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Integration by cell algorithm for Slater integrals in a spline basis
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DOI：10.1006/jcph.1999.6361.png)
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An algorithm for evaluating Slater integrals in a B-spline basis is introduced. Based on the piecewise property of the B-splines, the algorithm divides the two-dimensional (r(1), r(2)) region into a number of rectangular cells according to our chosen grid and implements the two-dimensional integration over each individual cell using Gaussian quadrature. Over the off-diagonal cells, the integrands are separable so that each two-dimensional cell-integral is reduced to a product of two one-dimensional integrals. Furthermore, the scaling invariance of the B-splines in the logarithmic region of the chosen grid is fully exploited such that only some of the cell integrations need to be implemented. The values of given Slater integrals are obtained by assembling the cell integrals. This algorithm significantly improves the efficiency and accuracy of the traditional method that relies on the solution of differential equations and renders the B-spline method more effective when applied to multi-electron atomic systems. (C) 1999 Academic Press.
Keyword:
Slater integral
B-spline
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3.8
论文数:
1.6W
被引数:
7.4W
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