Band-structure calculation using density-functional theory

Calculating the band structure for density-functional theory (DFT) requires multiple steps. On this page, you will find step-by-step instructions, as well as references to some practical examples to explore.

Obtaining the band structure requires solving the Hamiltonian to get eigenvalues and eigenvectors, which can then be plotted to obtain the band structure. In DFT, you need at least the density (charge and magnetization) and possibly higher derivatives depending on the XC functional.

The unified approach presented on this page applies to LDA (needs density), GGA (needs density and gradient) and deorbitalized meta-GGA (needs density, gradient and Laplacian) functionals. In contrast, meta-GGAs need the kinetic energy density and follow a different approach. A different approach is also required when using hybrid functionals.

For DFT, the Hamiltonian can be expressed in terms of the electronic charge and magnetization density. Both are written to to the CHGCAR file during an initial, self-consistent-field (SCF) run. The CHGCAR file obtained in such a run is required to restart a DFT calculation or compute the band structure. It allows to then perform an NSCF (=fixed density) calculation to obtain the eigenvalues at the desired high-symmetry path.

Step-by-step instructions

If you want to compute a DFT (LDA/GGA/deorbitalized meta-GGA) band structure, please adhere to the following steps:

1. Perform a self-consistent field calculation

If you already have a converged CHGCAR file of a self-consistent (SCF) calculation, you can skip this step.

Otherwise, in order to obtain a converged CHGCAR, perform a static (NSW=0, IBRION=-1) self-consistent-field (SCF) calculation for DFT. To achieve this, you will need:

• POSCAR containing structure information,

• INCAR containing any required tags (NSW=0, IBRION=-1, plus other tags as needed),

• KPOINTS containing a regular k mesh, using e.g. Γ-centered mesh or Monkhorst-Pack mesh,

• POTCAR containing the required pseudopotentials.

Warning: For the initial SCF run to obtain the converged CHGCAR file, do not specify the ICHARG tag. You may find mentions of the ICHARG tag related to DFT band-structure calculations: This is specific to later steps.

Once everything has been set up, start VASP and wait for the calculation to converge.

2. Set the high-symmetry path

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. Which k points are high-symmetry points depends on the space group of your structure.

Some external tools can be employed to find the space group and plot the Brillouin zone to pick a k path. Extract the coordinates corresponding to the desired k path to your KPOINTS file (they replace the previous regular k mesh from step 1). You may wish to preserve the SCF run from step 1 in a separate folder, then copy INCAR, POSCAR, POTCAR, CHGCAR and KPOINTS to a new folder before making edits to KPOINTS.

An example for what such a KPOINTS file might look like (example for fcc Si):

 k points for band structure
 10  ! intersections 
 line
 Fractional
   0.50000  0.50000  0.50000   L
   0.00000  0.00000  0.00000   G
   
   0.00000  0.00000  0.00000   G
   0.00000  0.50000  0.50000   X
   
   0.00000  0.50000  0.50000   X
   0.25000  0.62500  0.62500   U
   
   0.37500  0.7500   0.37500   K
   0.00000  0.00000  0.00000   G

Mind: As of VASP 6.3.0, you may write k points of high-symmetry paths to a KPOINTS_OPT file. This allows you to combine steps 1 & 3 into one single VASP run. If all you want to do is compute the band structure, this might be preferable, although the SCF run (step 1) is typically the expensive task and splitting them up is generally recommended. However, if you still want to do it all in one go: Set up your INCAR, POSCAR, KPOINTS & POTCAR files as explained in step 1. Your KPOINTS file holds a regular k mesh. Do not specify the ICHARG tag in your INCAR. Set up your KPOINTS_OPT file with the desired high-symmetry path. Start a VASP run. Proceed to step 4 to learn about plotting the band structure.

3. Calculate the band structure

Please follow the next steps exactly:

• You may wish to copy your INCAR, POSCAR, POTCAR, KPOINTS and CHGCAR from step 1 to a new folder before proceeding, as suggested in step 2. If you decide to do so, navigate to the new folder.

• Make sure the KPOINTS file now holds the high-symmetry path determined in step 2.

• We also need to add the ICHARG=11 tag to the INCAR file. Setting ICHARG=11 allows the DFT calculation to pick up from the CHGCAR at the same densities. Notice that the computed Fermi energy for this case will no longer be correct once a k path has been declared and the k mesh is no longer regular.

• Then, start another VASP run. This will restart the DFT calculation from the CHGCAR file.

4. Visualization using py4vasp (optional)

Plot the band structure, e.g., using py4vasp. In a python notebook in the directory of the calculation, you can run the following code:

import py4vasp
calc = p4vasp.Calculation.from_path(".")
calc.band.plot()
# calc.band.plot("kpoints_opt") # if the high-symmetry path is in KPOINTS_OPT

Mind: If you are using KPOINTS_OPT for the high-symmetry path as outlined in the side note in step 2 for VASP>6.3.0, you need to pass "kpoints_opt" as an argument to calc.band.plot: calc.band.plot("kpoints_opt")

Recommendations and advice

In case a KPOINTS_OPT file is present, VASP computes the band energies for the k points of the KPOINTS_OPT file after SCF is reached within the same submitted job. Therefore, there is no computational advantage to splitting the run into two steps (one for SCF, and one for computing the band structure at fixed density). However, reaching convergence for the SCF run and obtaining the converged CHGCAR file is typically more expensive, and storing these results somewhere might be beneficial. Besides, the SCF results may serve as a starting point for subsequent calculations.

Practical examples

We offer additional tutorials for calculating and visualizing DFT band structures:

• Bulk systems, Part 1: band structure of face-centered-cubic silicon.

• Bulk systems, Part 2: band structure of cubic-diamond silicon.

• Bulk systems, Part 3: band structure of face-centered-cubic nickel.

Related tags and articles

KPOINTS, KPOINTS_OPT, ICHARG, LDA, GGA, Band structure for meta-GGA functionals, Band structure for hybrid functionals