Theoret. Chim.Acta (Berl.)46, 157-164(1977) THEORETICA CHIMICA ACTA 9 by Springer-Verlag 1977 Multipole Expansion of Diatomic Overlap II. Application to Some Diatomic and Polyatomic Molecules Othmar Steinhauser and Peter Schuster Institut fiir TheoretischeChemie und Strahlenchemie der Universitfit Wien. WfihringerStraBe 17, A-1090Wien,Austria The systematic extension of Ruedenberg's expansion formula proposed in Part I [1] is applied to a series of diatomic and polyatomic molecules (BH, NH, HF, B%, C2, F2, CO, BH 3, CH4, NHa, H20, HCN and H2CO ). In general, good agreement with the results of full SCF calculations with the same minimum STO basis set is achieved. Thus, the errors due to this integral approximation scheme called MEDO (Multipole Expansion of Diatomic Overlap) are almost negligible compared to those introduced by basis set truncation. Key words: Diatomic overlap, multipole expansion of~ 1. Introduction In the first paper of this series (Part I [1]) we presented an approximative method for the evaluation of many-center integrals involving Slater type orbitals (STO's). The main strategy of this approximation scheme is to achieve an economic balance between numerical accuracy of integral evaluation and errors due to basis set truncation. Mathematically, the method consists in a multipole expansion ofdiatomic overlap (MEDO) and may be regarded as an extension of Ruedenberg's formula [2]. In Part I we have chosen LiH, Li2 and N 2 as illustrative numerical examples. In order to demonstrate the applicability of our procedure to a wider range of molecules, we performed calculations on a number of closed-shell diatomics BH, NH, HF, B%, C2, F2 and CO, as well as some polyatomic molecules BH3, CH4, NH3, HzO, HCN and HzCO, which are presented here.