Mixed quantum-classical treatment of electron transfer at electrocatalytic interfaces: Theoretical framework and conceptual analysis

Electron transfer in electrocatalysis involves strong short-range electronic interactions and occurs in an electrochemical double layer. Describing the two elements on an equal footing is an essential but challenging task for theoretical electrocatalysis. This work addresses this challenge using a mixed quantum-classical treatment. This treatment features the combination of chemisorption theory, electron transfer theory, and double layer theory in a unifying framework. Electrostatic free energy terms and solvent reorganization energy, key parameters modulating the electron transfer process, are calculated from a three-dimensional continuum double layer model that considers the reactant structure, steric effect, and solvent orientational polarization. The presented model is reduced back to the Marcus theory by neglecting electronic interactions and to the Schmickler theory of electrocatalysis by neglecting double layer effects. Emphasis is placed on understanding the multifaceted double layer effects in electrocatalysis. Apart from modifying the driving force and reactant concentration that are considered in the Frumkin corrections, double layer effects also modulate the interfacial solvent reorganization energy, thus adding a new term to the transfer coefficient. An additional level of intricacy comes into play if the reactant zone needs to replace solvent molecules originally adsorbed on the metal surface when it approaches the metal surface. The resulting free energy penalty shifts the transition state away from the metal surface and thus increases the activation barrier. Understanding how the metal surface charging condition modulates the interfacial stiffness opens an additional channel of deciphering electrolyte effects in electrocatalysis.