Electronic Band Structure Calculation

This tutorial explains how to calculate the electronic band structure of crystalline silicon in the standard cubic-diamond crystal structure, based on Density Functional Theory (DFT). Quantum ESPRESSO is used as the simulation engine.

Quantum ESPRESSO version

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

Accuracy of the results

This calculation uses standard DFT, which is known to underestimate the energy of unoccupied electronic states. More accurate methods such as HSE and GW are covered in separate tutorials.

1. Create a job

Silicon in its cubic-diamond crystal structure is the default material loaded on new job creation, unless the default was changed after account creation. If silicon is still the default, it is automatically loaded when the Job Designer is opened.

2. Select the workflow

Workflows for calculating the band structure 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.

3. Set sampling in reciprocal space

A high k-point density is critical for resolving the fine features of the band structure plot.

The band structure workflow is composed of two units. The first unit performs a self-consistent field (SCF) calculation of the energy eigenvalues and wave functions. The second unit performs a non-self-consistent calculation using the wave functions and charge density from the first step.

The k-point grid is set to 18 × 18 × 18 in the first workflow unit. This provides dense enough sampling to resolve the features in the band structure output. The validity of this grid size for yielding meV-level accuracy can be verified by performing a convergence study.

In addition, the recommended k-point path is applied to sample the electronic states throughout the Brillouin Zone, based on the crystal symmetry.

4. Submit the job

Before submitting the job, the Compute tab of Job Designer should be reviewed to verify the compute parameters. Silicon is a small structure, so 4 CPUs and 1 minute of calculation runtime are sufficient.

5. Examine the results

Once both unit computations complete, the Results tab of Job Viewer displays the band structure of silicon, plotted as a dispersion curve along the selected k-point path.

6. Video walkthrough

The animation below demonstrates the steps involved in the creation and execution of a band structure computation on silicon using Quantum ESPRESSO.