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 basis of this theory. The contrasting kinetic properties between nitrogen and oxygen acids versus carbon acids can also be rationalized.