The quantum description of vibrational and ro-vibrational states is a
subject of great interest because of the fundamental importance of
intramolecular energy transfer in many areas of chemical dynamics.  To
refine current theories of unimolecular decomposition, collisional
energy transfer, multiphoton excitation, and mode selective processes it
is imperative that we improve our understanding of highly excited
states.

Variational calculations of molecular spectra are important because they
enable one to test and determine potential energy surfaces, to predict
spectra, and to interpret and understand experimental data.  To
determine accurate global potentials one must optimise a potential
function by comparing calculated and experimental energy levels.  The
spectra of molecules with large amplitude vibrations enable us to
determine much of the potential energy surface because the vibrations
explore large regions of the surface.
The study of highly-excited molecules is also valuable because it
fosters the development of new concepts. The nature of quantum systems
in the classically chaotic regime is among the most fundamental issues
in modern chemical physics.  The characterisation of excited states is
important for the understanding of multiphoton excitation,
intramolecular energy redistribution (IVR), unimolecular reactions,
laser-molecule interactions, selective photodissociation, etc.

  Highly excited vibrational states
are interesting and important because they extend over large anharmonic
portions of the potential energy surface where there is significant
coupling between many modes but for these reasons it is also very
difficult to calculate their energies and wavefunctions.
One of the important factors that impedes the calculation of a spectrum
from a matrix (basis set) representation of a Hamiltonian, H, is the
difficulty of computing eigenvalues and eigenvectors of a large matrix.
The size of H increases exponentially with the number of degrees of
freedom.  We have developed good iterative methods for computing energy levels and
wavefunctions.