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Efficient and Rapid Numerical Evaluation of the Two-Electron, Four-Center Coulomb Integrals Using Nonlinear Transformations and Useful Properties of Sine and Bessel Functions

✍ Scribed by Hassan Safouhi

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 134 KB
Volume: 176
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.2001.6925

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✦ Synopsis

Two-electron, four-center Coulomb integrals are undoubtedly the most difficult type involved in ab initio and density functional theory molecular structure calculations. Millions of such integrals are required for molecules of interest; therefore rapidity is the primordial criterion when the precision has been reached. This work presents an extremely efficient approach for improving convergence of semiinfinite very oscillatory integrals, based on the nonlinear D-transformation and some useful properties of spherical Bessel, reduced Bessel, and sine functions. The new method is now shown to be applicable to evaluating the two-electron, four-center Coulomb integrals over B functions. The section with numerical results illustrates the unprecedented efficiency of the new approach in evaluating the integrals of interest.

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