Application of contracted distributed approximating functions to solving vibrational eigenvalue problems

Szalay, V. and Smith, S. C. (1999) Application of contracted distributed approximating functions to solving vibrational eigenvalue problems. Journal of Chemical Physics, 110 1: 72-79. doi:10.1063/1.478086


Author Szalay, V.
Smith, S. C.
Title Application of contracted distributed approximating functions to solving vibrational eigenvalue problems
Journal name Journal of Chemical Physics   Check publisher's open access policy
ISSN 0021-9606
Publication date 1999
Sub-type Article (original research)
DOI 10.1063/1.478086
Volume 110
Issue 1
Start page 72
End page 79
Total pages 8
Place of publication Woodbury, USA
Publisher American Institute of Physics
Collection year 1999
Language eng
Subject C1
250699 Theoretical and Computational Chemistry not elsewhere classified
780103 Chemical sciences
Abstract It has been shown that an approximately band-limited function can be reconstructed by using the function's values taken at appropriate equidistant grid points and a generalized Hermite-contracted-continuous-distributed-approximating-function (Hermite-CCDAF) as the reconstruction function. A sampling theorem prescribing the possible choices of grid spacing and DAF parameters has been derived and discussed, and discretized-Hermite-contracted DAFs have been introduced. At certain values of its parameters the generalized Hermite-CCDAF is identical to the Shannon-Gabor-wavelet-DAF (SGWDAF). Simple expressions for constructing the matrix of a vibrational Hamiltonian in the discretized-Hermite-contracted DAF approximation have been given. As a special case the matrix elements corresponding to sinc-DVR (discrete variational representation) are recovered. The usefulness and properties of sinc-DVR and discretized-Hermite-contracted-DAF (or SGWDAF) in bound state calculations have been compared by solving the eigenvalue problem of a number of one- and two-dimensional Hamiltonians. It has been found that if one requires that the same number of energy levels be computed with an error less than or equal to a given value, the SGWDAF method with thresholding is faster than the standard sinc-DVR method. The results obtained with the Barbanis Hamiltonian an described and discussed in detail. (C) 1999 American Institute of Physics. [S0021-9606(99)00501-2].
Keyword Physics, Atomic, Molecular & Chemical
Filter-diagonalization
Energy-levels
Quantum
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Chemistry and Molecular Biosciences
 
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