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Energy flow in molecules: to be or not to be statistical?

"No spectrum, no matter how simple, is dynamics-free. No dynamical process, no matter how complex, fails to reveal its essential characteristics in one or a series of well designed spectroscopic experiments."

"...patterns are made to be broken, and the breaking of standard patterns is the key to perceiving those dynamical features that demand explanation."

Glimpse of an energy shell with the resonance network. Dots show
quantum initial states. How will they move?

The quotes above are taken from the preface to a recent book titled The Spectra and Dynamics of Diatomic Molecules (Elsevier, 2004) by H. Lefebvre-Brion and R. W. Field. It elegantly sums up the current view in molecular spectroscopy. But why does one want to break the standard patterns? What are those dynamical features that demand our explanation? In short, the dynamical features refers to the intricate dance that the atoms in a molecule perform upon excitation i.e., intramolecular dynamics. Explaining and hence understanding this molecular choreography will let us control molecular reaction dynamics.

Chemistry is all about making and breaking of bonds and the rate at which they do so. To break a specific bond all that has to be done is to excite that bond and dump energy in excess of the bond strength. With some luck the deposited energy will stay put for a few vibrational time periods (about a few hundred femtoseconds) and then the bond snaps. Turns out that this viewpoint is far too naive due to the fact that molecules excited to such high energies have complicated intramolecular dynamics. The excited mode is coupled to many other modes and thus the initially localized energy flows rapidly into many other, perhaps undesirable, modes. In other words the molecular choreography is very complicated. Sometimes it is so complicated that it is simple!

This flow of energy within a molecule is called as the phenomenon of Intramolecular Vibrational energy Redistribution or IVR for short. The questions that we are, as many other chemical physicists in the world are, interested in: Where does the energy flow? How? Why? How fast? How is this classical notion of ball-and-spring vibrational motion encoded in the quantum eigenstates?

One of the best known and widely applied approach to estimating reaction rates makes the assumption that the time scale for IVR is much smaller than typical reaction timescales;this assumption neglects dynamics and renders the theory statistical. Does this basic assumption ring the death bell for mode-specific chemistry?

Recent experiments indicate that consolations are premature and even fairly large molecules at high levels of excitations can exhibit non-statistical dynamics. That is good and bad news. The good news is that one can hope to control the molecular dance. The bad news is that the dynamical details cannot be ignored and thus simple and elegant expressions for rates cannot be written down.

Our group is working on unraveling the IVR pathways in molecules from classical, semiclassical and quantum viewpoints. The same question, from a time-independent standpoint, has to do with the nature of the highly excited eigenstates - can we assign them? Assignment of eigenstates implies an intimate knowledge about the IVR processes.

We want to understand as to how much of the IVR can be explained on the basis of classical dynamics alone. A very important insight, originating from classical dynamics, is that IVR is facilitated in a molecule by chains of nonlinear resonances i.e., energy flows between two modes if their frequencies are in near-integer ratios. In fact the nonlinear resonances form a intricate network - sort of a transport network complete with highways, bylanes and dead-ends.

What part of this network is utilized by the classical dynamics? Does the quantum dynamics use similar regions of the resonance network or is it significantly different? On the other hand quantum mechanics can transport energy even though classical mechanics cannot. This is known as dynamical tunneling.

Ironically, even dynamical tunneling is intimately linked to the classical resonance network! Perhaps a detailed knowledge of this resonance road map will allow us to shut down some of the highways thereby controlling IVR and thus give mode-specific chemistry a fair chance to happen. Time-independently speaking, classical dynamics lets us assign the main features of the eigenstates. The tiny, subtle features require dynamical tunneling. But even that is controlled by the classical resonances and chaos.

Prof. K Srihari
Department of Chemistry
Indian Institute of Technology Kanpur

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