Evaluation of three-center two-electron repulsion integrals over Slater orbitals

The Slater orbitals are the natural basis functions in quantum molecular calculations. Three-center repulsion Coulomb-exchange integrals over Slater orbitals are evaluated analytically with arbitrary orbital exponents, first for linear conformation of the atomic centers. These integrals have been expressed as a linear combination of three-center one-electron overlap integrals, and those have been calculated using auxiliary functions in terms of one-electron auxiliary integrals. Only one infinite expansion has been introduced. The resulting integral converges to 20 decimal digits using about 25-30 terms. Hybrid-exchange three-center repulsion integrals will be investigated next using this method, as well as triangular conformation of the centers.