On the fast evaluation of three-center nuclear attraction integrals using one-range addition theorems for Slater functions

Using one-range addition theorems, the three-center nuclear attraction integrals are expressed through the overlap integrals containing χ - and χ α -Slater-type orbitals (χ -STOs and χ α -STOs), where - ∞ < α ⩽ 2 and χnlmα (ζ, r-vector) =(1)/(2ζr)α χnlm (ζ, r-vector). For the fast calculation, the partial summation is utilized for some indices of series expansion relations which correspond to progressively increasing upper limits. The binomial coefficients are stored in the memory of the computer. The convergence and accuracy of series are tested by calculating concrete cases. The best values are obtained for α = 0 . (paper)