4.6 DFT+U with an explicit model choice
These are unexecuted teaching inputs and starting settings to test. Original figures are schematics, not computed results. Use licensed VASP and PAW data, replace every placeholder, record the executable version and validate convergence.
4.6.1 Model, units and provenance
Use eV for energy, Å for length and eV/Å for force; 1 kbar = 0.1 GPa. State normalization per atom, molecule, primitive cell or simulation cell. Record PAW identifiers, release, ZVAL, ENMAX and permitted hashes; never redistribute POTCAR. SCF convergence addresses the chosen electronic problem; convergence of the target property requires separate tests.
Original schematic. Curves explain concepts; blank data areas await verified learner results. No calculation is claimed.
4.6.2 Worked case: procedure, interpretation and checks
Why this is more than a gap switch
Semilocal DFT can over-delocalize localized d or f electrons. DFT+U adds an orbital-subspace correction that changes the cost of fractional local occupations. It can alter magnetic order, orbital polarization, geometry, and energy differences as well as a gap. Treat it as a model with a stated correlated subspace and parameter definition, not a knob whose sole purpose is to match one experimental number. DFT+U formalism
A useful exercise is an antiferromagnetic transition-metal oxide. Construct a cell large enough to represent the desired order before starting. A nonmagnetic primitive cell cannot represent an arbitrary antiferromagnet merely by increasing U. Choose the PAW dataset, base functional, magnetic order, and a defensible U source together. A value from a different projector, oxidation environment, or method is not automatically transferable.
Species-resolved setup
For a hypothetical two-species POSCAR ordered M, O, with U applied to M d orbitals, the following is a template, not a material recommendation:
LDAUL selects the angular momentum channel, with −1 meaning no U for that species. LDAUU and LDAUJ are in eV and have one entry per species, not per atom. By contrast, MAGMOM is atom-resolved. For the Dudarev choice LDAUTYPE=2, the relevant interaction is U_eff=U−J; using J=0 makes the listed U equal U_eff. Other LDAUTYPE choices do not share that simplification. LDAUTYPE=3 is a response-perturbation workflow for estimating U, not an interchangeable production setting. LDAUL, LDAUU, LDAUTYPE
Work through competing states
First converge several physically motivated initial magnetic arrangements at the same structure and same U. Inspect moments and occupation matrices after convergence; an SCF energy tolerance alone does not identify which local minimum was found. Then relax the selected candidate structures using that same model, followed by static comparisons. If different initializations yield different orbital or magnetic states, preserve them in separate directories and report the search rather than silently keeping the first converged run.
For DOS and ordinary DFT+U band calculations, retain the U settings and the same PAW convention. Generate the source CHGCAR with sufficiently large LMAXMIX: 4 for d and 6 for f manifolds as appropriate. A restart with truncated on-site occupation information can change the potential. Do not remove U in the plotting step because “the geometry already contains its effect.” Geometry and electronic Hamiltonian are separate parts of the calculation.
Checks, caveats, exercise
Converge cutoff and k sampling within each fixed model. Compare phase energies or magnetic-order energies using identical U/J and comparable numerical settings; changing U changes the functional, so selecting the lowest absolute total energy across a U sweep is not a method for choosing U. Use a sensitivity study instead: how robust are the magnetic order, gap, lattice parameter, or orbital character across a justified range? Check more than one observable, and explain whether U came from literature, linear response, constrained screening, or fitting.
DFT+U remains a static mean-field treatment. It does not automatically capture dynamical correlation, temperature-dependent spectral satellites, or a paramagnetic ensemble. A calculated gap may still differ from photoemission or optical measurements for reasons beyond the chosen U. Exercise: at one fixed U, compare two allowed magnetic initializations; then change U for a sensitivity study without ranking different-U total energies as if they used one Hamiltonian. Submit the surviving states, moment patterns, DOS changes, and all parameter definitions.
4.6.3 Unexecuted inputs and analysis scaffolds
These are unexecuted teaching inputs and starting settings to test. Original figures are schematics, not computed results. Use licensed VASP and PAW data, replace every placeholder, record the executable version and validate convergence.
4.6.3.1 Input block 1
# Replace U_CHOSEN and the per-atom MAGMOM list before running
LDAU = .TRUE.
LDAUTYPE = 2
LDAUL = 2 -1
LDAUU = U_CHOSEN 0
LDAUJ = 0 0
LMAXMIX = 4
LASPH = .TRUE.
ISPIN = 2
LDAUPRINT = 1
# MAGMOM = <one collinear starting moment per atom, in POSCAR order>
4.6.4 Related learning paths
- 1.1 Four input files, one physical question
- 1.2 A convergence laboratory with an error budget
- 4.5 Bader populations and charge conventions
- 4.7 Hybrid band gaps and the correct band workflow