  The differential capacitance comprises the most relevant thermodynamic
information about an electrochemical system. Classical approaches to describe
electrochemical capacitance have difficulties to combine the treatment of the
ionic contribution of the electrolyte with the electronic contribution of the
electrode. Moreover, different approaches are typically required for the
description of the double-layer capacitance, on the one hand, and the
pseudocapacitive contribution due to adsorption or intercalation of reactive
species, on the other. In the present work, a new approach to describe
electrochemical capacitance from first principles is developed. The treatment
of a general electrochemical system at the level of multicomponent
density-functional theory (MCDFT) yields an exact analytical expression for the
total capacitance of the system, which corresponds to a formal series-circuit
partitioning into "quantum" capacitance contributions of the density of states
of electrons and ions, the (mean-field) electrostatic capacitance, as well as
capacitance contributions of exchange and correlation among all active species.
It is shown that the classical expression of the double-layer capacitance
involving the interfacial Galvani potential is obtained in the limit of
extended electrode and electrolyte regions. Importantly, the present formalism
also describes systems with confined electrode and electrolyte phases, where
the definition of the (classical) inner potentials of the electrode and
electrolyte domains becomes problematic. Moreover, the new approach unifies the
treatment of double-layer capacitance and pseudocapacitance resulting from
reactive processes.
