First-principles theory of electrochemical capacitance

Understanding and interpreting electrochemical capacitance has advanced both theory and experiment in electrochemistry for more than a century. From a theoretical perspective, the interfacial capacitance is commonly defined based on the original notion of the interfacial Galvani potential, i.e., the inner electric potential difference between electrode and electrolyte phases. With the emergence of accurate first-principles methods, the atomistic simulation of the capacitive properties of electrochemical systems is gaining significant attention. At the atomistic level, however, the classical picture of inner potentials becomes questionable and new concepts are required, e.g., to explain electronic ‘quantum’ contributions to the capacitance of low-dimensional electrodes. In this seminar talk, I will present a new approach to describe electrochemical capacitance based on multicomponent density functional theory (MCDFT), which is a general formalism to treat multicomponent systems including electrons and ions/nuclei from first principles. It will be shown that MCDFT provides the conceptual framework needed to formulate a “modern” theory of electrochemical capacitance, connecting classical concepts of double-layer capacitance, quantum capacitance, and, eventually, reactive (pseudo)capacitance contributions. The formalism yields exact analytical expressions for the total capacitance incorporating electric and non-electric capacitance contributions. In the bulk limit of extended electrode and electrolyte phases, it is shown to reduce to the known classical expressions, providing firm basis for the classical approach based on the concept of Galvani potentials. Future opportunities towards a modern theory of capacitance will be discussed.