On one-dimensional discrete variable representations with general basis functions

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For the case of standard orthogonal polynomial bases, the question of accuracy of the matrix elements of the potential energy operator derived via the transformation method has been made clear by Dickinson and Certain, who showed the relation of the transformation method and the Gaussian quadrature associated with the polynomial basis employed. Little is known, however, about the accuracy of these matrix elements when a general basis is used. The present work extends the proof of Dickinson and Certain and shows that the transformation method gives matrix elements of Gaussian quadrature accuracy even in the case of general bases. This explains the success of the potential optimized DVR method where the transformation method is employed in deriving a DVR corresponding to the potential optimized basis functions.

Original languageEnglish
Pages (from-to)10512-10518
Number of pages7
JournalJournal of Chemical Physics
Issue number20
Publication statusPublished - Nov 22 2003


ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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