Wannier functions for cRPA & DMFT with several correlated sites in unit-cell

Dear all,

I am interested in studying the effects of electron correlation in the Fen Ge Te2 (FGT) materials family. Each of these systems contains several Fe sub-lattices characterised by different chemical arrangements that contribute unequally to local and itinerant magnetism.

As a first step towards the description of such kind of systems with DFT+DMFT, I tried to replicate the cRPA tutorials on SrVO3 but with a supercell containing two slightly inequivalent Vanadium atoms. The input file is copied below (run with abinit 9.10.3). I notice that the computed averaged U and J are much lower in the supercell than in the reference unit cell calculation:

Supercell :

Orbital with l= 2 on atom 1 with spin’s orientations Up-Up


        Average U and J as a function of frequency

     omega           U(omega)            J(omega)
    0.000      0.7143   -0.0000      0.0883    0.0000

Unit cell :

Orbital with l= 2 on atom 1 with spin’s orientations Up-Up


        Average U and J as a function of frequency

     omega           U(omega)            J(omega)
    0.000      2.7546    0.0000      0.5997   -0.0000

I guess that the culprit for this difference is the definition of the correlated orbitals by projected Wannier functions. Indeed the computed bare interactions in Wannier basis are much smaller in the supercell than in the unit cell. As the bands used to build the Wannier functions, as well as the initial projectors are the same, I was hoping to end with the same correlated spaces in both the unit-cell and super-cell calculations. Is there a way to work around this issue and to define multiple well localised correlated sites ? or am I missing something?

Many thanks for your help,

Simon

INPUT FILE

----------------------------------------------------------------------------------

Tutorial: Computation of U in CRPA for SrVO3 for t2g and eg orbitals

B. Amadon, R. Outerovitch

----------------------------------------------------------------------------------

ndtset 4
jdtset 1 2 3 4
paral_kgb 0
prtvol 10
pawprtvol 3
prtgsr 0 # GSR file printing produces some unpredictable results
#==================================================================================
############ Parameters common to all DATASETS
#==================================================================================

CONVERGENCE PARAMETERS

nstep 40
nline 5 #Number of LINE minimisations
nnsclo 2 #Number of Non-Self Consistent LOops
tolvrs 1.0d-15

occopt 3 #OCCupation OPTion
tsmear 0.1 eV #Temperature of SMEARing

PHYSICAL PARAMETERS

acell 7.2605 7.2605 14.521
rprim 1.0 0.0 0.0 #Real space PRIMitive translations
0.0 1.0 0.0
0.0 0.0 1.0
natom 10 ntypat 3 typat 1 1 2 2 3 3 3 3 3 3

V Sr O*3

xred 0.00 0.00 0.00
0.00 0.00 0.5001
0.50 0.50 0.25
0.50 0.50 0.75
0.50 0.00 0.00
0.50 0.00 0.50
0.00 0.50 0.00
0.00 0.50 0.50
0.00 0.00 0.25
0.00 0.00 0.75

znucl 23.0 38.0 8.0

ngkpt 4 4 2 #K - PoinTs grid : Real space LATTice
nshiftk 1 #No shift
shiftk
0.0 0.0 0.0
istwfk *1

#For all the dataset
nsym 1
gw_icutcoul 6
symchi 0
symsigma 0 # Default in v9 is 1 but I don’t think UCPRA supports it (MG)

#----------------------------------------------------------------------------
#-- Parameters for screening for different datasets
#-- Except for the structure , only the parameters below should be changed
#----------------------------------------------------------------------------
nband 100
ecut 12.0 # Maximal kinetic energy cut-off, in Hartree
pawecutdg 20.0 # PAW - Energy CUToff for the Double Grid ( need only when usepaw=1=)
#ecutwfn 12.0
pawoptosc 1 # Choose the Shishkin Kresse way to compute oscillator matrix. In general Arnaud Alouani is much better, but too time consuming for this simple test.

– DFTU: 1st dataset and definition of correlated angular momentum

usepawu 1 # DFT+U is used just for printing usefull quantities.
dmatpuopt 1 # choose expression of the density matrix
lpawu 2 -1 -1
jpawu 0.0 0.0 0.0 eV
upawu 0.0 0.0 0.0 eV

– activate calculation of u and j

ucrpa 1 # the screening will use the wannier weights to suppress transitions.

##----------------------------------------------------------------------------#

DO not change parameters below this line unless you know what you do.

#----------------------------------------------------------------------------

#==================================================================================
############ FIRST DATASET: Read Wfc, produce KSS file and Wannier file
#==================================================================================
tolvrs1 1.0d-13

#==================================================================================
############ SECOND DATASET: Read Wfc, produce KSS file and Wannier file
#==================================================================================
getden2 -1

== Compute empty bands precisely

iscf2 -2
tolwfr2 1.0d-18 # Will stop when this tolerance is achieved

== Compute Projected Wannier functions

plowan_compute2 1 # Activate the computation of Wannier functions
plowan_bandi 41 # First band for Wannier functions
plowan_bandf 50 # Last band for Wannier functions
plowan_natom 2 # Number of atoms
plowan_iatom 1 2 # Index of atoms
plowan_nbl 1 1 # Number of orbitals on each atoms
plowan_lcalc 2 2 # Index of the orbitals (2 → d)
plowan_projcalc 5 5 # Projector for the orbitals (see pseudo-potential file)

#==================================================================================
############ THIRD DATASET: Calculation of the screening (epsilon^-1 matrix)
#==================================================================================
optdriver3 3 # Screening calculation
gwcalctyp3 2
getwfk3 -1 # Obtain WFK file from previous dataset
ecuteps3 5.0 # Cut-off energy of the planewave set to represent the dielectric matrix. It is important to adjust this parameter.

– Frequencies for dielectric matrix

nfreqre3 1
freqremax3 10 eV
freqremin3 0 eV
nfreqim3 0

– Ucrpa: screening

ucrpa_bands3 41 50 # In principle, it is useless for ucrpa=2. It is however still necessary for technical reasons even if is redundant with dmftbandi and dmftbandf.

plowan_compute3 10 # Read Wannier functions

– Parallelism

gwpara3 1

#==================================================================================
############ FOURTH DATASET: Calculation of the effective interaction (optdriver=4 and gwcalctyp=2 and ucrpa=1)
#==================================================================================
optdriver4 4 # Self-Energy calculation
gwcalctyp4 2 # activate HF or ucrpa
getwfk4 2 # Obtain WFK file from dataset 1
getscr4 3 # Obtain SCR file from previous dataset
ecutsigx4 30.0 # Dimension of the G sum in Sigma_x. It would be better to keep the default ecut value.
plowan_compute4 10 # Read Wannier functions

irdscr3 1

irdwfk3 1

– Frequencies for

nfreqsp4 1
freqspmax4 10 eV
freqspmin4 0 eV
nkptgw4 0 # number of k-point where to calculate the GW correction: all BZ
mqgrid4 300 # Reduced but fine at least for SrVO3
mqgriddg4 300 # Reduced but fine at least for SrVO3

– Parallelism

gwpara4 2 # necessary for dataset 3 DO NOT CHANGE IT if nsppol=2

pp_dirpath “/home/ucl/modl/sdubois/progs/abinit-9.10.5/tests/Psps_for_tests/”
pseudos “Pseudodojo_paw_pw_standard/V.xml, Pseudodojo_paw_pw_standard/Sr.xml, Pseudodojo_paw_pw_standard/O.xml”

Dear all,

after many trial and errors, it appears that my issue came from the definition of the k-point grid. If I replace the k-point grid by a 4x4x3 with shiftk=(.5, .5, 0.), I get averaged U and J that come much closer to the tutorial values.

Best regards,

Simon

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