Constant Potential and Constrained Charge Ensembles for Simulations of Conductive Electrodes

Abstract

Constant potential method molecular dynamics simulation (CPM MD) enables the accurate modeling of atomistic electrode charges when studying the electrode–electrolyte interface at the nanoscale. Here, we extend the theoretical framework of CPM MD to the case in which the total charge of each conductive electrode is controlled, instead of their potential difference. We show that the resulting thermodynamic ensemble is distinct from that sampled with a fixed potential difference but they are rigorously related as conjugate ensembles. This theoretical correspondence, which we demonstrate using simulations of an ionic liquid supercapacitor, underpins the success of recent studies with fixed total charges on the electrodes. We show that equilibration is usefully sped up in this ensemble and outline some potential applications of these simulations in the future.

Development of Heteroatomic Constant Potential Method with Application to MXene-Based Supercapacitors

“…We separately calculate the MXene atom charges in the absence of the Li + ion, q χ * , and then calculate the “induced charge” as the difference q χ=0 * ( R ) = q *( R ) – q χ * . For comparison, we calculate the HCPM-induced charges as OA –1 ( b ( R ) + Δψ d ), with the elements of b given by eq 6d , and Δψ is adjusted using the constrained charge ensemble 39 so that the HCPM and DFT electrodes have the same total induced charge. The HCPM-induced charges will depend parametrically on η j and A jj , and minimizing the difference in the values of q χ=0 * ( R ) from the DFT and HCPM calculations determines the optimal η j and A jj and the corresponding HCPM-induced charges.…”

Modeling Interfacial Dynamics on Single Atom Electrocatalysts: Explicit Solvation and Potential Dependence

“…However, these two approaches are based on a single transition path (usually from nudged elastic band calculation) with minimal solvation, which neglects completely the configurational changes and dynamics of the electrolyte along the reaction coordinate. Recent theoretical work has demonstrated that constant-charge and constant-potential ensembles are conjugated, and one can mathematically derive equilibrium constant-potential properties from a constant-charge trajectory . This approach better accounts for the configurational entropy but still can fail in systems with phase transition-like potential dependent configurational changes .…”

Understanding electrochemical interfaces through comparing experimental and computational charge density–potential curves

“…, the evolution of ion concentration with time during the charging process, is more reliable in CPM. In a recent work by Tee and Searles, 89 the theoretical framework of CPM-MD was extended to the case in which the total charge of each electrode is controlled, instead of their potential difference, with a typical ionic liquid–graphene supercapacitor. They too observed statistically identical plots of charge against bias voltage in both cases.…”