|"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.
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
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?
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.
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