A Theory that Connects Proton-Coupled Electron-Transfer and Hydrogen-Atom Transfer Reactions†

A theory for proton-coupled electron-transfer (PCET) reactions (Cukier, R. I.; Nocera, D. Ann. Rev. Phys. Chem. 1998, 49, 337) is generalized to also apply to hydrogen-atom transfer (HAT) reactions. PCET was described as a concerted transfer of an electron and proton, with both species weakly coupled between their respective initial and final states, a nonadiabatic regime for both electron and proton. Here, we treat the electron adiabatically, asserting that it is strongly coupled and the proton can span the nonadiabatic to adiabatic regimes. A rate constant expression is obtained that incorporates the heavy-atom framework dynamics surrounding the transferring hydrogen atom as well as the effects of inner-sphere vibrational modes. Features of the rate constant that emerge are that modest isotope effects are often to be expected. The observation that some hydrogen-atom transfer reactions have small rate constants, small activation energies, and relatively small isotope effects can be understood on the basi...