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

The quantum dynamics of a proton (PT) reaction in a polar solvent, treated as continuum, is considered taking as an example the PT process Flu− + HFlu → HFlu + Flu− 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 (KH) and the HD isotope effect cannot be consistently described within the present two-level scheme.