  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.
