[Pw_forum] a question about LDA+U

[Stefano Fabris]

Dear Ruijuan,

the Hubbard U term should disfavour the fractional occupation of the
Fe d orbitals. In practice, your calculations might get trapped in
some conducting local minima and/or show bad convergency. To check if
you are in one of these situations you should examine the occupation
matrix that is printed after each SCF iteration in the output file. In
particular, look for fractional occupancies, which are a clear sign
that the hubbard term is not doing what it should. In the physical 
insulating solution the eigenvalues should be close to
either 0 or 1.


I would suggest you to make the following instructive analysis:  run a
LDA+U calculation setting the U=0, get the conducting solution and
check that the occupancies are fractional (also, look at the
corresponding eigenvectors). Now compare these numbers with those of
your conducting LDA+U calculation with U=4.29.  What do you learn from
the comparison? Did the Hubbard-U contribution work the way you
expected? 

Good luck, Stefano.



On Fri, 22 Oct 2004, rjxiao wrote:

> Dear all, I am learning the LDA+U method by reading the PhD thesis
> of Matteo Cococcioni. I try to do the same calculation of FeO which
> is mentioned in the thesis. When I use the cell with 2 iron atoms
> (C1) and set the U=4.29eV abtained directly from the thesis, there
> is no energy gap appearing. Maybe it is because the interaction of
> the second nearest neighbours can not be described correctly in such
> a small cell according to the thesis.So I enlarge the model.Then I
> use the cell with 8 iron atoms (C4), but the self-consistency does
> not converge in both the calculation of U=4.29eV and of U=0eV(LDA+U
> is turned off) even when I change the mixing_beta to 0.1. I realy
> want to know where I have made mistakes.The input files are affixed.
> I have puzzled by this problem for many days. I am really thankful
> to you for your any opinion.
> 
> ----------
> Input file for C1:
> &CONTROL
> title = 'FeO' ,
> calculation = 'scf' ,
> restart_mode = 'from_scratch' ,
> outdir = '/home/rjxiao/tmp/' ,
> pseudo_dir = '/home/rjxiao/mydir/pwscf/pseudo/' ,
> prefix = 'FeO+U' ,
> /
> &SYSTEM
> ibrav = 5,
> celldm(1) = 10.026125,
> celldm(4) = 0.8333333,
> nat = 4,
> ntyp = 3,
> ecutwfc = 40 ,
> ecutrho = 400 ,
> occupations = 'tetrahedra' ,
> degauss = 0.005 ,
> smearing = 'marzari-vanderbilt' ,
> nspin = 2 ,
> starting_magnetization(1) = 1.0,
> starting_magnetization(2) = -1.0,
> starting_magnetization(3) = 0.0,
> lda_plus_u = .true. ,
> Hubbard_U(1) = 4.29,
> Hubbard_U(2) = 4.29,
> Hubbard_U(3) = 0.0,
> Hubbard_alpha(1) = 0.0,
> Hubbard_alpha(2) = 0.0,
> Hubbard_alpha(3) = 0.0,
> /
> &ELECTRONS
> /
> ATOMIC_SPECIES
> F1 55.84500 Fe.pz-nd-rrkjus.UPF 
> F2 55.84500 Fe.pz-nd-rrkjus.UPF 
> O 15.99940 O.pz-rrkjus.UPF 
> ATOMIC_POSITIONS alat 
> F1 0.000000000 0.000000000 0.000000000 
> F2 0.000000000 0.000000000 1.414213500 
> O 0.000000000 0.000000000 0.707106750 
> O 0.000000000 0.000000000 2.121320300 
> K_POINTS automatic 
> 4 4 4 0 0 0 
> 
> ----------------------
> INput file for C4:
> &CONTROL
> title = 'Fe4+U' ,
> calculation = 'scf' ,
> restart_mode = 'from_scratch' ,
> outdir = '/home/rjxiao/tmp/' ,
> pseudo_dir = '/home/rjxiao/mydir/pwscf/pseudo/' ,
> prefix = 'FeO-C4+U' ,
> /
> &SYSTEM
> ibrav = 5,
> celldm(1) = 11.577172,
> celldm(4) = 0.5,
> nat = 16,
> ntyp = 3,
> ecutwfc = 40 ,
> ecutrho = 400 ,
> occupations = 'tetrahedra' ,
> degauss = 0.005 ,
> smearing = 'marzari-vanderbilt' ,
> nspin = 2 ,
> starting_magnetization(1) = 1.0,
> starting_magnetization(2) = -1.0,
> starting_magnetization(3) = 0.0,
> lda_plus_u = .true. ,
> Hubbard_U(1) = 4.29,
> Hubbard_U(2) = 4.29,
> Hubbard_U(3) = 0.0,
> /
> &ELECTRONS
> mixing_beta = 0.2 ,
> /
> ATOMIC_SPECIES
> F1 55.84500 Fe.pz-nd-rrkjus.UPF 
> F2 55.84500 Fe.pz-nd-rrkjus.UPF 
> O 15.99940 O.pz-rrkjus.UPF 
> ATOMIC_POSITIONS crystal 
> F1 0.500000000 0.500000000 0.500000000 
> F1 0.000000000 0.500000000 0.500000000 
> F1 0.500000000 0.000000000 0.500000000 
> F1 0.000000000 0.000000000 0.500000000 
> F2 0.000000000 0.000000000 0.000000000 
> F2 0.500000000 0.000000000 0.000000000 
> F2 0.000000000 0.500000000 0.000000000 
> F2 0.500000000 0.500000000 0.000000000 
> O 0.250000000 0.250000000 0.250000000 
> O 0.750000000 0.750000000 0.750000000 
> O 0.750000000 0.250000000 0.250000000 
> O 0.250000000 0.750000000 0.750000000 
> O 0.250000000 0.750000000 0.250000000 
> O 0.750000000 0.250000000 0.750000000 
> O 0.250000000 0.250000000 0.750000000 
> O 0.750000000 0.750000000 0.250000000 
> K_POINTS automatic 
> 4 4 4 0 0 0 
> 
> 
> Best regards,
> 
> Sincerely,
> Ruijuan Xiao
> Institute of Physics,
> Chinese Academy of Sciences
> 
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Stefano Fabris                               fabris at democritos.it
INFM DEMOCRITOS - SISSA                      tel: +39 040 3787405
via Beirut 2-4, I-34014 Trieste, Italy       fax: +39 040 3787528
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