Perspective on Quantum Electrochemistry. A Simple Method for Measuring the Electron Transfer Rate Constant

Abstract It was recently shown that the electron transfer rate constant of an electrochemical reaction and the conductance quantum are correlated with electrochemical capacitance [1]. The association of these two separate concepts has an entirely quantum rate basis that encompasses the electron transfer rate theory as originally proposed by Rudolph A. Marcus [2]. Presently, we demonstrate that this quantum mechanical rate principle can be used to calculate the electron transfer rate constant of a diffusionless heterogeneous electrochemical reaction by taking a specific value of the current–voltage electrochemical curve. The latter is possible because the quantum of conductance is related to the quantum capacitance such that it follows specific electron spin (up and down) and redox state degeneracy rules. Once these rules are settled in the general definition of the quantum rate, the rate of electron transfer is observed to be solely a function of an experimentally measurable quantum capacitance, thus establishing a simple methodology for measuring the electron transfer rate constant. The calculated value of the electron transfer rate is, within the experimental error, in agreement with traditional methods.