One-Range Addition Theorems in Terms of ψ^α -ETOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials of Integer and Noninteger Indices

The expansion formulas in terms of complete orthonormal sets of ψ^α -exponential type orbitals are established for the Slater type orbitals and Coulomb-Yukawa-like correlated interaction potentials of integer and noninteger indices. These relations are used in obtaining their unsymmetrical and symmetrical one-range addition theorems. The final results are especially useful in the calculations of multicentre multielectron integrals occurring when Hartree-Fock-Roothaan and explicitly correlated methods are employed.