Band Structure with Quantum ESPRESSO (HSE)¶

This tutorial explains how to calculate the electronic band structure of crystalline silicon in its cubic-diamond crystal structure using the HSE (Heyd–Scuseria–Ernzerhof) hybrid functional with Quantum ESPRESSO.

Quantum ESPRESSO version

This tutorial applies to Quantum ESPRESSO versions 5.2.1, 5.4.0, 6.0.0, 6.3, and later.

The instructions here complement the general band structure tutorial. Only HSE-specific aspects are covered below.

1. Understand the HSE workflow¶

A Quantum ESPRESSO workflow for computing the band structure with HSE is composed of three subworkflow steps:

1.1. Preliminary SCF calculation¶

The first step is a standard self-consistent field (SCF) calculation of the ground-state energy eigenvalues and wave functions. This provides the k-point grid that is manually extracted in the next step.

1.2. Extract k-points¶

Unlike the standard band structure calculation, which proceeds via a non-self-consistent calculation, the HSE approach requires self-consistent evaluation of the Fock operator ¹ ² at each k-point on a commensurate grid.

The k-points generated in the SCF step are automatically extracted via a Python script that uses Regular Expressions to parse the output. The resulting list is saved as a JSON file for use in the next step.

1.3. HSE calculation¶

The final step contains two units. The main HSE calculation is performed in the first unit. HSE-specific parameters are triggered by including the HSE Refiner, set under the Subworkflow Editor.

Key aspects of the HSE input configuration:

Exchange-correlation functional: Activated via input_dft = 'hse' in the Quantum ESPRESSO input script.
q-grid for the Fock operator: Defined via nqx1, nqx2, nqx3. For basic band structure calculations, a size of 1 is sufficient. For accurate band gap estimates, see the HSE band gap tutorial.
k-point list: Imported from the extracted JSON rather than auto-generated.
k-path: A second list of k-points defining the path for the band structure dispersion curve, customizable under Important Settings.

Weight of k-path points

The k-path points are assigned very small weights (<1e-7) so they do not interfere with the HSE electronic structure computation — they are only needed for plotting the dispersion curve. The weights are not exactly zero because Quantum ESPRESSO requires non-zero values.

The final band structure is computed via the bands.x executable.

2. Import the HSE workflow from the bank¶

Workflows for the HSE band structure calculation with Quantum ESPRESSO can be imported from the Workflows Bank into the account-owned collection. The workflow can then be selected and added to the job being created.

Computational cost

HSE calculations are significantly more expensive than standard GGA-DFT. More CPU cores and/or walltime should be allocated as appropriate.

3. Video walkthrough¶

The animation below demonstrates the creation and execution of an HSE band structure computation on silicon using Quantum ESPRESSO, concluding with the dispersion plot in the Results tab of Job Viewer.