The Fourier transform method and the SD-bar approach for the analytical and numerical treatment of multicenter overlap-like quantum similarity integrals
- Campus Saint-Jean, University of Alberta, 8406 Rue Marie-Anne Gaboury, 91 Street, Edmonton, Alta., T6C 4G9 (Canada)
- Laboratoire SEESIB, UMR 6504, Universite Blaise Pascal, 63177 Aubiere Cedex (France)
Molecular overlap-like quantum similarity measurements imply the evaluation of overlap integrals of two molecular electronic densities related by Dirac delta function. When the electronic densities are expanded over atomic orbitals using the usual LCAO-MO approach (linear combination of atomic orbitals), overlap-like quantum similarity integrals could be expressed in terms of four-center overlap integrals. It is shown that by introducing the Fourier transform of delta Dirac function in the integrals and using the Fourier transform approach combined with the so-called B functions, one can obtain analytic expressions of the integrals under consideration. These analytic expressions involve highly oscillatory semi-infinite spherical Bessel functions, which are the principal source of severe numerical and computational difficulties. In this work, we present a highly efficient algorithm for a fast and accurate numerical evaluation of these multicenter overlap-like quantum similarity integrals over Slater type functions. This algorithm is based on the SD-bar approach due to Safouhi. Recurrence formulae are used for a better control of the degree of accuracy and for a better stability of the algorithm. The numerical result section shows the efficiency of our algorithm, compared with the alternatives using the one-center two-range expansion method, which led to very complicated analytic expressions, the epsilon algorithm and the nonlinear D-bar transformation.
- OSTI ID:
- 20767055
- Journal Information:
- Journal of Computational Physics, Vol. 216, Issue 1; Other Information: DOI: 10.1016/j.jcp.2005.11.020; PII: S0021-9991(05)00540-1; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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