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Quantum-rate theory defines a quantum mechanical rate $\nu$ that complieswith the Planck--Einstein relationship $E = h\nu$, where $\nu = e^2/hC_q$ is afrequency associated with the quantum capacitance $C_q$, and $E = e^2/C_q$ isthe energy associated with $\nu$. Previously, this definition of $\nu$ wassuccessfully employed to define a quantum mechanical meaning for theelectron-transfer (ET) rate constant of redox reactions, wherein faradaicelectric currents involved with ET reactions were demonstrated to be governedby relativistic quantum electrodynamics at roomtemperature~\citep{Bueno-2023-3}. This study demonstrated that the definitionof $\nu$ entails the relativistic quantum electrodynamics phenomenaintrinsically related to the perturbation of the density-of-states $\left(dn/dE \right) = C_q/e^2$ by an external harmonic oscillatory potential energyvariation. On this basis, the electronic structure of graphene embedded in anelectrolyte environment was computed. The electronic structure measured usingquantum-rate spectroscopy (QRS) is in good agreement with that measured throughangle-resolved photo-emission spectroscopy (ARPES) or calculated viacomputational density-functional theory (DFT) methods. Electrochemical QRS hasevident experimental advantages over ARPES. For instance, QRS enables obtainingthe electronic structure of graphene at room temperature and in an electrolyteenvironment, whereas ARPES requires low temperature and ultrahigh-vacuumconditions. Furthermore, QRS can operate \textit{in-situ} using a hand-held,inexpensive piece of equipment, whereas ARPES necessarily requires expensiveand cumbersome apparatus.

Electrochemical Measurement of the Electronic Structure of Graphene via Quantum Mechanical Rate Spectroscopy