Four‐center Slater‐type orbital molecular integrals without orbital translations

This article advocates the use of atomic orbitals which have direct physical interpretation, i.e., hydrogen‐like orbitals. They are exponential‐type orbitals (ETOs). Convenient nodeless linear combinations are used, namely Slater‐type orbitals (STOs), with a product of a single power of r and an exponential as radial factor. Until 2008, such orbital products on different atoms were difficult to manipulate for the evaluation of two‐electron integrals. The difficulty was mostly due to cumbersome orbital translations involving slowly convergent infinite sums. These are completely eliminated using Coulomb resolutions. They provide an excellent approximation that reduces these integrals to a sum of one‐electron overlap‐like integral products that each involve orbitals on at most two centers. Such two‐center integrals are separable in prolate spheroidal coordinates. They are thus readily evaluated. Only these integrals need to be re‐evaluated to change basis functions. The above is still valid or three‐center integrals. In four‐center integrals, the resolutions require translating one potential term per product. This is outlined here and detailed elsewhere. Numerical results are reported for the H 2 dimer. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010