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Symbolic tabulation of overlap integrals over Slater orbitals Michael P. Barnett

Summary: Symbolic tabulation of overlap integrals over Slater orbitals
Michael P. Barnett
Department of Chemistry, Princeton University, Princeton, NJ 08544-1009, USA
(November 12, 2001)
We have used computer algebra (CA) to tabulate closed expressions for over-
lap integrals of Slater orbitals with principal quantum numbers 1 to 12, con-
taining symbolic molecular parameters. Also, we have constructed precise
closed expressions for a range of overlap integrals de ned by higher quantum
numbers and numerical bond lengths and/or screening constants. Numerical
values obtained from both sets of expressions give good agreement with many
of the results in the literature, but suggest serious errors in some other recent
The digital erosion that occurs in xed precision evaluation of our for-
mulas can be monitored and avoided very easily. Evaluation is rapid, and its
accuracy can be extended without restriction. The results can be used to cali-
brate the accuracy of completely numerical schemes. Also, this work provides
the prospect of secular equations containing precise, symbolic elements. We
code the mathematical processes in a relatively natural programming style
that facilitates mechanical optimization. The calculations provide experience


Source: Allen, L.C.- Department of Chemistry, Princeton University


Collections: Chemistry