Addition theorem of Slater type orbitals: a numerical evaluation of Barnett–Coulson/Löwdin functions

When using the one-centre two-range expansion method to evaluate multicentre integrals over Slater type orbitals (STOs), it may become necessary to compute numerical values of the corresponding Fourier coefficients, also known as Barnett–Coulson/Löwdin Functions (BCLFs) (Bouferguene and Jones 1998 J. Chem. Phys. 109 5718). To carry out this task, it is crucial to not only have a stable numerical procedure but also a fast algorithm. In previous work (Bouferguene and Rinaldi 1994 Int. J. Quantum Chem. 50 21), BCLFs were represented by a double integral which led to a numerically stable algorithm but this turned out to be disappointingly time consuming. The present work aims at exploring another path in which BCLFs are represented either by an infinite series involving modified Bessel functions Kν( √ a2 + r2) or by an integral whose integrand is a smooth function. Both of these representations have the advantage of being symmetrical with respect to the cusp parameter a and the radial variable r. As a consequence, it is no longer necessary to split the integrals over r ∈ [0,+∞) into several components with a different analytical form in each of these. A numerical study is also carried out to help select the most appropriate method to be used in practice. PACS numbers: 02.60.−x, 02.30.Gp, 31.15.Kb (Some figures in this article are in colour only in the electronic version)