Proton-Coupled Electron Transfer Reactions:  Evaluation of Rate Constants

A recent theory [Cukier, R. I. J. Phys. Chem. 1995, 99, 16101] that predicts the rate of a proton-coupled electron transfer (PCET) reaction is developed further. In PCET, the electron and proton may transfer consecutively, electron transfer (ET) followed by proton transfer (PT), designated as ET/PT, or they may transfer concertedly, in one tunnel event, designated as ETPT. Since the proton charge is coupled to the solvent dipoles in a fashion similar to the electron−solvent coupling, the effect of solvation on the shape of the proton potential energy surface must be known in order to evaluate the PCET rate constant. We show how dielectric continuum theory can be used to obtain the proton-solvated surfaces that are dependent on whether the electron is in its initial or final state. The proton will affect the PCET rate via Franck−Condon factors between the proton surfaces for the initial and final electron states. The proton energy levels will also influence the activation energy for the PCET process. The rates corresponding to the ETPT and ET/PT channels are evaluated for several model reaction complexes that mimic electron donor−hydrogen-bonded interface−electron acceptor systems. The methodology is first illustrated with PCET in pyridinium−pyridine hydrogen-bonded cations, where the reaction complex symmetry restricts the number of system parameters. Then, PCET in amidinium−carboxylate donor−acceptor complexes is studied and compared with the available experimental data. Finally, we study PCET in a part of the photosystem II oxygen-evolving complex involving the oxidation of a tyrosine residue whose phenolic proton is hydrogen bonded to a nitrogen of a histidine residue.