User-defined Electrostatic Potentials in DFT Supercell Calculations: Implementation and Application to Electrified Interfaces

TL;DR

The paper presents a modular approach to applying user-defined electrostatic potentials within DFT calculations using the VASP-Python interface, including necessary energy and force corrections to preserve physical realism. It formalizes how to modify the energy functional with an external potential $V_{ext}$ and implements practical callbacks for potential, force, and occupancy updates, enabling quasi-static field simulations and time-dependent bias control via a thermopotentiostat. The method is demonstrated across case studies on adsorbed species under bias, field-driven surface phenomena relevant to atom probe tomography, electrified electrochemical interfaces, and QM/MM/implicit solvation models, highlighting both versatility and accuracy. This framework extends standard DFT workflows to robustly simulate electrified interfaces and solvated environments, with broad implications for catalysis, corrosion, and nanoscale device physics.

Abstract

Introducing electric fields into density functional theory (DFT) calculations is essential for understanding electrochemical processes, interfacial phenomena, and the behavior of materials under applied bias. However, applying user-defined electrostatic potentials in DFT is nontrivial and often requires direct modification to the specific DFT code. In this work, we present an implementation for supercell DFT calculations under arbitrary electric fields and discuss the required corrections to the energies and forces. The implementation is realized through the recently released VASP-Python interface, enabling the application of user-defined fields directly within the standard VASP software and providing great flexibility and control. We demonstrate the application of this approach with diverse case studies, including molecular adsorption on electrified surfaces, field ion microscopy, electrochemical solid-water interfaces, and implicit solvent models.

Figures (8)

• Figure 1: Flowchart of the VASP-Python plugin setup during a Molecular Dynamics-DFT simulation. $\Delta F_I$, $\Delta E_I$, $n_{e-}$, $V_{ext}$ and $Z_{I}$ refer to the forces, total energies, number of electrons, external potential and nuclear charges, respectively.
• Figure 2: (a) Energy of a hydrogen atom in a constant potential $V_{ext}$ before and after the core correction (see text). The black dashed line represents the energy equal to $1e\cdot V_{ext}$. (b) The force in the $z$ direction of a hydrogen atom in a linear potential corresponding to a constant field $\mathcal{E}^{\mathrm{ext}}$ before and after the correction. The black dashed line represents the force equal to $1e\cdot \mathcal{E}^{\mathrm{ext}}$.
• Figure 3: Schematics of simulating charged surface using the a) Ne computational counter electrode (CCE) setup and the b) charge density counter electrode (CDCE) setup. The working electrode has a net charge of $n_{electrode}$, which is compensated by the counter electrode, thus creating an electric field $\mathcal{E}$ across the simulation cell. The black lines represent the electrostatic potential $\Phi$.
• Figure 4: a) Electrostatic potential of the Au(111) surface for several electrode charges; the red curve corresponds to the Gaussian charge‑density counter electrode (CDCE). b) Adsorption energies of a single H atom on Au(111) as a function of the applied electric field. c) Charge‑density difference for $n_{\text{electrode}} = 0$, computed with Eq. \ref{['Eq:AuH_chg_diff']} and an isosurface value of $1.5\times10^{-6}\ e/\mathrm{\AA}^3$. d) Charge‑density difference for $n_{\text{electrode}} = -0.5\,e^{-}$, computed with Eq. \ref{['Eq:AuH_double_chg_diff']} and an isosurface value of $1.5\times10^{-7}\ e/\mathrm{\AA}^3$. Yellow denotes excess electronic charge (negative charge density), while cyan denotes a deficit of electronic charge (positive charge density).
• Figure 5: AIMD simulations of an acetaldehyde molecule adsorbed on the Au(111) surface under applied field, showing the dependence of Au-O distance with $n_{electrode}$.