Polynomials for evaluation of two-center overlap integrals

Expressions of products AkBk, where Ak and Bk are incomplete gamma functions, are given for evaluation of two-center overlap integrals (TCOIs) over unnormalized Slater-type orbitals (STOs). The polynomials of AkBk have been derived after the method proposed by Lofthus and pertain to two-center bonds of σ, π, δ, and φ axial symmetries. The functions of AkBk have been arranged in pairs of s, p, d, and f STOs with principal quantum numbers between 1 and 5. The contributions of these functions to various TCOIs have been evaluated and discussed. The formulae are applicable as input matrices for computations of TCOIs.