Formal and Computational Studies of Molecular Dynamics

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9403416 Kouri Univ. of Houston This project in the theory of reactive molecular dynamics is supported by the NSF Theoretical and Computational Chemistry Program. The time-independent wavepacket (TIW) approach to quantum mechanics will be developed and implemented into reactive scattering codes using polynominal representations of the full Green's operators with absorbing potentials and the spectral density operator. Both scattering and bound-state Fermion systems will be treated. The possibility of deriving a TIW Kohn-type S-matrix variational principle will be explored. The TIW method will be implemented using distributed approximations functions to represent a function evaluated on a discrete grid of points. The TIW method, recently invented jointly by Donald Kouri and David Hoffman, offers an alternative to traditional methods of solving the time-independent Schroedinger equation for scattering states in the continuum (the S-matrix formalism) or solving the time-dependent Schroedinger equation for wavepackets that evolve in time. The new TIW method has computational advantages over each of these. Kohn has previously derived a variational principle for traditional S-matrix calculations. One of the major goals of this research project is the development of an analogous variational principle for TIW calculations. The hope and expectation is that this research in formal theory and computational methodology will significantly improve our ability to make accurate and detailed predictions of molecular processes in the gas phase. Possible future applications of this technology include computer models of ozone depletion in the earth's atmosphere or high temperature combustion processes in jet engines and waste incinerators.