Effective Screening Medium (ESM) Calculation¶

This tutorial demonstrates how to extract potential/charge profiles via the Effective Screening Medium (ESM) approach for simulating surfaces and interfaces, based on Density Functional Theory (DFT). The example system is a water (H₂O) molecule, and 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.

1. Understand the ESM workflow¶

Expand to view input parameter details

The workflow for ESM calculations with Quantum ESPRESSO contains a single main computational unit. Examples of ESM in Quantum ESPRESSO are available in Ref. ¹. The key input parameters are:

assume_isolated = 'esm' — treats the system as isolated (molecule or cluster). For polarized or charged slab calculations, this embeds the simulation cell within an effective semi-infinite medium along z. Embedding regions can be vacuum or semi-infinite metal electrodes. An optional electric field can be applied via esm_efield. The simulation cell must have the \(c\) lattice vector along z, with the slab centered around z=0.

esm_bc — determines the boundary conditions used for either side of the slab.

esm_w — the position offset of the start of the effective screening region, measured relative to the cell edge:

\[ z = \pm [L_z/2 + \text{esm\_w}] \]

esm_efield — magnitude of the electric field applied between semi-infinite ESM electrodes. Applicable only with the metal-slab-metal (bc2) boundary condition.

lfcpopt — if set to .TRUE., performs a constant bias potential (constant-μ) calculation ². Requires calculation = 'relax' and bc2 or bc3 boundary conditions.

fcp_mu — target Fermi energy when lfcpopt = .TRUE..

Two workflow flavors are available: a basic ground-state SCF calculation and a variant that includes structural relaxation during the ESM computation (enabled via calculation = 'relax').

2. Prepare the water molecule¶

The H₂O structure can be imported from the Materials Bank into the account-owned collection.

The structure should then be imported into the Materials Designer to edit its boundary conditions via the Advanced menu.

For this example, select the "Vacuum-Slab-Vacuum" (bc1) boundary condition. Leave the "Offset" to its default zero value, which shifts the vacuum boundaries by half the lattice \(c\) constant.

After setting the boundary conditions, save the structure and exit the Materials Designer.

3. Create the job and import the material¶

Open the Job Designer to create a new Job. The water structure should be selected and imported via the Materials tab.

4. Import the ESM workflow from the bank¶

Workflows for ESM calculations with Quantum ESPRESSO can be imported from the Workflows Bank. Search for the "ESM" keyword in the bank. The workflow can then be selected and added to the job.

5. Configure the important settings¶

Open Important Settings within the Workflow Tab to configure the following boundary condition parameters:

Type of boundary conditions
Offset
Electric Field
Target Fermi Energy

For this example, keep the bc1 boundary conditions and leave the remaining options at their default zero values. Set the k-point grid to 1 × 1 × 1, since the system is a molecule rather than a periodic crystal.

6. Submit the job¶

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

7. Examine the results¶

7.1. Potential energy profile¶

The Results tab of Job Viewer displays the potential energy profile of the water-vacuum system, plotted as energy (eV) versus distance along the z-coordinate, away from the central water slab. The local and Hartree contributions to the potential energy are shown separately.

7.2. Charge density profile¶

The charge density profile is also displayed, showing the charge density (in electron charge units/Å) as a function of the z-coordinate. The 2D (xy-plane) average charge density and electrostatic potentials are printed to the file with the .esm1 extension, accessible via the Files tab.

8. Video walkthrough¶

The animation below demonstrates the creation and execution of an ESM computation on a water molecule using the "Relax" variant of the Quantum ESPRESSO ESM workflow.