Band Gap and Density of States with Quantum ESPRESSO (HSE)¶
This tutorial explains how to calculate the electronic band gap and Density of States (DOS) 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 gap tutorial and the HSE band structure tutorial. Only HSE-specific aspects of the band gap and DOS calculation are covered below.
1. Understand the HSE band gap workflow¶
Unlike the HSE band structure computation, where k-points must be extracted and inserted manually, the band gap and DOS calculation uses a k-point grid defined automatically, as in a standard SCF calculation.
The HSE-specific parameters are triggered by including the HSE Refiner, set under the Subworkflow Editor Interface.
For band-gap computations, the "band_gaps" property calculation option must be enabled under the Detailed View tab of the Subworkflow Editor before job execution.
1.1. Workflow units¶
The workflow contains a single subworkflow with two units: the main HSE computation and the DOS extraction via the projwfc.x executable.
1.2. Configure the q-grid¶
An accurate band gap estimate requires a sufficiently large q-grid (k1-k2 mesh for the Fock operator), defined via the nqx1, nqx2, nqx3 input keywords. The q-grid must be a divisor of the k-grid. For this tutorial, the recommended setting is a k-grid of 8 × 8 × 8 with a q-grid of 4 × 4 × 4, configurable under the Important Settings tab of the Subworkflow Editor.
Even k-grid sizes required
The default HSE workflow sets the q-grid to half the k-grid size, so an even k-grid size is always required. If an odd number is entered, it is automatically increased by one (e.g. 5 × 5 × 5 → 6 × 6 × 6, yielding a 3 × 3 × 3 q-grid). This behavior can be overridden by editing the input script directly through the unit editor.
2. Import the HSE workflow from the bank¶
Workflows for the HSE band gap and DOS 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
The recommended grid dimensions require approximately 20–30 minutes on 16 CPU cores. HSE calculations are significantly more expensive than standard GGA-DFT. More CPU cores and/or walltime should be allocated as appropriate.
3. Examine the results¶
The final result of ~1.193 eV for the indirect band gap of silicon is in excellent agreement with the experimental zero-temperature value of 1.17 eV. HSE provides a marked improvement in band gap accuracy compared to the Generalized Gradient Approximation, which significantly underestimates band gaps.
4. Video walkthrough¶
The animation below demonstrates the creation and execution of the HSE band gap and DOS workflow on silicon using Quantum ESPRESSO, concluding with the numerical result in the Results tab of Job Viewer.