My research in theoretical chemistry is focused upon two areas of chemical dynamics, including the quantum theory of chemical reactions and the theory of intramolecular energy transfer. In both of these areas, the main questions concern the flow of energy: where does it go, and how long does it take to get there. We are involved with both methods of development and with the application of new methods to problems of current experimental interest.
Reaction dynamics In the area of reaction dynamics, we are primarily concerned with the development and application of new methodologies in quantum scattering theory. During the past few years, we have emphasized variational approaches in which one sets up a functional involving the so far unknown scattering wavefunction. Optimization of the functional yields equations for the “best” scattering wavefunction. We have applied this approach to several chemical reactions, including H + D2 and F + H2. The resulting cross sections and product state distributions have been in encouraging agreement with recent experimental data. More recent theoretical developments have allowed the inclusion of the so-called geometric phase in the variational formulation. These powerful methods use matrix linear algebra and are thus highly suited for applications executed on supercomputers.
Intramolecular dynamics In the area of intramolecular dynamics, we have developed a powerful algorithm for computing time-dependent transition probabilities. Instead of attempting to diagonalize very large matrices, we extract the useful information using a matrix recursion algorithm. The resulting algorithm, termed the RRGM, has permitted the largest calculations yet performed on high energy spectra and molecular energy flow. Particular emphasis has been placed upon analysis of the energy transfer pathways in the laser excited benzene molecule. In addition to these large recursive calculations, we have recently developed new codes to study the high energy vibrational dynamics in acetylene, which can isomerize to the short-lived intermediate vinylidede. When completed, these calculations will be very useful in the interpretation of experimental data obtained with the stimulated emission pumping technique. Other calculations related to the origin of mode selective dissociation in small molecules are planned.