[Pw_forum] occupancies of density matrix in LDA+U
Gianluca Giovannetti
gianluca.giovannetti at gmail.com
Mon Jun 7 12:44:39 CEST 2010
Dear Gabriele,
thank you for your reply.
i think i get what i wanted from your explanation.
ciao
Gianluca
On Mon, Jun 7, 2010 at 12:03 PM, Gabriele Sclauzero <sclauzer at sissa.it>wrote:
> 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 i`m 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
>
>
>
>
> thank you in advance.
>
> ciao
>
> Gianluca
>
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>
>
> § Gabriele Sclauzero, EPFL SB ITP CSEA
> * PH H2 462, Station 3, CH-1015 Lausanne*
>
>
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