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Orthogonal Functions, Discrete Variable Representation and Generalized Gauss Quadratures

Published

Author(s)

B I. Schneider, N Nygaard

Abstract

The numerical solution of most problems in theoretical chemistry involve either the use of a basis set expansion (spectral method) or a numerical grid. For many basis sets, there is an intimate connection between the spectral form and numerical quadrature. When this connection exists, the distinction between spectral and grid approaches becomes blurred. In fact, the two approaches can be related by a similarity transformation. By exploiting this idea, calculations can be considerably simplified, and the need to compute difficult matrix elements of the Hamiltonian in the original representation can be moved.
Citation
Journal of Physical Chemistry

Keywords

approximation of functions, discrete variable representation, numerical integration, numerical quadrature, orthogonal polynomials, quantum chemistry

Citation

Schneider, B. and Nygaard, N. (2008), Orthogonal Functions, Discrete Variable Representation and Generalized Gauss Quadratures, Journal of Physical Chemistry (Accessed April 21, 2024)
Created October 16, 2008