Evaluation of potential of electric field produced by molecule using symmetrical one-range addition theorems for Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices

Using symmetrical one-range addition theorems the series expansion formulae in terms of multicenter charge density expansion coefficients for noninteger n Slater type orbitals (STO), parameters of Coulomb-Yukawa like correlated interaction potentials (CIP) of noninteger indices and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule. The final results are useful for the study of interaction between atomic-molecular systems containing any number of closed and open shells when the Hartree–Fock–Roothaan (HFR) approximation and the explicitly correlated methods based upon the use of STO as basis functions and Coulomb–Yukawa like CIP are employed. As an example of application, the calculations have been performed for the Coulomb interaction potential produced by the ground state of CH ₂ molecule (1a₁² 2a₁² 1b₁² 3a₁¹ 1b₁¹,³B₁ ){(1a_1^2 2a_1^2 1b_1^2 3a_1^1 1b_1^1,^3B_1 )}.