Density functional theory and an experimentally-designed energy functional of electron density

We herein demonstrate that capacitance spectroscopy (CS) experimentally allows access to the energy associated with the quantum mechanical ground state of many-electron systems. Priorly, electrochemical capacitance, C_{[small mu, Greek, macron]}[ρ], was previously understood from conceptual and computational density functional theory (DFT) calculations. Thus, we herein propose a quantum mechanical experiment-based variational method for electron charging processes based on an experimentally-designed functional of the ground state electron density. In this methodology, the electron state density, ρ, and an energy functional of the electron density, E_{[small mu, Greek, macron]}[ρ], can be obtained from CS data. CS allows the derivative of the electrochemical potential with respect to the electron density, (δ[small mu, Greek, macron][ρ]/δρ), to be obtained as a unique functional of the energetically minimised system, i.e., β/C_{[small mu, Greek, macron]}[ρ], where β is a constant (associated with the size of the system) and C_{[small mu, Greek, macron]}[ρ] is an experimentally observable quantity. Thus the ground state energy (at a given fixed external potential) can be obtained simply as E_{[small mu, Greek, macron]}[ρ], from the experimental measurement of C_{[small mu, Greek, macron]}[ρ]. An experimental data-set was interpreted to demonstrate the potential of this quantum mechanical experiment-based variational principle.