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Nonproduct quadrature grids for solving the vibrational Schrödinger equation

J. Chem. Phys. 131, 174103 (2009); doi:10.1063/1.3246593

Published 2 November 2009

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Gustavo Avila and Tucker Carrington, Jr.
Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada
The size of the quadrature grid required to compute potential matrix elements impedes solution of the vibrational Schrödinger equation if the potential does not have a simple form. This quadrature grid-size problem can make computing (ro)vibrational spectra impossible even if the size of the basis used to construct the Hamiltonian matrix is itself manageable. Potential matrix elements are typically computed with a direct product Gauss quadrature whose grid size scales as ND, where N is the number of points per coordinate and D is the number of dimensions. In this article we demonstrate that this problem can be mitigated by using a pruned basis set and a nonproduct Smolyak grid. The constituent 1D quadratures are designed for the weight functions important for vibrational calculations. For the SF6 stretch problem (D=6) we obtain accurate results with a grid that is more than two orders of magnitude smaller than the direct product Gauss grid. If D>6 we expect an even bigger reduction. ©2009 American Institute of Physics
History: Received 7 August 2009; accepted 22 September 2009; published 2 November 2009; publisher error corrected 3 November 2009
Permalink: http://link.aip.org/link/?JCPSA6/131/174103/1
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KEYWORDS and PACS

Keywords
PACS
  • 33.20.Tp
    Vibrational analysis (molecular spectra)
  • YEAR: 2009

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

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