A density matrix approach to double well transfer: effects of asymmetry on the tunneling rate

Abstract

Previous approaches to the calculation of the transfer rate between the wells of a double well potential are discussed and the greater conceptual complexity of the dynamics in an asymmetric double well potential, as opposed to the resonance assisted dynamics of a symmetric potential, is noted. A method based on a solution of the equation of motion of the density matrix for the system is presented. The density matrix provides a quantum mechanically exact description of the internal dynamics for both tunneling and over the barrier levels, within the limitations of the finite basis set method. A simple extension of the strong collision assumption is used to describe the interaction of the system with the environment. An approximate method is also developed and is shown to be in good agreement with the exact method. The effects of asymmetry are examined through calculations with model potentials. We observe that the tunneling rate is generally dramatically reduced in an asymmetric well and that the relaxation process itself in this case depends crucially on the interaction with the environment. We also compare the methods with a previous calculation by Flanigan and de la Vega which was proposed as a model for the proton transfer process in water.