Dynamical tunnelling in molecules: quantum routes to energy flow

Abstract

Dynamical tunnelling, introduced in the molecular context, is more than two decades old and refers to phenomena that are classically forbidden but allowed by quantum mechanics. The barriers for dynamical tunnelling, however, can arise in the momentum or more generally in the full phase space of the system. On the other hand the phenomenon of intramolecular vibrational energy redistribution (IVR) has occupied a central place in the field of chemical physics for a much longer period of time. Despite significant progress in understanding IVR a priori prediction of the pathways and rates is still a difficult task. Although the two phenomena seem to be unrelated several studies indicate that dynamical tunnelling, in terms of its mechanism and timescales, can have important implications for IVR. It is natural to associate dynamical tunnelling with a purely quantum mechanism of IVR. Examples include the observation of local mode doublets, clustering of rotational energy levels, and extremely narrow vibrational features in high-resolution molecular spectra. Many researchers have demonstrated the usefulness of a phase space perspective towards understanding the mechanism of IVR. Interestingly dynamical tunnelling is also strongly influenced by the nature of the underlying classical phase space. Recent studies show that chaos and nonlinear resonances in the phase space can enhance or suppress dynamical tunnelling by many orders of magnitude. Is it then possible that both the classical and quantum mechanisms of IVR, and the potential competition between them, can be understood within the phase space perspective? This review focuses on addressing the question by providing the current state of understanding of dynamical tunnelling from the phase space perspective and the consequences for intramolecular vibrational energy flow in polyatomic molecules.

Acknowledgements

It is a pleasure to acknowledge several useful discussions with Arul Lakshminarayan and Peter Schlagheck on the topic of dynamical tunnelling. I am grateful to Prof. Steve Wiggins for his hospitality at Bristol where parts of this review were written in addition to discussions on the wavelet technique. Financial support for the author's research reported here came from the Department of Science and Technology and the Council for Scientific and Industrial Research, India.