Explaining Kinetic Isotope Effects in Proton-Coupled Electron Transfer Reactions

Conspectus Proton-coupled electron transfer (PCET) is essential for a wide range of chemical and biological processes. Understanding the mechanism of PCET reactions is important for controlling and tuning these processes. The kinetic isotope effect (KIE), defined as the ratio of the rate constants for hydrogen and deuterium transfer, is used to probe PCET mechanisms experimentally but is often challenging to interpret. Herein, a theoretical framework is described for interpreting KIEs of concerted PCET reactions. The first step is to classify the reaction in terms of vibronic and electron-proton nonadiabaticities, which reflect the relative time scales of the electrons, protons, and environment. The second step is to select the appropriate rate constant expression based on this classification. The third step is to compute the input quantities with computational methods. Vibronically adiabatic PCET reactions occur on the electronic and vibrational ground state and can be described within the transition state theory framework. The nuclear−electronic orbital (NEO) method, which treats specified protons quantum mechanically on the same level as the electrons, can be used to generate the electron-proton vibronic free energy surface for hydrogen and deuterium and to compute the corresponding free energy barriers. Such reactions typically exhibit moderate KIEs that arise from zero-point energy and shallow tunneling effects. Vibronically nonadiabatic PCET reactions involve excited electron-proton vibronic states and can be described with a golden rule formalism corresponding to nonadiabatic transitions between pairs of reactant and product vibronic states. Such reactions can exhibit KIEs ranging from unity, or even slightly less than unity, to more than 500. These KIEs can be explained in terms of multiple, competing reaction pathways corresponding to electron and proton tunneling between different pairs of vibronic states. The tunneling probability is determined by the vibronic coupling, which can be computed using a general expression but often is proportional to the overlap between the reactant and product proton vibrational wave functions. In this regime, the KIE is influenced by the vibronic couplings, the proton donor-acceptor equilibrium distance and motion, and contributions from excited vibronic states. Three illustrative examples of vibronically nonadiabatic PCET are discussed. The unusually large KIEs in soybean lipoxygenase of ∼80 for the wild-type enzyme and ∼700 for a double mutant are explained in terms of a large equilibrium proton donor-acceptor distance and nonoptimal orientation, leading to a small overlap between vibrational wave functions and therefore a large difference in hydrogen and deuterium tunneling probabilities. The KIEs for benzimidazole-phenol molecules ranging from unity to moderate are explained in terms of the dominance of different pairs of vibronic states with different vibrational wave function overlaps. The potential-dependent KIE observed for proton discharge from triethylammonium acid to a gold surface in acetonitrile is explained in terms of different pairs of vibronic states contributing for hydrogen and deuterium, with the reaction channels exhibiting different dependencies on the applied potential. These examples show that the KIE can vary widely, depending on which pairs of vibronic states dominate and their corresponding vibronic couplings. This work has broad implications for the interpretation of experimentally measured KIEs of PCET reactions.