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Phonon Dispersions and Density of States Calculation

This tutorial page explains how to calculate the Phonon Dispersion Curves and Phonon Density of States of materials 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.

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

Workflows for calculating the Phonon Dispersion Curves and Density of States 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 q-point density in order to resolve enough details for the phonon dispersion plot.

The Phonon calculation workflow based on Quantum ESPRESSO is composed of multiple units. The first unit specifies the settings for the self-consistent calculation of the energy eigenvalues and wave functions. The subsequent units are narrated in detail in the theoretical explanation contained in Ref. [^1] of this page.

We set the size of the grid of q-points (q-grid) to 3 x 3 x 3 under the Important Settings of Workflow Designer. This provides a dense enough q-point sampling in order to resolve the fine features present within the output of the phonon dispersion computation. In order to make the q- and k-point grids commensurate and make the phonon calculation less computationally demanding, we also reduce the size of the grid of electronic k-points from its original default value to 6 x 6 x 6.

In addition, the associated "interpolated" grid or i-grid necessary for performing the transformation to and from the reciprocal and real space, and subsequent interpolation, should be set to 18 x 18 x 18.

Finally, we also apply the recommended q-point path to effectively sample the vibrational states throughout the Brillouin Zone of the crystal, based on the crystal symmetry.

Submit Job

Before submitting the job, the user should click on the "Compute" tab of Job Designer and examine the compute parameters included therein.

Phonon calculations are quite computationally expensive and therefore, despite Silicon being a small structure, with the aforementioned settings for the sampling grids the user should account for at least 45 minutes of calculation runtime executed on 16 compute cores for example.

Examine Final Results

When all unit computations are complete at the end of Job execution, switching to the Results tab of Job Viewer will show the phonon lattice vibrations of silicon, plotted as a dispersion curve on the q-point path chosen in the preceding steps.

The plot for the Phonon Density of States can also be retrieved in the Results tab, directly above the dispersion curve.


We demonstrate the above-mentioned steps involved in the creation and execution of a phonon lattice vibration calculation for silicon, using the Quantum ESPRESSO simulation engine, in the following animation.