  Numerous experimental and theoretical studies have established that
intramolecular vibrational energy redistribution (IVR) in isolated molecules
has a heirarchical tier structure. The tier structure implies strong
correlations between the energy level motions of a quantum system and its
intensity-weighted spectrum. A measure, which explicitly accounts for this
correaltion, was first introduced by one of us as a sensitive probe of phase
space localization. It correlates eigenlevel velocities with the overlap
intensities between the eigenstates and some localized state of interest. A
semiclassical theory for the correlation is developed for systems that are
classically integrable and complements earlier work focusing exclusively on the
chaotic case. Application to a model two dimensional effective spectroscopic
Hamiltonian shows that the correlation measure can provide information about
the terms in the molecular Hamiltonian which play an important role in an
energy range of interest and the character of the dynamics. Moreover, the
correlation function is capable of highlighting relevant phase space structures
including the local resonance features associated with a specific bright state.
In addition to being ideally suited for multidimensional systems with a large
density of states, the measure can also be used to gain insights into the phase
space transport and localization. It is argued that the overlap intensity-level
velocity correlation function provides a novel way of studying vibrational
energy redistribution in isolated molecules. The correlation function is
ideally suited to analyzing the parametric spectra of molecules in external
fields.
