Electronic Band Structure Calculation¶
This tutorial page explains how to calculate the electronic band structure based on Density Functional Theory. We will be studying crystalline Silicon in the standard cubic-diamond crystal structure, and we will use Quantum ESPRESSO as our simulation engine.
Quantum ESPRESSO version considered in this tutorial
The present tutorial is written for Quantum ESPRESSO at versions 5.2.1, 5.4.0, 6.0.0 or 6.3.
Accuracy of the results
Please note that this calculation is performed using standard Density Functional Theory, and therefore an underestimation of the energy of unoccupied electronic states is expected. Further modifications to the input files and settings to correctly predict the band gap are possible, and will be explored later.
Silicon in its cubic-diamond crystal structure is the default material that is shown on new job creation, unless this default was changed by the user following account creation. If silicon is still the default choice, it will as such be automatically loaded at the moment of the opening of Job Designer.
Workflows for calculating the band structure of materials with Quantum ESPRESSO can readily be imported from the Workflows Bank into the account-owned collection. This workflow can later be selected and added to the Job being created.
Set Sampling in Reciprocal Space¶
It is critical to have a high k-point density in order to resolve enough details for the band structure plot.
The band structure workflow is composed of two units. The first unit specifies the settings for the self-consistent calculation of the energy eigenvalues and wave functions. The second unit calculation is a non self-consistent calculation using the wave functions and charge density of the previous calculation.
We set the size of the grid of k-points to 18 x 18 x 18 in the first workflow unit. This provides a dense enough k-point sampling in order to resolve the fine features present within the output of the band structure computation. The validity of this choice of k-grid size for yielding accurate results of order meV in the final energy can be verified by performing the relevant convergence study.
In addition, we also apply the recommended k-point path to effectively sample the electronic states throughout the Brillouin Zone of the crystal, based on the crystal symmetry.
Before submitting the job, the user should click on the "Compute" tab of Job Designer and examine the compute parameters included therein. Silicon is a small structure, so 4 CPUs and 1 minute of calculation runtime should be sufficient.
Examine Final Results¶
When both unit computations are complete at the end of Job execution, switching to the Results tab of Job Viewer will show the band structure of silicon, plotted as a dispersion curve as a function of the special k-point paths chosen.
We demonstrate the above-mentioned steps involved in the creation and execution of a band structure computation on silicon using the Quantum ESPRESSO simulation engine in the following animation.