First principles approaches and concepts for electrochemical systems

TL;DR

This paper surveys first-principles strategies for modeling electrified solid/liquid interfaces, arguing that open thermodynamic boundary conditions are essential to reproduce realistic potential fluctuations and reaction energetics. It analyzes surrogate double-layer models, a spectrum of electrostatic boundary conditions, and band-structure constraints that influence interfacial fields and stability. A key contribution is the thermopotentiostat framework, grounded in the fluctuation-dissipation theorem, which enables open-electrode charge control and realistic sampling of voltage and charge distributions during electrochemical processes. The authors advocate moving beyond constant-field or constant-charge schemes toward fully open simulations to capture both rapid electrode responses and slow double-layer relaxations, while acknowledging computational challenges and outlining avenues—such as machine learning potentials and QM/MM hybrids—to reach practically relevant time scales and more complex reaction networks.

Abstract

Ab initio techniques have revolutionised the way in which theory can help practitioners to explore critical mechanisms that govern reactions or properties, and to develop new strategies for materials discovery and design. Yet, their application to electrochemical systems is still limited, due to the challenges electronic structure calculations face in achieving a realistic description of electrified solid/liquid interfaces including, e.g., potential and pH control or free energies of barrier configurations. A well-known example of how novel concepts can extend the scope of simulations is the development of thermostats, which introduced temperature control to electronic structure Density Functional Theory (DFT) calculations. The analogous technique for modelling electrochemical systems - potential control, inherent to most electrochemical experiments - is just emerging. In this review, we critically discuss state-of-the-art approaches to describe electrified interfaces between a solid electrode and a liquid electrolyte in realistic environments. By exchanging energy, electronic charge and ions with their environment, electrochemical interfaces are thermodynamically open systems. In addition, large fluctuations of the electrostatic potential and field occur on the time and length scales relevant to chemical reactions. We systematically discuss the key challenges in incorporating these features into realistic ab initio simulations, as well as the available techniques and approaches to overcome them, in order to facilitate the development and use of these novel techniques by the wider community. These methodological developments provide researchers with a new level of realism to explore fundamental electrochemical mechanisms and reactions from first principles.

Figures (5)

• Figure 1: Schematic representation of an electrochemical system at the three major length- and time-scales - macroscopic, mesoscopic and microscopic - together with the corresponding electrostatic potential perpendicular to the solid/liquid interface and laterally averaged. Each of the three electrostatic potentials in the microscopic scale image represents a different configuration obtained from an ab initio molecular dynamics simulation. The fluctuation induced distributions of key electrochemical quantities such as surface charge, potential (with $\sigma_\Phi$ being the variance in the potential) and temperature are shown for the microscopic (top-left) and the meso/macro-scale (bottom-right). They show the variation of these quantities over the different snapshots.
• Figure 2: a) Comparison between the potential in the macroscopic system and the potential obtained in DFT supercell simulations via a surrogate model for the electric double layer. The potentials need to agree within the microscopic electrochemically active region. To ensure charge neutrality, the residual fraction of the double layer charge that is outside of the supercell must be placed on the double layer surrogate model. Therefore, at larger distances both potentials differ by a constant amount. A suitable correction can be performed a posteriori. For the electrostatic potential $\Phi$ we follow the sign convention common to ab initio calculations, but note that this is opposite to the sign convention used in classical electrostatics. b) The active region described within the supercell. The potential distribution of the macroscopic system is replicated via introducing a surrogate model for the electrochemical double layer. The surrogate model carries a net charge for compensating the surface charge on the explicit working electrode (see Fig. \ref{['fig3']} for common realizations of the surrogate model). Note that under reactive conditions, the compensating charge on the surrogate model is not constant but needs to be treated dynamically.
• Figure 3: The various approaches used to achieve a charged (electrified) electrode-electrolyte interface within a DFT supercell. Electrodes are shown as grey rectangles at the edge(s) of the supercell (marked by a dotted line) and the electrolyte as a blue area within it. Ions and charges at the electrodes are shown as spheres containing a plus or minus, while atoms are shown as coloured spheres. The resulting electrostatic potential curve is depicted by the red line. The realization and distribution of the countercharge introduced by each of these methods to keep the total charge of the supercell at zero is shown in green (filled spheres represent explicit ions, hatched green spheres represent virtual charges that are a consequence of the respective method and do not need to be added explicitly, and green shapes represent continuous densities, e.g. introduced by a constant background (jellium) in Fig. a).
• Figure 4: a) Schematic representation of the supercell with an applied voltage between the working electrode and the surrogate double layer model. Voltages are measured between the working electrode and regions in close vicinity to the electrode surface ($U_g$) or deeper within the electrolyte region ($U_i$), respectively. b/c) Measured voltage distributions for different electrostatic boundary conditions flucts, see text. The height of the delta peak in b) is rescaled for better visibility.
• Figure 5: a) Schematic representation of the band structure across an electrode-electrolyte interface. The field is applied via a semiconducting computational counter electrode (CCE) outside the electrolyte region. The Fermi level can be adjusted freely within the electronic gap of the electrolyte and the CCE. b) Sufficiently strong applied fields are able to tilt the bands of the electrolyte, so that the Fermi level straddles either the valence or conduction band edge. Dielectric breakdown will occur. A corresponding charge transfer between the working electrode and the CCE reduces the field so that the Fermi level is moved back to the band edge. c) Stronger fields can be applied at the same voltage without dielectric breakdown by moving the counter charge closer to the working electrode surface.