[QE-users] calculation of Hund's J (linear response method)

[Christoph Wolf]

Dear all,

I am giving the linear response method for Hubbard U and Hund J another go.
A recent publication has obtained quite resonable values for U and J based
on a hexahydrated transition metal model and I thought it might be
worthwhile trying (
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.235157) ;
however, either I am too stupid or there is a bug in the Hubbard_beta
routine that I cannot figure out. Anyways, if someone else has managed to
do this please do comment!

The procedure should be easy, I make a series of calculation for values of
Hubbard_beta keeping Hubbard_U and Hubbard_alpha=1D-40; the on-site
magnetization is define by m=n(up)-n(down) which I can get from the scf
output

bare response:
 --- enter write_ns ---
 LDA+U parameters:
U( 3)     =  0.00000000
J0( 3)     =  0.00000000
alpha( 3) =  0.00000000
beta( 3) =  0.05000000
atom    1   Tr[ns(na)] (up, down, total) =   *4.95101*  *1.38740*  6.33841

converged response
atom    1   Tr[ns(na)] (up, down, total) =   *4.95032*  *1.39090*  6.34122

If I do this for a series of calculations I obtain the following:

# beta bare conv
-0.08 3.57155 3.57023
-0.05 3.56860 3.56776
-0.02 3.56561 3.56528
0.02  3.56160 3.56194
0.05  3.55856 3.55942
0.08  3.55548 3.55686
# slopes: bare= -0.100419 conv= -0.0835161

the respective \partial m/\partial \beta look linear in the region of the
chosen Hubbard_beta.

but the resulting J=-2*(bare^-1-conv^-1) makes no sense and even the sign
is wrong.

The value for Hubbard_U obtained by this method using \partial n/\partial
\alpha is around 5.4, which seems perfectly suitable by the way.

Input for a single calculation is attached below.

Thanks for your help in advance!

Chris


&CONTROL
calculation = "scf",
...
/
&SYSTEM
ibrav=1,A=15.000000,ecutwfc=30, ecutrho=400,
starting_magnetization(3)=0.7,
 nspin=2,occupations="fixed", tot_magnetization=4.000000
nat=19,ntyp=3,tot_charge=2.000000
lda_plus_U=.true.,U_projection_type="ortho-atomic"
Hubbard_U(3)=1D-40,Hubbard_alpha(3)=1D-40, Hubbard_beta(3)=-0.08
/
&ELECTRONS
startingwfc="file", startingpot="file"
mixing_beta=0.6,conv_thr=1D-12,diago_thr_init=1D-14,electron_maxstep=150,
mixing_mode="local-TF"
/
ATOMIC_SPECIES
H 1.008 H.pbe-kjpaw_psl.1.0.0.UPF
O 15.999 O.pbe-n-kjpaw_psl.1.0.0.UPF
Fe1 55.845 Fe.pbe-spn-kjpaw_psl.0.2.1.UPF
ATOMIC_POSITIONS (angstrom)
Fe1 7.500000000 7.500000000 7.500000000
O 7.500000000 7.500000000 9.491812807
O 7.500000000 9.491814995 7.500000000
O 9.491776410 7.500000000 7.500000000
O 5.508226144 7.500000000 7.500000000
O 7.500000000 5.508190791 7.500000000
O 7.500000000 7.500000000 5.508184515
H 6.674174667 10.066164672 7.500000000
H 8.326002124 10.065917296 7.500000000
H 10.065724550 7.500000000 8.326098474
H 10.066137163 7.500000000 6.674195836
H 7.500000000 6.674283010 4.933686902
H 7.500000000 8.326129049 4.934261135
H 6.674236823 4.933772022 7.500000000
H 8.326063477 4.934192685 7.500000000
H 4.934274010 7.500000000 6.673909845
H 4.933876539 7.500000000 8.325806755
H 7.500000000 6.674482948 10.066592251
H 7.500000000 8.326364525 10.065407565
K_POINTS (automatic)
1 1 1 0 0 0



-- 
Postdoctoral Researcher
Center for Quantum Nanoscience, Institute for Basic Science
Ewha Womans University, Seoul, South Korea
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