Rapid Evaluation of Coulomb Integrals

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Abstract
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.