7.1 DFT+U and correlated-subspace choices
7.1.1 Question, prerequisites and version boundary
Why can a transition-metal oxide converge smoothly yet yield a misleading electronic state? A semilocal functional can favor excessive delocalization of localized electrons. DFT+U changes the functional within a chosen correlated subspace. It does not repair every error in a pseudopotential, numerical orbital, crystal structure or magnetic model.
This case is an unexecuted learning template pinned to the ABACUS 3.9.0 keyword documentation. Do not transplant projector selectors from older articles: this release distinguishes radius-adjustable projections with dft_plus_u 1 from the older first-zeta numerical-orbital projection with dft_plus_u 2. Later releases must be checked against their own manual. The example deliberately teaches the explicitly documented older LCAO projection as a controlled comparison; it is not a recommendation that it is the best production method.
Complete the first LCAO calculation and collinear magnetism. For the real oxide, replace the silicon structure and every species-dependent asset together. Obtain a physically justified NiO structure with Ni then O as the species order, compatible PBE pseudopotentials and matching numerical orbitals. An antiferromagnetic cell needs enough sites to represent alternating moments; do not call a two-atom chemical cell an antiferromagnetic reference without examining its periodic spin pattern.
7.1.2 The subspace is part of the model
In the rotationally invariant simplified picture,
The occupation matrix \(n^{I\sigma}\) depends on the localized projectors. A fractional occupation is penalized relative to an integer occupation; the correction also changes the self-consistent potential. Consequently, two definitions of the local subspace need not produce the same gap or moment for the same numerical U. A U borrowed from a different code, orbital radius or pseudopotential is a hypothesis, not a transferable constant.
The figure is an original conceptual construction. Its occupation curve is the analytic correction above, not an ABACUS result. The two projector envelopes indicate different definitions of what counts as local; their sizes are not fitted material parameters.
7.1.3 Worked INPUT delta and species mapping
Copy an independently converged NiO LCAO PBE magnetic parent, keeping its full INPUT, STRU and KPT. Replace existing keys rather than appending duplicates. The following is the advanced-method delta, not a complete NiO input:
# ABACUS 3.9.0; conditional Ni,O species order in STRU
suffix NiO_U4_legacy
basis_type lcao
dft_functional pbe
nspin 2
dft_plus_u 2
orbital_corr 2 -1
hubbard_u 4.0 0.0
out_chg 1
Here orbital_corr 2 -1 selects Ni d orbitals and excludes O. hubbard_u is an eV-valued, species-ordered vector of effective U, so 4.0 is only a teaching trial. The vector length must equal the number of species in STRU, Use one Ni species and assign alternating per-atom initial moments with the documented STRU syntax when constructing an antiferromagnetic cell; no arbitrary species-alias syntax is assumed here.
For the newer projector route in 3.9.0, select dft_plus_u 1 and use a justified onsite_radius from the matching official example and orbital construction. This course does not invent a radius or claim the two projector routes are equivalent. Record its documented units and normalization for your installed release before running that branch. First establish a U=0 comparison with otherwise identical files.
7.1.4 Workflow and reading the output
Keep the ions fixed for the first study. Run semilocal and corrected calculations with the same structure, orbital set, cutoff, KPT, occupations and convergence thresholds. Use multiple initial magnetic patterns, and inspect the electronic residual and final local moments rather than only the last total-energy line. A well-converged metastable occupation is possible.
Read OUT.<suffix>/running_scf.log for the version banner, accepted basis and functional, SCF termination and energies. Preserve the complete output directory. If your release writes onsite.dm, archive that occupation information as well: subsequent DFT+U NSCF work may require it in addition to the charge density. Do not infer that a cube file alone contains the correlated occupation state. Use the version-specific DOS workflow before comparing gaps.
Build separate folders for U trials and magnetic seeds. The U sweep is a sensitivity study of different models, not ordinary numerical convergence. Total energies from different U values are not a phase-ranking dataset for one fixed Hamiltonian. Compare magnetic states at a fixed U, projector definition and stoichiometry; compare observables across U to an explicitly chosen physical reference.
7.1.5 Convergence record and decision rule
Leave these cells empty until calculations have actually been performed. Tighten the orbital set, integration grid and k mesh at fixed U before discussing its effect.
| Ueff (eV) | Projector definition | k mesh / orbital hash | Initial magnetic state | SCF accepted? | Gap (eV) | Site moments | Relative energy within fixed U (eV) |
|---|---|---|---|---|---|---|---|
| 0 | recorded | ||||||
| 2 | recorded | ||||||
| 4 | recorded | ||||||
| 6 | recorded |
Choose tolerances from the scientific question. A phase splitting of a few meV demands much tighter numerical agreement than a qualitative insulating-versus-metallic diagnosis. If increasing the orbital quality changes the local occupations strongly, the subspace or basis needs attention before interpreting U dependence. If the SCF falls into different solutions from different seeds, report that multiplicity instead of hiding it behind a single value.
7.1.6 Pitfalls, exercises and answers
Pitfalls. A species-order mistake can correct oxygen instead of the metal. Treating Ueff as U and supplying an additional undocumented J double counts the intended adjustment. Reusing a charge file from a different spin representation, geometry or projector route obscures the baseline. Relaxing each U structure before comparing vertical electronic changes mixes a structural response into the electronic effect. Occupation matrices and Mulliken moments are basis-dependent descriptors, not directly identical experimental observables.
Exercise 1. STRU lists O then Ni. Write the vectors for a trial Ueff=4 eV on Ni. Answer: orbital_corr -1 2 and hubbard_u 0.0 4.0; then confirm the labels map to the intended pseudopotential and orbital assets.
Exercise 2. A U=4 run has a larger gap than U=2 but a smaller total energy. Does it prove U=4 is more accurate? Answer: no. The functionals differ, and accuracy needs an external target or a principled U construction. Compare numerical convergence and magnetic branches within each model, then describe the observable sensitivity without selecting U solely to obtain a desired gap.
7.1.7 Sources and next case
- ABACUS 3.9.0 DFT+U keywords: projector selector, species vectors and effective-U semantics.
- ABACUS 3.9.0 release record: the release boundary used here.
- Dudarev and colleagues, simplified rotationally invariant correction: the physical model behind the equation.
Continue with hybrid functionals, another model change with its own numerical controls.