Boltzmann wavepacket dynamics of tunnelling of molecules through symmetric and asymmetric energy barriers on non-periodic potential functions

Abstract

This paper describes the results of a computational study of tunnelling of molecules possessing a single large amplitude vibrational mode subject to symmetric and asymmetric non-periodic potential energy functions. The paper compares a time domain description of tunnelling and its consequences for measurable physical properties, with the frequency domain description given in terms of transitions between stationary states largely localised in distinct potential wells. In particular, the behaviour of Boltzmann wavepackets possessing ensemble average characteristics on such potential functions is discussed. As an illustration, it is shown that these wavepackets embody a classical description of the oscillating dipole moment components in molecules like cyanamide, ammonia and chlorocyclobutane, which can be reconciled with the quantum mechanical measurement of the relevant transition moments in such cases. Resonance enhancement of tunnelling between inequivalent energy domains of asymmetric potential functions is also described.