Symbolic tabulation of overlap integrals over Slater orbitals

Abstract

We have used computer algebra CA to tabulate closed expressions for over lap integrals of Slater orbitals with principal quantum numbers to 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 publications 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 of working with formula les that occupy tens of megabytes Gp c p Typeset using REVTEX

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