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

[Gianluca Giovannetti]

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
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