Changes in the surface energy during the reconstruction of Au(100) and Au(111) electrodes

Practical Applications of Grand-canonical Electronic Structure Calculations in Electrochemical Simulation

Modeling electrified interfaces has long been a great challenge in electrochemistry. In recent years, the grand-canonical treatment for electrons has gradually been developed, and its combination with density functional theory has been widely used to simulate electrochemical processes on an atomistic scale. In this Perspective, we aim to discuss several practical applications of this powerful technique after a short review of necessary fundamentals. We will begin with capacitor-based parametrization method of grand-canonical calculated results. If considering the electrodes under different applied potentials as different materials, the parametrization can be viewed as a kind of "quadratic scaling relation", which might reduce the overall computational costs by data postanalysis rather than algorithm development. Following an example of the abnormal potential-independent energetic curve within the bandgap area, we turn the topic to the semiconducting electrodes. Meanwhile, the specific behaviors of the bandgap also indicate that besides the reaction thermodynamics and kinetics, the detailed electronic structure of the system can also be well described by the grand-canonical treatment on electrons. Several possibilities for further applications are proposed correspondingly and summarized at the end of paper. We believe that the grand-canonical treatment for electronic structure calculations can greatly enrich our understanding of the fundamental mechanisms under electrochemical environments.

Controlled Electrochemical Barrier Calculations without Potential Control

The knowledge of electrochemical activation energies under applied potential conditions is a prerequisite for understanding catalytic activity at electrochemical interfaces. Here, we present a new set of methods that can compute electrochemical barriers with accuracy comparable to that of constant potential grand canonical approaches, without the explicit need for a potentiostat. Instead, we Legendre transform a set of constant charge, canonical reaction paths. Additional straightforward approximations offer the possibility to compute electrochemical barriers at a fraction of computational cost and complexity, and the analytical inclusion of geometric response highlights the importance of incorporating electronic as well as the geometric degrees of freedom when evaluating electrochemical barriers.

Implicit self-consistent electrolyte model in plane-wave density-functional theory

The ab initio computational treatment of electrochemical systems requires an appropriate treatment of the solid/liquid interfaces. A fully quantum mechanical treatment of the interface is computationally demanding due to the large number of degrees of freedom involved. In this work, we develop a computationally efficient model where the electrode part of the interface is described at the density-functional theory (DFT) level, and the electrolyte part is represented through an implicit solvation model based on the Poisson-Boltzmann equation. We describe the implementation of the linearized Poisson-Boltzmann equation into the Vienna Ab initio Simulation Package, a widely used DFT code, followed by validation and benchmarking of the method. To demonstrate the utility of the implicit electrolyte model, we apply it to study the surface energy of Cu crystal facets in an aqueous electrolyte as a function of applied electric potential. We show that the applied potential enables the control of the shape of nanocrystals from an octahedral to a truncated octahedral morphology with increasing potential.