  Quantum-rate theory defines a quantum mechanical rate $\nu$ that complies
with the Planck--Einstein relationship $E = h\nu$, where $\nu = e^2/hC_q$ is a
frequency associated with the quantum capacitance $C_q$, and $E = e^2/C_q$ is
the energy associated with $\nu$. Previously, this definition of $\nu$ was
successfully employed to define a quantum mechanical meaning for the
electron-transfer (ET) rate constant of redox reactions, wherein faradaic
electric currents involved with ET reactions were demonstrated to be governed
by relativistic quantum electrodynamics at room
temperature~\citep{Bueno-2023-3}. This study demonstrated that the definition
of $\nu$ entails the relativistic quantum electrodynamics phenomena
intrinsically related to the perturbation of the density-of-states $\left(
dn/dE \right) = C_q/e^2$ by an external harmonic oscillatory potential energy
variation. On this basis, the electronic structure of graphene embedded in an
electrolyte environment was computed. The electronic structure measured using
quantum-rate spectroscopy (QRS) is in good agreement with that measured through
angle-resolved photo-emission spectroscopy (ARPES) or calculated via
computational density-functional theory (DFT) methods. Electrochemical QRS has
evident experimental advantages over ARPES. For instance, QRS enables obtaining
the electronic structure of graphene at room temperature and in an electrolyte
environment, whereas ARPES requires low temperature and ultrahigh-vacuum
conditions. Furthermore, QRS can operate \textit{in-situ} using a hand-held,
inexpensive piece of equipment, whereas ARPES necessarily requires expensive
and cumbersome apparatus.
