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Gaussian approximation of exponential type orbitals based on B functions
Author(s) -
Pinchon Didier,
Hoggan Philip E.
Publication year - 2008
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21705
Subject(s) - gaussian , laplace transform , inverse laplace transform , gaussian quadrature , exponential function , fourier transform , mathematics , maple , gaussian function , two sided laplace transform , gaussian integral , mathematical analysis , quantum mechanics , physics , fractional fourier transform , fourier analysis , integral equation , botany , biology , nyström method
Abstract This work gives new, highly accurate optimized gaussian series expansions for the B functions used in molecular quantum mechanics. These functions are generally chosen because of their compact Fourier transform, following Shavitt. The inverse Laplace transform in the square root of the variable is used for Gauss quadrature in this work. Two procedures for obtaining accurate gaussian expansions have been compared for the required extended precision arithmetic. The first is based on Gaussian quadratures and the second on direct optimization. Both use the Maple computer algebra system. Numerical results are tabulated and compared with previous work. Special cases are found to agree before pushing the optimization technique further. The optimal gaussian expansions of B functions obtained in this work are available for reference. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009