Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.