Optimal separable bases and molecular collisions

Thesis/Dissertation · Mon Dec 01 04:00:00 EST 1997

DOI:https://doi.org/10.2172/650344· OSTI ID:650344

Poirier, Lionel W. ^[1]

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1. Univ. of California, Berkeley, CA (United States)

A new methodology is proposed for the efficient determination of Green`s functions and eigenstates for quantum systems of two or more dimensions. For a given Hamiltonian, the best possible separable approximation is obtained from the set of all Hilbert space operators. It is shown that this determination itself, as well as the solution of the resultant approximation, are problems of reduced dimensionality for most systems of physical interest. Moreover, the approximate eigenstates constitute the optimal separable basis, in the sense of self-consistent field theory. These distorted waves give rise to a Born series with optimized convergence properties. Analytical results are presented for an application of the method to the two-dimensional shifted harmonic oscillator system. The primary interest however, is quantum reactive scattering in molecular systems. For numerical calculations, the use of distorted waves corresponds to numerical preconditioning. The new methodology therefore gives rise to an optimized preconditioning scheme for the efficient calculation of reactive and inelastic scattering amplitudes, especially at intermediate energies. This scheme is particularly suited to discrete variable representations (DVR`s) and iterative sparse matrix methods commonly employed in such calculations. State to state and cumulative reactive scattering results obtained via the optimized preconditioner are presented for the two-dimensional collinear H + H₂ → H₂ + H system. Computational time and memory requirements for this system are drastically reduced in comparison with other methods, and results are obtained for previously prohibitive energy regimes.

• Research Organization: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Energy Research (ER)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 650344
• Report Number(s): LBNL--41182; ON: DE98052319
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
74 ATOMIC AND MOLECULAR PHYSICS
ATOM-MOLECULE COLLISIONS
CHEMICAL REACTIONS
DWBA
EIGENSTATES
GREEN FUNCTION
HARMONIC OSCILLATORS
HYDROCHLORIC ACID
HYDROGEN
NUMERICAL SOLUTION
OXYGEN
SCATTERING