Driving Force Dependence of Rates for Nonadiabatic Proton and Proton-Coupled Electron Transfer: Conditions for Inverted Region Behavior

The driving force dependence of the rate constants for nonadiabatic electron transfer (ET), proton transfer (PT), and proton-coupled electron transfer (PCET) reactions is examined. Inverted region behavior, where the rate constant decreases as the reaction becomes more exoergic (i.e., as Delta G(0) becomes more negative), has been observed experimentally for ET and FIT. This behavior was predicted theoretically for ET but is not well understood for PT and PCET. The objective of this Letter is to predict the experimental conditions that Could lead to observation of inverted region behavior for PT and PCET. The driving force dependence of the rate constant is qualitatively different for PT and PCET than for ET because of the high proton vibrational frequency and substantial shift between the reactant and product proton vibrational wave functions. As a result, inverted region behavior is predicted to be experimentally inaccessible for PT and PCET if only the driving force is varied. This behavior may be observed for PT over a limited range of rates and driving forces if the solvent reorganization energy is low enough to cause observable oscillations. Moreover, this behavior may be observed for PT or PCET if the proton donor-acceptor distance increases as Delta G(0) becomes more negative. Thus, a plausible explanation for experimentally observed inverted region behavior for PT or PCET is that varying the driving force also impacts other properties of the system, such as the proton donor-acceptor distance.