 
Summary: Some Elementary TwoCenter Integrals over Slater Orbitals
Michael P. Barnett
L.C.Allen Research Group, Department of Chemistry, Princeton University,
Princeton, NJ 08540
December 16, 1998
Abstract
A table of formulas for some integrals containing exponentials based on two centers has been computed
mechanically. The tabulation, which serves as a prototype for more extensive calculations, uses an
extension of the Gegenbauer addition theorem, that we call the function expansion. Some general
problems that a ect the mechanized construction of documents that contain mathematical derivations
and results were resolved in the process.
1 Introduction
The evaluation of the full range of molecular integrals over Slater orbitals (ETOs) remains an
unsolved problem. The so called function method showed promise in the early days of computa
tional chemistry 1, 2], but convergence problems arose in particular circumstances 3]. Gaussian
orbitals have dominated the eld since then (see, for example, 4]). Several attempts to solve
the ETO problem were reported in 5]. With the advent of supercomputers, the author restarted
the exploration of the function method. A way was found to sum the slowly convergent series
and applied to a prototype 6]. Good results were obtained, using numerical quadrature to com
pute the successive terms of the series. Now, the analytical reduction of these terms has been
