Exact formulas for multipole moments using Slater-type molecular orbitals

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Abstract
A triple infinite sum of formulas expressed as an expansion in Legendre polynomials is generated by use of computer algebra to represent the potential from the midpoint of two Slater-type orbitals; the charge density that determines the potential is given as the product of the two orbitals. An example using 1s orbitals shows that only a few terms are needed to obtain four-figure accuracy. Exact formulas are obtained for multipole moments by means of a careful study of expanded formulas, allowing an ‘‘extrapolation to infinity.’’ This Löwdin alpha-function approach augmented by using a C matrix to characterize Slater-type orbitals can be readily generalized to all cases.