Our research is focused on understanding the mechanisms, and hence controlling, intramolecular vibrational energy redistribution (IVR) in molecules. The study of IVR is essential to obtain insights into the dynamical processes that govern the making and breaking of chemical bonds. Consequently, singular attention from experimentalists and theorists alike has lead to a critical evaluation of the validity of various models for calculating chemical reaction rates ranging from the celebrated transition state theory (TST) to the highly influential Rice-Ramsperger-Kassel-Marcus (RRKM) theory. Despite such advances there are crucial questions that are yet to be answered and by all accounts IVR has proven to be a worthy adversary! From a time-domain point of view one would like to know if the IVR rates, timescales, and mechanisms (pathways) can be understood from a functional group point of view. Thus, is it possible to identify the role of moieties like methyl rotors, hydrogen bonds, and alkyl chains, and their relative contributions to the energy flow process in molecules? Answering such a question would go a long way in achieveing one of the, long sought-after, holy grails in chemical physics. On the other hand, from a frequency domain perspective, at excitation energies relevant for reactive processes one still does not understand the nature of the quantum eigenstates - are they `assignable'? The interest stems from the fact that the existence of assignable eigenstates even at such high energies implies the existence of new, stable modes, different from the low-energy normal/local modes in the molecule. In other words, at high energies the molecules are capable of performing entirely new, and sometimes surprisingly simple, dynamical motions. How does one detect these novel modes? Do the eigenstates indicate that mode-specificity might just about survive at very high energies? Are there reactions of specific type/kind that would not be describable by either the TST or the RRKM approach? In our group we are attempting to provide answers to some of these questions.

Considerable body of work done earlier had established that the nature of highly excited eigenstates of molecules and the equivalent manifestation in the high resolution spectra in terms of complicated intensity and splitting patterns could be understood in exquisite detail by studying and comparing both the classical and quantum dynamics of the systems i.e., a classical-quantum correspondence approach. A significant bottleneck to such an approach arises due to the fact that a detailed characterization of the phase space is difficult, if not impossible, for systems with three degrees of freedom or more - a generic case for molecules! Despite the difficult nature of the question we have recently come up with a technique that allows us to identify dominant classical structures associated with a specific quantum eigenstate. This technique utilizes the parametric variations of the energy eigenvalues, `level velocities', of a given Hamiltonian (1). It has been established that the level-velocities of the quantum eigenstates truly reflect the phase space nature of the eigenstates and can predict the existence of new modes (2, 3, 4). Furthermore, in a recent work the level-velocities were correlated with spectral intensities and it was shown that such an intensity-velocity correlator gives clear indication of deviations from ergodicity and identifies the important perturbations responsible for the hierarchical IVR features in a high resolution spectrum (5, 6). The generality of our approach makes the method very attractive to analyze molecular spectroscopy in external fields with obvious repercussions to the subject of IVR control (coherent or otherwise). Recently we have established that the correlator provides a global control landscape even for a supreme quantum effect like tunneling (7). More generally, there is still the outstanding issue of the link between chaotic quantum states (arising due to strong fields) and the topology of the optimal control landscapes and level-sets. Insights into the problem, hopefully, will allow one to 'morph' undesirable optimal fields to more realistic and practical fields. Our new, correlator-based, approach seems to be ideal for the purpose. Our long term goal is to peer into the inner workings of quantum optimal control techniques.

Time-dependent studies of IVR in systems with multiple degrees of freedom has been performed by utilizing a wavelet based time-frequency analysis. The time-frequency analysis yields the local frequencies allowing us to construct the dynamical Arnol'd web which, in turn, provides information on the dominant nonlinear resonances that transport energy through the molecule. The Arnol'd web is like a road network complete with highways, bylanes, and dead-ends. Does the quantum dynamics use the Arnol'd web? If so then how long does the classical-quantum correspondence last? Recent work has, for the first time, provided a glimpse of the Arnol'd web on the energy shell and the corresponding IVR dynamics. Apart from confirming some of the conjectures put forward nearly a decade ago, the results highlight the importance of dynamical traps to the IVR process and hence hint towards the anomalous nature of the energy diffusion in molecules (8). Along similar lines, the resonance web for a system modeling the coupling of an aromatic ring with methyl rotor has been constructed to understand the mechanism of possible IVR accelaration due to the internal rotor. In this instance the classical mechanism of IVR, suggested nearly two decades ago as due to thick-layer diffusion, was confirmed but surprisingly the quantum dynamics does not follow the classical dynamics (9)!

The above work focused on uncovering the classical routes to IVR at high excitations. In reality there are quantum routes as well and arguably compete with the classical mechanisms of mixing. It is crucial, from control perspectives, to study the competition between the classical and quantum routes to IVR. Particularly important in this regard is the phenomenon of dynamical tunneling. Although dynamical tunneling was studied nearly two decades ago in the context of molecular spectra there has been very little effort since then to understand its role in IVR. Recently we have shown that even the dynamical tunneling i.e., quantum route to IVR is critically dependent on the Arnol'd web. Surprisingly, the tiniest structures in the classical phase space have a profound effect on the splittings and lead to unassignable, highly mixed states interspersed between dynamically assignable states. Our work on the competition between the quantum and classical mechanisms of IVR established that control of dynamical tunneling is possible once the key structures in phase space are identified (10, 11, 12, 13).