ABSTRACT:A general formula has been established for the expansion of the product of two normalized associated Legendre functions centered on the nuclei a and b. This formula has been utilized for the evaluation of two-center overlap and nuclear attraction integrals over Slater-type orbitals (STOs) with integer and noninteger principal quantum numbers. The formulas given in this study for the evaluation of two-center overlap and nuclear attraction integrals show good rate of convergence and great numerical stability under wide range of quantum numbers, orbital exponents, and internuclear distances.

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As an example of the use of the analytical formulas derived for electric multipole moment integrals over STOs in our previous work (I.I. Guseinov, et al., J. Mol. Struct. (Theochem) 465 (1999) 5), the -pole electric moments have been calculated for the ground electronic states of LiH, BH and FH of the first-row diatomic hydride molecules. Calculated electric multipole moment values are in agreement with literatures. By the use of these analytical formulas the -pole moments for multiatomic molecules can be evaluated most efficiently and accurately by employing STOs as basis sets.

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