I happen to be a frog, but many of my best friends are birds..It would be
stupid to claim that birds are better than frogs because they see farther,
or that frogs are better than birds because they see deeper. (Freeman Dyson)
I study molecular dynamics, but to tell the truth I am interested more
in the dynamics than in the molecules, and I care most about questions
of principle. (Phil Pechukas)
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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).
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