Dynamics of proton transfer reactions in polar solvent in the non-adiabatic two-state approximation: Test calculations for carbon-carbon reaction centre

The quantum dynamics of a proton transfer (PT) reaction in a polar solvent, treated as continuum, is considered taking as an example the PT process Flu^- + HFlu → HFlu + Flu^- (a) in ether, where FluH means fluorene. Using the model three-dimensional free-energy surface (FES) derived from quantum-chemical SCRF calculations, the dynamical description is reduced to a two-level stochastic Liouville equation in the two-dimensional subspace spanned by the solute vibrational mode (representing a relative motion of heavy atoms constituting the PT reaction centre) and a solvent collective coordinate. The two quantum states involved in a reactive event are a pair of lowest proton levels obtained by means of quantum-mechanical averaging the basic three-dimensional FES. The new methodology of a direct evaluation of the coupling matrix element is elaborated. The rate calculation involves a treatment of extremely small ( ∼ 10^-5-10^-10) transmission factors for which two different approximate non-adiabatic approaches are tested. The whole variety of experimental data on reaction (a) involving both the absolute values of the rate constant (K^H) and the H/D isotope effect cannot be consistently described within the present two-level scheme.