Electron-proton free-energy surfaces for proton transfer reaction in polar solvents: test calculations for carbon-carbon reaction centres

Abstract

The proton transfer reaction R− + HR → RH + R− of benzyl-type compounds in a polar solvent has been studied theoretically in terms of a proton adiabatic dynamical treatment of a mixed quantum-classical reacting system. The gas phase potentials were obtained using the PM3 method and then approximated by appropriate (LEPS type) quasi-analytical functions. Polar medium degrees of freedom were introduced, similar to the Marcus electron transfer theory, in terms of a two-state electronic Hamiltonian. At this level, three-dimensional free energy surfaces were obtained, including a pair of intrasolute coordinates, the CH stretch and heavy-atom vibrational mode of the reaction centre, together with the collective medium polarization mode. At the next stage, two-dimensional electron-proton free energy surfaces (EP FESs) corresponding to the adiabatic approximation with respect to CH stretch were generated for the two lowest proton levels. Their main features are described. The reaction with R = benzyl proved to be proton-adiabatic. Its rate constant transmission factor calculated in terms of the Kramers-Grote-Hynes theory is significantly less than unity (∼0.4–0.6) because the reaction coordinate at the transition state of the ground state EP FES coincides with the medium mode. The reaction with R = fluorenyl does not obey the proton-adiabaticity condition and needs a special kinetic treatment. A remarkable observation is that the double adiabatic electron-proton approximation is incapable of providing sufficiently high classical barriers (> 10 kcal/mol) on ground-state two-dimensional EP FESs for proton transfer reactions in polar solvents.