Transitions induced in a double minimum system by interaction with a quantum mechanical heat bath

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Abstract
A quantum mechanical treatment of a double minimum system interacting with a heat bath is presented for the purpose of interpreting experimental data on transfer kinetics in condensed hydrogen-bonded systems. The model describes the transfer motion in one or two dimensions. The heat bath is represented by a set of harmonic oscillators and the interaction by a term linear in the system coordinates and in the bath coordinates. Extending an earlier random field approach, the present treatment consistently accounts for the quantum nature of the total system. With crystalline benzoic acid dimer used as an example, the master equation for the populations of the energy levels of the hydrogen transfer motion is derived. Transition probabilities consistent with the principle of detailed balance are obtained, based on a representation with explicit off-diagonal tunnel interactions for pairs of states localized on different sides of the barrier and with diagonal terms describing the rearrangement of the heat bath as a consequence of the tunneling motion. The activation of the double minimum transfer process with increasing temperature is related to the excitation of the local vibrations in the two potential wells.