Evaluation of intermolecular interaction energy using one-range addition theorems for $${\psi ^\alpha}$$ – ETO and Coulomb-Yukawa like correlated interaction potentials with integer and noninteger indices

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Using one-range addition theorems for complete orthonormal sets of \({\psi^\alpha }\) – exponential type orbitals (α = 1, 0, −1, −2, . . .) intruduced by the author, the series expansion relations are established for the energy of interaction between molecules which have any number of closed and open shells. The final results are expressed through the linear combination coefficients of molecular orbitals, the parameters of Coulomb-Yukawa like correlated interaction potentials with integer and noninteger indices and the multicenter overlap integrals. The formulas obtained are useful for the study of interaction between atomic-molecular systems when the \({\psi^\alpha}\) – exponential type orbital basis functions in Hartree-Fock-Roothaan and explicitly correlated methods are employed.