/v110/i9/p4199_s1 ) but it’s beyond
> my scope. ****
>
> ** **
>
> Did I miss something? Any suggestions and advices will truly be
> appreciated…****
>
> ** **
>
> Sincerely,****
>
> ** **
>
> Chan-Woo****
>
> ** **
>
> ** **
>
> *-------
> Chan-Woo Lee, Ph.D.*
>
> *Postdoctoral Research Associate*
>
> * *
>
> *Department of Chemistry
> University of Pennsylvania
> 231 South 34th Street
> Philadelphia, PA 19104-6323
> Phone: 1-215-898-3564 (Office)
> *Email: leechanw at sas.upenn.edu / cwandtj at gmail.com****
>
> ** **
>
> ** **
>
> ** **
>
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