This is a collection of input and output files that were used to produce all the data reported 
 in the following publication:

 G. Gebreyesus, L. Bastonero, M. Kotiuga, N. Marzari, I. Timrov,
 "Understanding the role of Hubbard corrections in the rhombohedral phase of BaTiO3",
 accepted in Phys. Rev. B (2023); arXiv:2309.04348.

 Calculations were performed using:
   - The open-source Quantum ESPRESSO distribution (version 7.1)
     which can be downloaded from www.quantum-espresso.org.
     The following codes of Quantum ESPRESSO were used:
     pw.x      - the code that performs self-consistent-field (SCF) ground-state calculations 
                 (to obtain total energy, forces, stress, and other properties) using 
                 Hubbard-corrected density-functional theory (DFT+U and DFT+U+V);
     hp.x      - the code that computes the Hubbard U and V parameters using density-functional
                 perturbation theory (DFPT);
     dos.x     - the code to compute the total density of states (DOS);
     projwfc.x - the code to compute the projected density of states (PDOS).

   - The open-source Phonopy package (version 2.7.1)
     which can be downloaded from https://phonopy.github.io/phonopy/

 DESCRIPTION AND CONTENT OF FOLDERS:

 /QuantumESPRESSO
  - /1_Self-consistent_calculation_of_Hubbard_parameters (calculation of Hubbard parameters and structural optimization)
    - /Calculation_of_U
       /U-on-Ti-3d
       /U-on-Ti-3d-and-O-2p
    - /Calculation_of_U_and_V
       /U-on-Ti-3d_and_V_Ti3d-O2p
       /U-on-Ti-3d-and-O-2p_and_V_Ti3d-O2p 
    These folders contain the following files:
       * BaTiO3.scf.in   - input file for the SCF calculation using pw.x
       * BaTiO3.scf.out  - output file from the SCF calculation using pw.x
       * BaTiO3.hp.in   - input file for the Hubbard U and V parameters calculations using hp.x 
       * BaTiO3.hp.out  - output file from the the Hubbard U and V parameters calculations using hp.x
       * BaTiO3.Hubbard_parameters.dat - a file that contains the computed values of U and V
       * HUBBARD.dat   - a file that contains the computed values of U and V that is used in in the “HUBBARD” card in BaTiO3.scf.in. 
       * BaTiO3.vc-relax.in  - input file for vc-relax calculations using pw.x
       * BaTiO3.vc-relax.out - output file from vc-relax calculation using pw.x

  - /2_Structural_properties (optimized 'a' and 'alpha' as a function of U)
        -/U=0.0  -/U=0.5  -/U=1.0    -/U=1.5   -/U=2.0   -/U=2.5
        -/U=3.0  -/U=3.5  -/U=4.0    -/U=4.5   -/U=5.0   -/U=4.5160 -/U=5.5
        -/U=6.0  -/U=7.0  -/U=8.0    -/U=9.0   -/U=10.0
      * BTO.vcrelax.in  - input file for vc-relax calculations using pw.x
      * BTO.vcrelax.out - output file from vc-relax calculation using pw.x
       
  - /3_PDOS (projected density of states)
    - /PDOS_PBEsol
    - /PDOS_PBEsol+U
    - /PDOS_PBEsol+U+V
    These folders contain the following files:
       * BaTiO3.scf.in   - input file for the SCF calculation using pw.x
       * BaTiO3.scf.out  - output file from the SCF calculation using pw.x
       * BaTiO3.pdos.in  - input  file for the PDOS calculation using projwfc.x
       * BaTiO3.pdos.out - output file from the PDOS calculation using projwfc.x
       * BaTiO3.pdos_tot - output file containing the DOS and summed PDOS
       * BaTiO3.pdos_atm#*(*)_wfc#*(*) - output files from projwfc.x with the PDOS for each orbital of each atom

  /Phonopy
    The phonons are computed using the optimized struture (for PBEsol+U is a cubic phase).  
    The phonons at Gamma and the phonon dispersions computed using Phonopy employing the following commands:
       *phonopy --qe -d --dim="1 1 1" -c BTO.scf.in - to create a 1x1x1 cell (eight cells with displacements are created).
       *phonopy --qe -d --dim="3 3 3" -c BTO.scf.in - to create a 3x3x3 supercell (eight supercells with displacements are created).
       *phonopy -f BaTiO3-001.out BaTiO3-002.out BaTiO3-003.out BaTiO3-004.out BaTiO3-005.out BaTiO3-006.out BaTiO3-007.out BaTiO3-008.out 
       *phonopy --qe -c BaTiO3.scf.in -p band.conf
     -/PBEsol
       -/1x1x1
          -/001  -/002  -/003  -/004  -/005 -/006 -/007 -/008
       -/3x3x3
          -/001  -/002  -/003  -/004  -/005 -/006 -/007 -/008
     -/PBEsol+U
       -/1x1x1
          -/001  -/002  -/003  -/004  -/005 -/006 -/007 -/008
       -/3x3x3
          -/001  -/002  -/003  -/004  -/005 -/006 -/007 -/008
     -/PBEsol+U+V
       -/1x1x1
          -/001  -/002  -/003  -/004  -/005 -/006 -/007 -/008
       -/3x3x3
          -/001  -/002  -/003  -/004  -/005 -/006 -/007 -/008
     -/PBEsol+U+V@PBEsol_geometry
       -/1x1x1
          -/001  -/002  -/003  -/004  -/005 -/006 -/007 -/008
     These folders contain the following files:
       * BTO.scf-00#.in   - Supercells input files for the SCF calculations to obtain force on atoms 
                            (# is for each atomic displacement. In this case, it runs from 1 - 8) using pw.x
       * BTO.scf-00#.out  - Supercells output files containing the force on atoms 
                            (# is for each atomic displacement. In this case, it runs from 1 - 8) from the SCF calculations using pw.x

  /Pseudopotentials (folder containing pseudopotentials)
     Pslibrary v1.0.0
     - Ba.pbesol-spn-rrkjus_psl.1.0.0.UPF - pseudopotential for Ba
     - Ti.pbesol-spn-rrkjus_psl.1.0.0.UPF - pseudopotential for Ti
     - O.pbesol-n-rrkjus_psl.1.0.0.UPF    - pseudopotential for O
  
  /Figures (folder with the source figures)
     - Fig2.xmgr  - Xmgrace figure 2  (structural properties)
     - Fig3.xmgr  - Xmgrace figure 3  (projected density of states)
     - Fig4a.xmgr - Xmgrace figure 4a (phonon dispersion, rhombohedral BTO)
     - Fig4b.xmgr - Xmgrace figure 4b (phonon dispersion, rhombohedral BTO)
     - Fig5.xmgr  - Xmgrace figure 5  (phonon dispersion, cubic BTO)
     - Fig6.xmgr  - Xmgrace figure 6  (Raman spectrum)