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A Prototype Three-Center Integral Michael P. Barnett

Summary: A Prototype Three-Center Integral
Michael P. Barnett
L.C.Allen Research Group, Department of Chemistry, Princeton University,
Princeton, NJ 08540
August 27, 1998
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 one-electron integrals 8].


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


Collections: Chemistry