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Two-center overlap integrals, three dimensional adaptive integration, and prolate ellipsoidal coordinates

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Abstract

Numerical, adaptive algorithm evaluating the overlap integrals between the Numerical Type Orbitals (NTO) is presented. The described algorithm exploits the properties of the prolate ellipsoidal coordinates, which are the natural choice for two-center overlap integrals. The algorithm is designed for numerical atomic orbitals with the finite support. Since the cusp singularity of the atomic orbitals vanish in the prolate ellipsoidal coordinate system, the adaptive integration algorithm in \({\mathbb{R}^3}\) generates small number of subdivisions. The efficiency and reliability of the algorithm is demonstrated for the overlap integrals evaluated for the selected pairs of Slater Type Orbitals (STO).

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Authors and Affiliations

  1. Interdisciplinary Centre for Materials Modelling, ul. Pawinskiego 5a, 02-106, Warsaw, Poland

    Zbigniew Romanowski

  2. Department of Chemistry, The University of Arizona, Tucson, AZ, USA

    Abraham F. Jalbout

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  1. Zbigniew Romanowski
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  2. Abraham F. Jalbout
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Correspondence to Zbigniew Romanowski.

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Romanowski, Z., Jalbout, A.F. Two-center overlap integrals, three dimensional adaptive integration, and prolate ellipsoidal coordinates. J Math Chem 46, 97–107 (2009). https://doi.org/10.1007/s10910-008-9401-8

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  • DOI: https://doi.org/10.1007/s10910-008-9401-8

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