Modeling interfacial electrochemistry: concepts and tools

This paper presents a grand canonical formalism to treat electrochemical effects at interfaces. This general formalism is linked with the classical chemical hydrogen electrode (CHE) approximation and an improved approximation is proposed. This new approximation including a higher order correction that (i) keeps the low computational cost of classical CHE approach, (ii) does not require to know the type of reaction (electrochemical/not electrochemical) and (iii) should give better estimates in many problematic cases. Beyond the applicability domain of this new approximation, the homogeneous background method (HBM) which is a potential dependent density functional theory method is then presented. HBM allows computing and extracting, at ab initio level, electrochemical properties of molecules either adsorbed or in the double layer. In particular, quantitative redox potential and number of exchanged electrons can be computed giving access to non-integer electron exchange or decoupled electron/proton transfer reactions. Tools for rationalizing electrochemical reactivity consisting of potential dependant projected density of states, Fukui function and metallicity index are defined. The methodology and tools are applied to examples relevant to the energy domain in order the compare reactivity in the outer Helmholtz plane and at the surface. Then, the combination of HBM and reactivity create a toolbox usable to predict and investigate the different redox, degradation and ageing processes occurring at an electrochemical interface such as the one found in energy materials but also in all electrochemical applications.