[QE-users] Magnetic force theorem in DFT+U formalism

[Saritas, Kayahan]

Dear QE users,
I am trying to run the Force theorem example (see [1] below for the link) with DFT+U. The original example is using PBE. The calculation procedure is the following:

  1.  Run collinear SCF calculation
  2.  Use SCF collinear calculation density and potentials to run NSCF SOC calculations with different magnetization angles and lforcet=True and use the energy differences
I used Re atom in vacuum to test the procedure and here are the inputs I use:
For step 1:
&CONTROL
   calculation     = 'scf'
   outdir          = 'pwscf_output'
   prefix          = 'pwscf'
   pseudo_dir      = './'
   wf_collect      = .true.
/
&SYSTEM
   degauss         = 0.001
   ecutwfc         = 100
   ibrav           = 0
   input_dft       = 'pbe'
   nat             = 1
   nosym           = .false.
   nspin           = 2
   ntyp            = 1
   occupations     = 'smearing'
   smearing        = 'gauss'
   starting_magnetization(1) = 1
   tot_charge      = 2
/
&ELECTRONS
   conv_thr        = 1e-07
/

ATOMIC_SPECIES
   Re 186.2 Re.pz-spn-rrkjus_psl.1.0.0.UPF
ATOMIC_POSITIONS bohr
   Re      -1.66168343      -0.00000189       0.00000756
K_POINTS automatic
   1 1 1  0 0 0
CELL_PARAMETERS bohr
        18.89726133       0.00000000       0.00000000
         0.00000000      18.89726133       0.00000000
         0.00000000       0.00000000      18.89726133
HUBBARD atomic
U Re-5d 4
Then for step 2, I copied the entire SCF calculation folder into another folder and modified the input file as the following:
&CONTROL
   calculation     = 'nscf'
   outdir          = 'pwscf_output'
   prefix          = 'pwscf'
   pseudo_dir      = './'
   wf_collect      = .true.
/
&SYSTEM
   angle1(1)       = 90
   angle2(1)       = 0
   degauss         = 0.001
   ecutwfc         = 100
   ibrav           = 0
   input_dft       = 'pbe'
   lspinorb        = .true.
   lforcet         = .true.
   nat             = 1
   nbnd            = 14
   noncolin        = .true.
   nosym           = .true.
   ntyp            = 1
   occupations     = 'smearing'
   smearing        = 'gauss'
   starting_magnetization(1) = 1
   tot_charge      = 2
/
&ELECTRONS
   conv_thr        = 1e-07
/

ATOMIC_SPECIES
   Re 186.2 Re.rel-pz-spn-rrkjus_psl.1.0.0.UPF
ATOMIC_POSITIONS bohr
   Re      -1.66168343      -0.00000189       0.00000756
K_POINTS automatic
   1 1 1  0 0 0
CELL_PARAMETERS bohr
        18.89726133       0.00000000       0.00000000
         0.00000000      18.89726133       0.00000000
         0.00000000       0.00000000      18.89726133
HUBBARD atomic
U Re-5d 4
Notice, that between step 1 and 2 parameters in the &CONTROL and &SYSTEM cards are different and step 1 uses a scalar relativistic potential, while step 2 uses full relativistic potential from pslibrary.

Step 1 completes successfully, but the step 2 gives the following error:
     Error in routine read_scf (1):
     Reading ldaU ns
I used QE 7.4 to run these calculations. Both step 1 and step 2 are completed without any error if I use PBE only (no hubbard-U).

I am suspecting that the error is because in the NSCF-SOC calculation expects a Hubbard calculation manifold double in size (10x10 in noncollinear vs 5x5 in collinear in d-orbitals).

I am not sure if there are any fundamental reasons why the force theorem would not work in DFT+U formalism, because the above examples work when Hubbard-U is disabled (PBE only).

[1] https://gitlab.com/QEF/q-e/-/blob/f184591e9f34cfcc7767505a23977a92286e8ba6/PP/examples/ForceTheorem_example/run_example
Best,
Kayahan

Dr. Kayahan Saritas
R&D Associate, Materials Theory Group
Materials Sciences and Technology Division
Oak Ridge National Laboratory

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