# [Pw_forum] occupancies of density matrix in LDA+U

Gabriele Sclauzero sclauzer at sissa.it
Mon Jun 7 12:03:04 CEST 2010

Dear Gianluca,

Il giorno 04/giu/10, alle ore 07:43, Gianluca Giovannetti ha scritto:

> Dear All,
>
> i write you as i need to know the occupancies of d states in my
> calculations and i would like to do it by looking at the occupation
> matrix.
>
> i have made a self-consistent calculation with the following input
> file:
>
> FeSe
>  &control
>     calculation     =  'scf'
>     restart_mode    =  'from_scratch'
>     prefix          =  'fese'
>     tprnfor         =  .true.
>     pseudo_dir      =  './'
>     outdir          =  './'
>     iprint          =   2
> /
>  &system
>     ibrav           =  8
>     celldm(1)       =  10.0852834932257
>     celldm(2)       =  1.00000000000000
>     celldm(3)       =  1.03521095322306
>     nat             =  8
>     ntyp            =  5
>     ecutwfc         =  35.0
>     ecutrho         =  350.0
>     nbnd            =  120
>     occupations     =  'smearing'
>     smearing        =  'methfessel-paxton'
>     degauss         =  0.01
>     nspin = 2
>     starting_magnetization(1) = -1.0
>     starting_magnetization(2) = 1.0
>     starting_magnetization(3) = -1.0
>     starting_magnetization(4) = 1.0
>     starting_magnetization(5) =  0.0
>     lda_plus_u      =.true.
>     lda_plus_u      =.true.
>     Hubbard_U(1)    =  1.d-8
>     Hubbard_U(2)    =  1.d-8
>     Hubbard_U(3)    =  1.d-8
>     Hubbard_U(4)    =  1.d-8
>     Hubbard_alpha(1) = 1.d-8
>     Hubbard_alpha(2) = 1.d-8
>     Hubbard_alpha(3) = 1.d-8
>     Hubbard_alpha(4) = 1.d-8
> /
>  &electrons
>     conv_thr        =   1.0d-8
>     diagonalization =  'cg'
> /
> ATOMIC_SPECIES
>  Fe1 55.845   Fe.pbe-sp-van.UPF
>  Fe2 55.845   Fe.pbe-sp-van.UPF
>  Fe3 55.845   Fe.pbe-sp-van.UPF
>  Fe4 55.845   Fe.pbe-sp-van.UPF
>  Se 78.96    Se.pbe-van.UPF
> ATOMIC_POSITIONS { crystal }
> Fe1   0.00000000  0.50000000  0.00000000
> Fe2   1.00000000  0.00000000  0.00000000
> Fe3   0.50000000  0.50000000  0.00000000
> Fe4   0.50000000  0.00000000  0.00000000
> Se   0.24999979  0.74999981  0.73480000
> Se   0.75000021  0.74999981  0.26520000
> Se   0.75000021  0.25000019  0.73480000
> Se   0.24999979  0.25000019  0.26520000
> K_POINTS {automatic}
> 10 10 8 0 0 0
>
> Calculations are fine.
> As you can see:
> (i) Fe-Fe bonds are along x and y axes so im in the correct
> framework for calling d states as they are,

What does this mean?
In my understanding, as soon as you break spherical simmetry, d states
can mix among themselves and they can also hybridize with states with
different angular momentum.

> (ii) i used U=0 to have printed the occupation matrix calculated in
> LDA+U scheme.
>
> In the output file of QE i can read:
> -------------------------------------------------------------------------------------------------------------
> atom  4  spin  1
> eigenvalues:  0.9283366 0.9383877 0.9483978 0.9712519 0.9740784
>  eigenvectors
>  1  -0.1720270  0.0000000  0.0000000 -0.9850922  0.0000000
>  2   0.0000000  1.0000000  0.0000000  0.0000000  0.0000000
>  3   0.0000000  0.0000000 -1.0000000  0.0000000  0.0000000
>  4   0.0000000  0.0000000  0.0000000  0.0000000 -1.0000000
>  5  -0.9850922  0.0000000  0.0000000  0.1720270  0.0000000
>  occupations
>  0.973  0.000  0.000 -0.008  0.000
>  0.000  0.938  0.000  0.000  0.000
>  0.000  0.000  0.948  0.000  0.000
> -0.008  0.000  0.000  0.930  0.000
>  0.000  0.000  0.000  0.000  0.971
> atom  4  spin  2
> eigenvalues:  0.3553238 0.3753074 0.4625234 0.5670451 0.6892263
>  eigenvectors
>  1   0.0000000  0.0000000  0.0000000  0.0000000  1.0000000
>  2   0.0000000 -1.0000000  0.0000000  0.0000000  0.0000000
>  3   0.7516066  0.0000000  0.0000000  0.6596117  0.0000000
>  4   0.0000000  0.0000000  1.0000000  0.0000000  0.0000000
>  5   0.6596117  0.0000000  0.0000000 -0.7516066  0.0000000
>  occupations
>  0.561  0.000  0.000 -0.112  0.000
>  0.000  0.375  0.000  0.000  0.000
>  0.000  0.000  0.567  0.000  0.000
> -0.112  0.000  0.000  0.591  0.000
>  0.000  0.000  0.000  0.000  0.355
> -------------------------------------------------------------------------------------------------------------
>
> what are these quantities?

The eigenvalues and eigenvectors of the occupation matrix built by
project KS eigenstates onto the d atomic orbitals (as defined, for
instace, in PP/projwfc.f90) and summing over the BZ.

> How can i extract the occupancies of d states for this data?

You can get the occupancies by "grepping" the lines which start with
"eigenvalues". The eigenvectors tell you which of the original d
states take part in each eigenstate and their weight.

> What is the order (the relation between label of d state and its
> occupancy)?
> I want to make a table having how many electrons i have in z2, xz,
> yz, x2-y2, xy for up and down components.

The "occupations" matrix should be what you want. It is the n_{I,m,m',
\sigma} matrix before the diagonalization procedure of above, hence it
contains the occupations on the orginal atomic orbitals (not mixed).

Please have a look at the PRB of Cococcioni & de Gironcoli (2005) and
at subroutines write_ns.f90 and new_ns.f90 in the PW/ folder.

HTH

GS

>
>
>
> ciao
>
> Gianluca
>
> _______________________________________________
> Pw_forum mailing list
> Pw_forum at pwscf.org
> http://www.democritos.it/mailman/listinfo/pw_forum

§ Gabriele Sclauzero, EPFL SB ITP CSEA
PH H2 462, Station 3, CH-1015 Lausanne

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20100607/30627c04/attachment.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: smime.p7s
Type: application/pkcs7-signature
Size: 1753 bytes
Desc: not available
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20100607/30627c04/attachment.p7s>
`