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Ab initio Calculations Using Q-Espresso Code

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How to calculate the projected DOS of FeO using DFT and DFT+U

Abderrahmane REGGAD January 03, 2022

We will take the antiferromagnetic state of FeO

 



We need 3 input files, 2 pseudopotentials and a script  

algerien1970@linux-wipm:~/abinitio/QE-tutorials/DFT+U> ls
Fe.pbesol-spn-kjpaw_psl.0.2.1.UPF O.pbesol-n-kjpaw_psl.0.1.UPF plot_pdos.gnu  projwfc.FeO.in  pw.FeO.nscf.in  pw.FeO.scf.in

 

 pw.FeO.scf.in

&control
    calculation='scf'
    restart_mode='from_scratch',
    prefix='FeO'
    pseudo_dir = './'
    outdir='./tmp/'
    verbosity='high'
 /
 &system
    ibrav = 0,
    celldm(1) = 8.19,
    nat = 4, 
    ntyp = 3,
    ecutwfc = 30.0,
    ecutrho = 240.0,
    occupations = 'smearing',
    smearing = 'mv',  
    degauss = 0.02,
    nspin = 2,
    starting_magnetization(1) =  0.5,
    starting_magnetization(2) = -0.5
    lda_plus_u = .true.,
    lda_plus_u_kind = 0,
    U_projection_type = 'atomic',
    Hubbard_U(1) = 1.d-8
    Hubbard_U(2) = 1.d-8
 /
 &electrons
    conv_thr =  1.d-9
    mixing_beta = 0.3
 /
ATOMIC_SPECIES
Fe1  55.845  Fe.pbesol-spn-kjpaw_psl.0.2.1.UPF
Fe2  55.845  Fe.pbesol-spn-kjpaw_psl.0.2.1.UPF
O     16.0   O.pbesol-n-kjpaw_psl.0.1.UPF
CELL_PARAMETERS {alat}
 0.50  0.50  1.00
 0.50  1.00  0.50
 1.00  0.50  0.50
ATOMIC_POSITIONS {crystal}
 Fe1  0.00  0.00  0.00
 Fe2  0.50  0.50  0.50
 O    0.25  0.25  0.25
 O    0.75  0.75  0.75
K_POINTS {automatic}
 3 3 3 0 0 0

pw.FeO.nscf.in   modified pw.FeO.scf.in file

&control
    calculation='nscf'
    .    
    Hubbard_U(1) = 1.d-8
    Hubbard_U(2) = 1.d-8
    nbnd = 35
       .
    K_POINTS {automatic}
    6 6 6 0 0 0

projwfc.FeO.in

&projwfc
    prefix='FeO'
    outdir='./tmp/'
    ngauss = 0,
    degauss = 0.005,
    Emin = -15.0,
    Emax =  30.0,
    DeltaE = 0.01
 /

Script  plot_pdos.gnu 

set terminal post eps enhanced solid color "Helvetica" 20 
set arrow from 0, 0 to 0, 4.4 nohead
set output "FeO_PDOS.eps" 
set xrange [-10:8] 
set yrange [0:5] 
set xtics -10, 2, 8 
set ytics   0, 1, 5
set xlabel "E - Ef (eV)" 
set ylabel "PDOS (states/eV/atom)" 
plot "FeO.pdos_atm#1(Fe1)_wfc#5(d)" u ($1-13.7042):($2) w l lw 2 title 'Fe-3d (majority spin)', \
     "FeO.pdos_atm#2(Fe2)_wfc#5(d)" u ($1-13.7042):($2) w l lw 2 title 'Fe-3d (minority spin)', \
     "FeO.pdos_atm#3(O)_wfc#2(p)"   u ($1-13.7042):($2) w l lw 2 title ' O-2p'

Fe.pbesol-spn-kjpaw_psl.0.2.1.UPF

You can download the file using the following command
$ wget https://www.quantum-espresso.org/upf_files/Fe.pbesol-spn-kjpaw_psl.0.2.1.UPF --no-check-certificate

 or from Reference

O.pbesol-n-kjpaw_psl.0.1.UPF

You can download the file using the following command
$ wget https://www.quantum-espresso.org/upf_files/O.pbesol-n-kjpaw_psl.0.1.UPF --no-check-certificate

  or from Reference

 

1. Standard DFT case

Perform a SCF calculation using pw.x

algerien1970@linux-wipm:~/abinitio/QE-tutorials/DFT+U> pw.x < pw.FeO.scf.in |tee pw.FeO.scf.out

Perform a NSCF calculation using pw.x

algerien1970@linux-wipm:~/abinitio/QE-tutorials/DFT+U> pw.x < pw.FeO.nscf.in |tee pw.FeO.nscf.out

 

Perform a calculation of PDOS using projwfc.x

algerien1970@linux-wipm:~/abinitio/QE-tutorials/DFT+U> projwfcw.x < projwfc.FeO.in |tee projwfc.FeO.out

Plot PDOS using the script for gnuplot

gnuplot> load "plot_pdos.gnu"


The solution with DFT is metallic
 


2. DFT+U case

Modify input files pw.FeO.scf.in and pw.FeO.nscf.in by setting the following:

   Hubbard_U(1) = 5.2

   Hubbard_U(2) = 5.2

   Here, Hubbard_U(1) and Hubbard_U(2) are the Hubbard parameters for Fe1-3d and Fe2-3d states (in eV). 


The value of U = 5.2 eV was chosen for demonstration purposes; Hubbard U can be computed ab initio (see e.g. PRB 98, 085127 (2018)).

 pw.FeO.nscf.in   and pw.FeO.scf.in files

    U_projection_type = 'atomic',
    Hubbard_U(1) = 5.2
    Hubbard_U(2) = 5.2

Repeat all steps as in 1), and ultimately determine PDOS in the DFT+U case.
  
   Note: change the value of the Fermi energy in "plot_pdos.gnu", you can find the value of the Fermi energy at the end of the file pw.FeO.scf.out. 


     the Fermi energy is    13.8742 ev

!    total energy              =    -735.17461423 Ry

     total all-electron energy =     -5385.550636 Ry
     estimated scf accuracy    <          5.1E-10 Ry
     smearing contrib. (-TS)   =       0.00000000 Ry
     internal energy E=F+TS    =    -735.17461423 Ry


Script  plot_pdos.gnu 

plot "FeO.pdos_atm#1(Fe1)_wfc#5(d)" u ($1-13.8742):($2) w l lw 2 title 'Fe-3d (majority spin)', \
     "FeO.pdos_atm#2(Fe2)_wfc#5(d)" u ($1-13.8742):($2) w l lw 2 title 'Fe-3d (minority spin)', \
     "FeO.pdos_atm#3(O)_wfc#2(p)"   u ($1-13.8742):($2) w l lw 2 title ' O-2p'

 

 The solution with DFT+U is also metallic...

3. DFT+U case (with the starting_ns_eigenvalue option)

Modify the input file pw.FeO.scf.in by setting the following:

   starting_ns_eigenvalue(5,2,1) = 1.0
 
   starting_ns_eigenvalue(5,1,2) = 1.0

  pw.FeO.nscf.in   and pw.FeO.scf.in files

    Hubbard_U(1) = 5.2
    Hubbard_U(2) = 5.2
    starting_ns_eigenvalue(5,2,1) = 1.0
    starting_ns_eigenvalue(5,1,2) = 1.0

 

 

Repeat all steps as in 1), and ultimately determine PDOS in the DFT+U case
   (with the starting_ns_eigenvalue option).

   Note: change the value of the Fermi energy in "plot_pdos.gnu",
   you can find the value of the Fermi energy at the end of the file pw.FeO.scf.out.

The solution with DFT+U is insulating

 

Reference: https://gitlab.com/QEF/material-for-ljubljana-qe-summer-school/-/tree/master/Day-2

algerien1970@linux-wipm:~/abinitio/QE-tutorials/material-for-ljubljana-qe-summer-school-master/Day-2> ls
example1.relax  example2.vc-relax  example3.neb  example4.functionals  example5.pwtk  handson-day2-functionals.pdf  handson-day2.pdf  README.md
 
algerien1970@linux-wipm:~/abinitio/QE-tutorials/material-for-ljubljana-qe-summer-school-master/Day-2/example4.functionals/ex1.DFT+U> ls
plot_pdos.gnu  projwfc.FeO.in  pw.FeO.nscf.in  pw.FeO.scf.in  README.md  reference

 

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