 
Summary: A Prototype ThreeCenter Integral
Michael P. Barnett
L.C.Allen Research Group, Department of Chemistry, Princeton University,
Princeton, NJ 08540
August 27, 1998
Abstract
A prototype three center exchange integral over Slater orbitals is reduced to an in nite series. A
closed expression is given for the general term. The generalization to the orbitals of arbitrary quantum
number is outlined. The derivations and the production of this paper were mechanized.
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 the 1960s (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 it was applied to a prototype 6]. Good results were obtained, using numerical quadrature
to compute the successive terms of the series. Now, the analytical reduction of these terms has
been accomplished, using symbolic computation 7], and some general methods have been tested
on a set of relatively simple oneelectron integrals 8].
