4.7 Hybrid band gaps and the correct band workflow
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.
4.7.1 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.
4.7.2 Worked case: procedure, interpretation and checks
What changes relative to semilocal DFT
A hybrid functional includes an orbital-dependent exact-exchange contribution. The Hamiltonian therefore requires information from occupied orbitals on a regular mesh; a CHGCAR alone cannot reconstruct it. This is why the semilocal trick “replace KPOINTS with a path and set ICHARG=11” is wrong for hybrid bands. Higher computational cost does not excuse an inconsistent sampling procedure.
Begin with a converged PBE structure and orbitals for a small nonmagnetic semiconductor. State whether the geometry is PBE-relaxed or hybrid-relaxed. Those choices isolate different effects. HSE06 often provides a useful comparison with PBE, but agreement with a measured optical onset is not guaranteed: excitons, temperature, zero-point motion, and geometry may matter.
Ground state and path in a supported release
For an HSE06 branch, retain the converged physical setup and use:
HFSCREEN is in Å⁻¹: 0.2 corresponds to the usual HSE06 range separation in this PBE-based setup. LHFCALC alone does not mean HSE06. The illustrative damping timestep may need reduction if minimization oscillates. Avoid ALGO=Fast for this branch; choose a documented hybrid-compatible optimizer. HFSCREEN, LHFCALC
With VASP 6.3.0 or newer, retain the regular mesh in KPOINTS and provide the cell-specific path separately in KPOINTS_OPT. Use a compatible source WAVECAR when restarting; verify that VASP actually reads it. The official hybrid-band guidance recommends a suitable Coulomb singularity treatment, with HFRCUT=-1 particularly useful for gapped systems. Converge the mesh for the chosen treatment rather than viewing that flag as a universal numerical cure. Hybrid band workflow, HFRCUT
An older alternative combines the weighted regular-mesh points with zero-weight path points in one explicit KPOINTS list. Preserve the mesh weights and symmetry assumptions. A small total-energy change can stop the run before zero-weight orbitals have converged; assess those eigenvalues independently, especially when restarting from already converged hybrid orbitals. Do not set the entire path to nonzero equal weights, which would change the ground-state integration. The OPT route is simpler when available.
Readout, convergence, and exercise
Extract the path eigenvalues from the output appropriate to that route. Use the regular-mesh reference for alignment, and separately establish the global valence maximum and conduction minimum. A high-symmetry drawing alone cannot prove the fundamental gap. Compare PBE and HSE at identical geometry first, then study geometry effects if relevant. Label “generalized Kohn–Sham gap,” not “measured optical gap.”
Converge the regular mesh, cutoff, empty-band coverage, and electronic tolerance. If exchange downsampling is introduced for cost reasons, benchmark it against a denser exchange treatment before interpreting small differences. Inspect discontinuities at path boundaries and repeated points. Repeating a path point should reproduce its energy within the numerical tolerance after the same alignment; a jump is a diagnostic, not an exotic dispersion to explain away.
Exercise: compute a short hybrid path with the regular mesh retained, then repeat with a denser SCF mesh. Compare a chosen direct transition and the minimum gap on a separate mesh search. Document what changes when geometry is held fixed. Do not fit AEXX to one experimental gap and then call the result a parameter-free prediction.
4.7.3 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.
4.7.3.1 Input block 1
GGA = PE
LHFCALC = .TRUE.
AEXX = 0.25
HFSCREEN = 0.2
ALGO = Damped
TIME = 0.4
NSW = 0
EDIFF = 1E-7
ISMEAR = 0
SIGMA = 0.02
LWAVE = .TRUE.
# Keep the regular SCF KPOINTS mesh. Do not set ICHARG=11.
4.7.4 Related learning paths
- 1.1 Four input files, one physical question
- 1.2 A convergence laboratory with an error budget
- 4.6 DFT+U with an explicit model choice
- 4.8 SOC and noncollinear magnetism
- 4.2 Bands and effective masses