The low temperature reactive tunneling in condensed phase. I. The rate expression

We study how the quantization of energy levels affects the deep tunneling rate expression for a double-well system immersed in a harmonic bath. The model of tunneling transitions implies that the energy of a tunneling system is not conserved during a transition because its interaction with the environment is explicitly taken into account. The Golden Rule approach invoked usually cannot be directly applied for such a model. We consider its modification in which the expression for the rate constant depends symmetrically on spectral line shapes of energy levels in both reactant and product wells. The derivation is based on the Breit-Wigner resonance expansion of a dynamical transition probability which is extended on condensed phase systems and averaged at the next stage over fluctuations of the energy levels promoted by system/environment interactions. Test computations for a one-dimensional model case demonstrate novel features inherent to this approach which are clearly revealed in the low-temperature kinetic regime. (C) 2001 American Institute of Physics.