Semiempirical modeling free energy surfaces for proton transfer in polar aprotic solvents Original Research Article

A method of calculation of a free-energy surface (FES) of the proton transfer (PT) reaction in a polar aprotic solvent is developed. This is based on the two-state (valence bond) VB description of the solute combined with recent continuum medium models. Its essential new feature is an explicit quantum-chemical treatment of VB wave functions, including internal electronic structure of a chemical subsystem. The FES includes a pair of intrasolute coordinates, R, the distance between hydrogen-bonded atoms and s, the proton coordinate, together with the collective medium polarization mode. Two hydrogen-bonded systems immersed in a polar solvent (Freon) were considered. The first one is the H5O2+ ion, a model system which was used as a benchmark testifying the validity of our semiempirical calculations. The second system is the neutral (CN)(CH3)N–H⋯N(CH3)3 complex in Freon. PT for this system has been studied experimentally. The dependencies of basic parameters controlling FES properties (the overlap integral, the coupling matrix element and the reorganization energy Er) on intrasolute coordinates R and s are evaluated and discussed. In particular, for the neutral complex, Er depends on s linearly, and its dependence on R is weak. The FES, for the neutral system, has two potential wells separated by the energy barrier of ∼7 kcal/mol. Quantum-mechanical averaging over the proton coordinate, s, reduces the barrier from 7.0 to 1.2 kcal/mol. The value of the nonadiabatic parameter on the averaged FES is equal to 0.13. This implies that the PT in the second system corresponds to an intermediate dynamic regime and that proton tunneling effects are hardly significant for this reaction.