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Calculate Surface Energy

This tutorial explains how to calculate the surface energy of crystalline gold (Au) in its equilibrium face-centred cubic (fcc) crystal structure using Density Functional Theory (DFT) 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.

Further information on surface energy calculations and results on a sample material set can be found in Ref. 1.

1. Create the surface

A surface of crystalline gold is created using the Materials Designer following the instructions in this page.

For this example, a simple Au (111) surface with 50% vacuum ratio is used, keeping the supercell dimensions along x-y to 1 and the slab thickness to 3 layers (~10 Å). This yields a total of 3 gold atoms.

2. Understand the workflow structure

Expand to view unit details

The workflow is composed of the following units:

io-slab — An I/O unit that retrieves material identification information from the account-owned collection via the REST API.

slab — An assignment unit that stores the material information as the "SLAB" variable.

io-bulk — Queries the collection for the bulk material identifier stored as metadata within the "SLAB" variable.

bulk — Assigns the bulk material data to the "BULK" variable.

assert-bulk — Verifies that the bulk material exists in the collection. If not, an error is raised.

Missing bulk data

If the bulk material information is not already in the collection, a Total Energy calculation can be prepended to the surface energy workflow.

io-e-bulk — Extracts the Total Energy property of the bulk material.

e-bulk — Assigns the bulk total energy to the "E_BULK" variable.

assert-e-bulk — Asserts that the bulk total energy exists in the collection.

surface — Uses Python logic to compute the magnitude of the vector normal to the surface.

n-bulk / n-slab — Count the total number of atoms in the bulk and slab materials respectively.

pw_scf — Performs an SCF computation to calculate the slab energy. Since the slab is much thinner than it is wide, the k-point grid is set with a smaller z-dimension (e.g. 8 × 8 × 1).

e-slab — Assigns the slab energy to the "E_SLAB" variable.

surface-energy — Computes the final surface energy from "E_BULK" and "E_SLAB" according to the formula.

3. Select the workflow and create the job

Workflows for surface energy calculations 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.

4. Submit the job

Before submitting the job, review the Compute tab of Job Designer to verify the compute parameters. The gold slab is a relatively small structure, so 4 CPUs and a few minutes of runtime are sufficient.

5. Examine the results

Once all units complete, the Results tab of Job Viewer displays the surface energy for Au (0.049 eV/Ų). This result is in good agreement with the tabulated value for the same surface orientation 2.

6. Video walkthrough

The animation below demonstrates the full surface energy workflow on gold using Quantum ESPRESSO.

  1. Tran R., Xu Z., Radhakrishnan B., Winston D., Sun W., Persson K.A., Ong S.P.: "Surface energies of elemental crystals"; Nature Sci. Data., 3 (2016) ↩

  2. Crystalium Surfaces Database ↩