The properties of Fourier transforms and single‐center expansions of Slater‐type orbitals are used to obtain formulas for general Coulomb integrals as finite linear combinations of overlap and nuclear attraction integrals, thereby permitting the explicit expression of Coulomb integrals in terms of the auxiliary functions normally used in one‐electron integral calculations. The formulas are relatively simple and have a form which indicates the avoidance of numerical difficulties found in other evaluation methods. Working formulas are given for all integrals arising from orbitals of principal quantum numbers 1 and 2.
REFERENCES
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M. Kotani, A. Amemiya, E. Ishiguro, and T. Kimura, Table of Molecular Integrals (Maruzen Co., Ltd., Tokyo, 1955).
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In using Roothaan’s formulas in conjunction with the expressions listed in this paper, care must be taken to ensure consistency. Our coordinate system is the same as Roothaan’s for Center A, but is reversed from his at Center B. Roothaan’s normalization of charge distributions also differs from that used here.
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© 1969 American Institute of Physics.
1969
American Institute of Physics
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