# [Pw_forum] Problem with determination of U using linear response

Prasenjit Ghosh prasenjit.jnc at gmail.com
Wed May 27 09:13:29 CEST 2015

```Dear all,

I am using linear response to determine U for Fe. In my system, there are
two types of Fe atom, one in which the Fe is in an O octahedron and the
second in which it is in an O terahedron.
When I am plotting the occupation number of the Fe d as a function of
perturbation alpha (-0.2 .le. alpha .le 0.2), for the non interacting
electron system, I am not getting a linear plot for the whole range of
alpha while for the interacting one it remains linear.
For example when Fe is in the O octahedra, the response does not remain
linear for alpha is greater than 0.05 or less than -0.05. However, for the
interacting case, it remains linear for the whole regime (please refer to
the attached plot for Fe in O octahedra).
Further for this case for alpha=0, the occupation for the interacting and
non interacting ones are not exactly same. While for the non-interacting
one the occupation is 6.60012, it is 6.60162 for the interacting one.

Similarly for the tethedra, for alpha=-0.2, the non-interacting response
does not remain linear while for the interacting one it remains linear.

I was wondering whether one has faced similar situations and if so can
provide me some hints as to what might be the probable reason for the same?

Below is the input file I am using for the calculation:

for alpha in -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

do

mkdir /scratch/pghosh/octfe/alpha\$alpha

cd /scratch/pghosh/octfe/alpha\$alpha

ethr=`grep ethr /home/pghosh/Ca2Fe2O5/octfe/scf.out | tail -1 | awk '{print
\$3}'`

rm -rf Ca2Fe2O5-noU-vcrel-AFM.*

cp -r ../Ca2Fe2O5-noU-vcrel-AFM.* .

cat > scf-octFe.\$alpha.in << EOF
&control
calculation = 'scf',
prefix = 'Ca2Fe2O5-noU-vcrel-AFM',
outdir = '/scratch/pghosh/octfe/alpha\$alpha'
pseudo_dir = '/home/pghosh/pseudo'
/
&system
ibrav =  0,
celldm(1)=10.25176385
nat = 36,
ntyp = 5,
ecutwfc = 45
ecutrho = 320
nspin=2
starting_magnetization(2)=-1.0
starting_magnetization(3)=1.0
starting_magnetization(4)=-1.0
occupations='smearing'
degauss=0.001
smearing='gaussian'
lda_plus_u = .true.,
U_projection_type = 'atomic',
Hubbard_U(2) = 1.d-10
Hubbard_U(3) = 1.d-10
Hubbard_U(4) = 1.d-10
Hubbard_U(5) = 1.d-10
Hubbard_alpha(4) = \$alpha
/
&electrons
mixing_beta = 0.3
conv_thr = 1.0d-8,
startingwfc = 'file',
startingpot = 'file',
diago_thr_init = \$ethr
/

ATOMIC_SPECIES
Ca 87.62 Ca.pw91-nsp-van.UPF
Fe1 47.867 Fe.pw91-sp-van_ak.UPF
Fe2 47.867 Fe.pw91-sp-van_ak.UPF
Fe3 47.867 Fe.pw91-sp-van_ak.UPF
O 15.999 O.pw91-van_ak.UPF
ATOMIC_POSITIONS (crystal)
Ca       0.479439516   0.108738866   0.023376810
Ca       0.979439516   0.391261134   0.476623190
Ca       0.520560484   0.608738866   0.976623190
Ca       0.020560484   0.891261134   0.523376810
Ca       0.520560484   0.891261134   0.976623190
Ca       0.020560484   0.608738866   0.523376810
Ca       0.479439516   0.391261134   0.023376810
Ca       0.979439516   0.108738866   0.476623190
Fe3      0.000000000   0.000000000  -0.000000000
Fe1      0.500000000   0.500000000   0.500000000
Fe1      0.000000000   0.500000000  -0.000000000
Fe1      0.500000000  -0.000000000   0.500000000
Fe2      0.948517158   0.250000000   0.935170308
Fe2      0.448517158   0.250000000   0.564829692
Fe2      0.051482842   0.750000000   0.064829692
Fe2      0.551482842   0.750000000   0.435170308
O        0.262959232   0.985181682   0.237331409
O        0.762959232   0.514818318   0.262668591
O        0.737040768   0.485181682   0.762668591
O        0.237040768   0.014818318   0.737331409
O        0.737040768   0.014818318   0.762668591
O        0.237040768   0.485181682   0.737331409
O        0.262959232   0.514818318   0.237331409
O        0.762959232   0.985181682   0.262668591
O        0.027189198   0.140319152   0.069344138
O        0.527189198   0.359680848   0.430655862
O        0.972810802   0.640319152   0.930655862
O        0.472810802   0.859680848   0.569344138
O        0.972810802   0.859680848   0.930655862
O        0.472810802   0.640319152   0.569344138
O        0.027189198   0.359680848   0.069344138
O        0.527189198   0.140319152   0.430655862
O        0.586951586   0.250000000   0.888451999
O        0.086951586   0.250000000   0.611548001
O        0.413048414   0.750000000   0.111548001
O        0.913048414   0.750000000   0.388451999
K_POINTS (automatic)
9 3 9 1 1 1
CELL_PARAMETERS (alat)
0.991167212   0.000000000   0.000000000
0.000000000   2.746908521   0.000000000
0.000000000   0.000000000   1.023657125
EOF

With regards,

Prasenjit
--
PRASENJIT GHOSH,
IISER Pune,
Pune, Maharashtra 411008, India

Phone: +91 (20) 2590 8203
Fax: +91 (20) 2589 9790
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