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Calculate Electronic Density of States

This tutorial page explains how to calculate the electronic density of states using Density Functional Theory. We study crystalline silicon in its standard equilibrium cubic-diamond crystal structure, and use Quantum ESPRESSO as our main simulation engine during the present tutorial.

Accuracy of the results

Please note that this calculation is performed using Density Functional Theory and the Generalized Gradient Approximation, which is known to under-estimate the energy of unoccupied electronic states.

Create job

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.

Choose Workflow

The Density of States in typically calculated in conjunction with the electronic band structure of the material under investigation, whose computation is the object of a separate tutorial.

Workflows for calculating the band structure together with the Density of States through 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 calculate the density of states with sufficient accuracy. The method for treating partial electronic occupancies is also important in establishing the quality of the computation: the tetrahedron method, for example, is more precise for Density of States calculations.

In Quantum Espresso, the band structure + Density of States workflow has five units in total. The first unit specifies the settings for the self-consistent calculation of the eigenvalues and wave functions. The second unit calculation is a non self-consitent calculation using the wave functions and charge density of the previous calculation. Subsequent units calculate the density of states, and also the projection of those states for partial density of states analysis.

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 Density of States 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.

Submit job

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 four CPUs and one minute of calculation runtime should be sufficient.

Examine results

When all five unit computations are complete at the end of Job execution, switching to the Results tab of Job Viewer will show the density of states for the silicon sample under investigation, together with the partial density of states due to each atom in the structure as well as their s and p electron-like character. Moving the mouse cursor along each data series will highlight the atom's electronic character that the data series corresponds to.

Partial contributions

The numbers represent the order of the current orbital as included inside the pseudopotential, and not the principal quantum number.

Animation

We demonstrate the above-mentioned steps involved in the creation and execution of a Density of States computation on silicon using the Quantum ESPRESSO simulation engine in the following animation.