Overlap integrals for Dirac–Slater orbitals

The problem of computing overlap integrals of Slater-type orbitals on different centers for relativistic orbitals with a behavior of r^s at the nuclei is considered. The integrals can be expressed as integrals in momentum space involving a spherical Bessel function j_L(kR). The problem of the oscillatory behavior of j_L(kR) at large kR can be eliminated by transforming the integral to a contour integral in the upper half-plane. A method of carrying out the numerical integration is described and the number of integration points required for a large number of cases are given. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004