Exactly solvable quantum model for electrochemical electron-transfer reactions

We consider electron exchange between a metal electrode and a solvated reactant coupled to a harmonic oscillator bath. In the wide-band approximation the time development of the occupation probability for the reactant orbital can be calculated explicitly. From the behavior at long times we derive an expression for the reaction rate that is valid for all strengths of the electronic interaction between the metal and the reactant. The rate constant is related to the scattering matrix for electron exchange between a metal substrate and a scanning tunneling microscope via an electroactive adsorbate.