Hydrogen transfer in double minimum potential: Kinetic properties derived from quantum dynamics

Abstract

The interaction of hydrogen transfer in a double minimum potential with a condensed phase environment is studied. For a symmetric double minimum system, the tunneling motion in the vibrational ground state is retarded efficiently by fluctuation as well as by rearrangement of the lattice consisting of harmonic oscillators. Environmental displacements with large inertia cause dynamic asymmetry by failing to cooperate with the transfer motion and favor a thermally activated process even at low temperatures. To describe such processes, an effective Hamiltonian is derived, which consists of a leading term referring to a one-dimensional transfer motion along an asymmetric potential profile and of a random perturbation term linear in the transfer coordinate. The power spectral density is derived for the perturbation given as a superposition of the time-dependent quantum mechanical expectation values of the vibrational displacements in the environment. A master equation treatment is proposed to describe the kinetic properties and is applied to a model for benzoic acid dimers in the crystalline state. The model reproduces the full temperature dependence of the observed NMR T1 data for (C6H5COOH)2 and (C6H5COOD)2 with plausible parameters and relates the temperature-dependent apparent activation energy to the energy level scheme of the transfer motion.