Gaussian approximation of exponential type orbitals based on B functions |
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Authors: | Didier Pinchon Philip E Hoggan |
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Institution: | 1. Toulouse Institute of Mathematics, UMR 5219 CNRS, University Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France;2. LASMEA, UMR 6602 CNRS, University Blaise Pascal, 24 avenue des Landais, 63177 Aubiere Cedex, France |
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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 |
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Keywords: | B functions Gaussian approximation Gauss quadrature method best mean‐square approximation |
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