Higher-order interaction energies for a system of N arbitrary molecules in the light of spherical tensor theory

Abstract

The Rayleigh–Schrödinger perturbation treatment accompanied by a multipole expansion of the interaction potential can be used in the quantum-mechanical studies of long-range intermolecular forces. The total third-order interaction energy in a system of N molecules separates into several induction and dispersion categories. Only some of them are purely pairwise additive. In the present paper the closed expressions for all possible categories of the third-order anisotropic interaction energy in a collection of N arbitrary molecules are derived, in which the orientational dependence is pushed to its limits. The derivation is based on the spherical tensor formalism. The formulas for the induction energies are directly related to the spherical multipole moments and irreducible (hyper)polarizabilities of the interacting molecules in body-fixed frames. The same is achieved for the dispersion categories after employing some simple approximations. The present paper can be treated as an extension of the spherical tensor description of the two-body long-range molecular interactions for the most important quantum-mechanical pairwise nonadditive forces.