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.