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Some Elementary Two-Center Integrals over Slater Orbitals Michael P. Barnett
 

Summary: Some Elementary Two-Center 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

  

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

 

Collections: Chemistry