[Pw_forum] occupancies of density matrix in LDA+U

[Gianluca Giovannetti]

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 i`m in the correct framework for
calling d states as they are,
(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?
How can i extract the occupancies of d states for this data?
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.

thank you in advance.

ciao

Gianluca
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