Band-structure calculation using hybrid functionals

For hybrid functionals, the Hamiltonian cannot be expressed in terms of the electronic charge density alone. Instead, the Kohn-Sham orbitals on a regular k mesh are required for any calculation within the formalism of hybrid functionals. The regular k mesh must be supplied in the KPOINTS file. Consequently, restarting a hybrid calculation requires the WAVECAR file of the previous self-consistent-field (SCF) run. This is in contrast to density-functional theory (DFT) where the electronic charge density written to the CHGCAR file suffices to restart a DFT calculation.

Step 1: Run an SCF calculation to obtain a converged WAVECAR file.

Band-structure calculations generally compute the Kohn-Sham orbitals and eigenenergies along a path in reciprocal space which usually connects high-symmetry points in the first Brillouin zone. Some external tools help to identify the high-symmetry points and k points along a high-symmetry path for materials of any symmetry.

Step 2: Determine the high-symmetry points along which VASP should compute the band structure.

There are two options to simultaneously supply a regular k mesh and k points along a high-symmetry path to VASP.

1. Read an explicit list of k points with zero-weighted k points.

Here, the explicit list of the irreducible k points of the regular k mesh can be copied from the IBZKPT file of a previous run to the KPOINTS file. These irreducible k points must be weighted by their multiplicity according to the symmetry of the system. Additionally, the k points along a high-symmetry path must be added to the KPOINTS file with the value of all weights set to zero.

2. Read an additional KPOINTS_OPT file that can specify the high-symmetry path in line mode.

Generally, the KPOINTS file and the KPOINTS_OPT file accept the same format. But again, the regular k mesh needs to be supplied in the KPOINTS file and the high-symmetry path in the KPOINTS_OPT file. We therefore recommend using the Γ-centered mesh or Monkhorst-Pack mesh and providing the high-symmetry path in line mode, respectively.

EXAMPLE FILE!!

Step 3: Supply a regular k mesh and k points along a high-symmetry path either using the explicit list including zero-weighted k points or using a KPOINTS_OPT file and restart the hybrid calculation from the converged WAVECAR file.

For instance, for fcc Si with the following POSCAR file

 system Si
 5.430 
 0.0 0.5 0.5
 0.5 0.0 0.5
 0.5 0.5 0.0
 2
 cart
 0.00 0.00 0.00
 0.25 0.25 0.25

from Γ to X

 Explicit k-points list
     14
 Reciprocal lattice
   < ... >
   0.0000000000     0.0000000000     0.0000000000 0
   0.1000000000     0.0000000000     0.1000000000 0
   0.2000000000     0.0000000000     0.2000000000 0
   0.3000000000     0.0000000000     0.3000000000 0
   0.4000000000     0.0000000000     0.4000000000 0
   0.5000000000     0.0000000000     0.5000000000 0

 Special k-points for band structure
 <...>  ! intersections 
 line-mode
 reciprocal
   0.0000000000     0.0000000000     0.0000000000 Γ
   0.5000000000     0.0000000000     0.5000000000 X 

The KPOINTS_OPT file can also be provided when starting from scratch. While this reduces the number of steps required to compute the band structure, it affects how the Coulomb-convergence can be treated during the SCF run. In other words, FOCKCORR=2 should not be used when computing the band structure with either option of supplying the k points.

KPOINTS_OPT_NKBATCH for controlling the batch size.

Warning: The electronic charge density must not be fixed for calculations using hybrid functionals, i.e., never set ICHARG=11!

This is in stark contrast to density functionals where the electronic charge density can be fixed during a band-structure calculation (ICHARG=11) and no regular k mesh is required.

Related tags and articles

KPOINTS, KPOINTS_OPT, Hybrid functionals