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In quantum-mechanical/molecular-mechanical (QM/MM) treatment of chemical reactions in condensed phases, one solves the electronic Schrodinger equation for the solute (or an active site) under the electrostatic field from the environment. This Schrodinger equation depends parametrically on the solute nuclear coordinates R and the external electrostatic potential V. This fact suggests that one may use R and V as natural collective coordinates for describing the entire system, where V plays the role of collective solvent variables. In this paper such an (R,V) representation of the QM/MM canonical ensemble is described, with particular focus on how to treat charge transfer processes in this representation. As an example, the above method is applied to the proton-coupled electron transfer of a ubiquinol analog with phenoxyl radical in acetonitrile solvent. Ab initio free-energy surfaces are calculated as functions of R and V using the reference interaction site model self-consistent field method, the equilibrium points and the minimum free-energy crossing point are located in the (R,V) space, and then the kinetic isotope effects (KIEs) are evaluated approximately. The results suggest that a stiffer proton potential at the transition state may be responsible for unusual KIEs observed experimentally for related systems.

Ab initio calculation of proton-coupled electron transfer rates using the external-potential representation: A ubiquinol complex in solution