Theoretical analysis of the unusual temperature dependence of the kinetic isotope effect in quinol oxidation.

In this paper we present theoretical calculations on model biomimetic systems for quinol oxidation. In these model systems, an excited-state [Ru(bpy)(2)(pbim)](+) complex (bpy = 2,2'-dipyridyl, pbim = 2-(2-pyridyl)benzimidazolate) oxidizes a ubiquinol or plastoquinol analogue in acetonitrile. The charge transfer reaction occurs via a proton-coupled electron transfer (PCET) mechanism, in which an electron is transferred from the quinol to the Ru and a proton is transferred from the quinol to the pbim(-) ligand. The experimentally measured average kinetic isotope effects (KIEs) at 296 K are 1.87 and 3.45 for the ubiquinol and plastoquinol analogues, respectively, and the KIE decreases with temperature for plastoquinol but increases with temperature for ubiquinol. The present calculations provide a possible explanation for the differences in magnitudes and temperature dependences of the KIEs for the two systems and, in particular, an explanation for the unusual inverse temperature dependence of the KIE for the ubiquinol analogue. These calculations are based on a general theoretical formulation for PCET reactions that includes quantum mechanical effects of the electrons and transferring proton, as well as the solvent reorganization and proton donor-acceptor motion. The physical properties of the system that enable the inverse temperature dependence of the KIE are a stiff hydrogen bond, which corresponds to a high-frequency proton donor-acceptor motion, and small inner-sphere and solvent reorganization energies. The inverse temperature dependence of the KIE may be observed if the 0/0 pair of reactant/product vibronic states is in the inverted Marcus region, while the 0/1 pair of reactant/product vibronic states is in the normal Marcus region and is the dominant contributor to the overall rate. In this case, the free energy barrier for the dominant transition is lower for deuterium than for hydrogen because of the smaller splittings between the vibronic energy levels for deuterium, and the KIE increases with increasing temperature. The temperature dependence of the KIE is found to be very sensitive to the interplay among the driving force, the reorganization energy, and the vibronic coupling in this regime.