Abstract
This paper aims at enlightening the link between surface properties, conceptual density functional theory (DFT), and electrochemistry. The energy of a metallic charged surface is expanded into classical terms such as electrochemical potential or chemical hardness and into new terms such as electromechanical coupling vector, electrochemical Hessian matrix change, etc. These quantities are shown to be crucial parameters to understand interface electrochemistry and in particular the surface zero-charge potential, the capacitance and its derivatives, and the surface structural polarization at the atomic scale. Furthermore, the Fukui function initially introduced to rationalize molecular reactivity is here shown to directly probe the electrochemical activity of the surface. First, it gives the spatial repartition on the surface of the charge added during an electrochemical step, and second it quantifies the electrochemical parameters of the system: the electrochemical potential and the electromechanical coupling vector mainly arise from the interaction of the Fukui function with the local surface dipole and the nucleus electric field, while the capacitance mostly comes from the Fukui function self-electrostatic interaction. The electrochemical Hessian change matrix controls part of the bond modifications induced by the electrochemical process and directly depends on the Fukui function derivatives with respect to atomic displacements. This description not only allows linking the electrochemical bond modification with conceptual DFT and molecular orbital theories but can also be used quantitatively to extract electrochemical properties from response theory.