One-range addition theorems for combined Coulomb and Yukawa like central and noncentral interaction potentials and their derivatives

In this work we present the combined one-range addition theorems for arbitrary Coulomb and Yukawa like central and noncentral interaction potentials and their first and second derivatives occurring in the Hartree-Fock-Roothaan approximation and explicitly correlated methods, and also in the study of electric field and its gradient induced by electrons at the nuclei of a molecule. The relationships obtained for addition theorems are valid for the arbitrary parameters of potentials.