Quantum and dynamical effects of proton donor-acceptor vibrational motion in nonadiabatic proton-coupled electron transfer reactions. Journal   The Journal of chemical physics. Citation   J Chem Phys. 122(1):14505 Publication date   2005 Jan 1 Authors   Soudackov A Hatcher E Hammes-Schiffer S Grant agencies   National Institute of General Medical Sciences Grants   NIGMS GM 56207 Abstract   This paper presents a general theoretical formulation for proton-coupled electron transfer (PCET) reactions. The solute is represented by a multistate valence bond model, and the active electrons and transferring proton(s) are treated quantum mechanically. This formulation enables the classical or quantum mechanical treatment of the proton donor-acceptor vibrational mode, as well as the dynamical treatment of the proton donor-acceptor mode and the solvent. Nonadiabatic rate expressions are presented for PCET reactions in a number of well-defined limits for both dielectric continuum and molecular representations of the environment. The dynamical rate expressions account for correlations between the fluctuations of the proton donor-acceptor distance and the nonadiabatic PCET coupling. The quantities in the rate expressions can be calculated with a dielectric continuum model or a molecular dynamics simulation of the full system. The significance of the quantum and dynamical effects of the proton donor-acceptor mode is illustrated with applications to model PCET systems.