[Pw_forum] occupancies of density matrix in LDA+U vs output polarization in Lowdin Charges

[Dmitry Korotin]

Dear Gianluca,
as I remember, in projwfc.x atomic states are orthogonalized and normalized
in pw.x atomic states are used as in PP

try to set
U_projection_type='ortho-atomic' in the input file.

2010/6/21 Gianluca Giovannetti <gianluca.giovannetti at gmail.com>:
> Dear All,
>
> i have a question for you.
>
> I made the following self-consistent calculation:
>
> -------------------------------------------------------------
> 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.
> In the output i can find at the last electronic iteration:
>
> 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
> nsum =  28.8394618
>
> If i sum up the eigenvalues of spin 1 i get: 4.7604524
> If i sum up the eigenvalues of spin 2 i get: 2.449426.
> The difference is: 2.3110264.
> This difference is the polarization at Fe sites.
> Then i can use projwfc.x to calculate the polarization at each atom.
> I get in output file:
>
>      Atom #   4: total charge =  16.3558, s =  2.3950, p =  7.2026, d =
> 6.7582,
>                  spin up      =   9.4347, s =  1.2029, p =  3.6081, d =
> 4.6237,
>                  spin down    =   6.9211, s =  1.1921, p =  3.5945, d =
> 2.1345,
>                  polarization =   2.5136, s =  0.0108, p =  0.0135, d =
> 2.4892,
>
> Now: 2.3110264 is different from 2.5136.
>
> Can someone explain me this difference? :-)
> Is this due to the broadening of DOS?
> Is it correct to consider numbers coming from eigenvalues of density matrix
> of LDA+U (calculated with U=0)?
> In this latter case if my system of reference is correct they are solved
> respect to l=1,2,3,4,5. :-)
>
> i thank you in advance.
>
> cheers,
>
> Gianluca Giovannetti
>
>
> _______________________________________________
> Pw_forum mailing list
> Pw_forum at pwscf.org
> http://www.democritos.it/mailman/listinfo/pw_forum
>
>



-- 
Best regards,
Dmitry Korotin

Ph. D. Student,
Institute of Metal Physics
S. Kovalevskaya, 18
620041 Ekaterinburg GSP-170
Russia