Optimal separable bases and molecular collisions

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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 ... continued below

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150 p.

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Poirier, L.W. December 1, 1997.

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This thesis or dissertation is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this document can be viewed below.

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  • Poirier, L.W. Lawrence Berkeley National Lab., CA (United States)

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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 + H{sub 2} {yields} H{sub 2} + 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.

Physical Description

150 p.

Notes

INIS; OSTI as DE98052319

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  • Other Information: TH: Thesis (Ph.D.)

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  • Other: DE98052319
  • Report No.: LBNL--41182
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 650344
  • Archival Resource Key: ark:/67531/metadc709081

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Office of Scientific & Technical Information Technical Reports

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  • December 1, 1997

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  • Sept. 12, 2015, 6:31 a.m.

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  • April 5, 2016, 5:52 p.m.

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Poirier, L.W. Optimal separable bases and molecular collisions, thesis or dissertation, December 1, 1997; California. (digital.library.unt.edu/ark:/67531/metadc709081/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.