Higher order interaction energies for systems of asymmetric molecules

Long-range electrical interactions in a system of N asymmetric molecules are examined in the third order of Rayleigh-Schrödinger perturbation theory. The total third-order interaction energy separates into five categories. Two of the categories correspond to classical electric induction interactions between asymmetric molecules and three of the categories correspond to dispersion-type interactions. The induction interactions consist of a set of terms which are linear in the first hyperpolarizability tensor and its generalizations and a set of terms which are bilinear in the polarizability tensor and its generalizations. One category of dispersion interactions is a generalization of the pairwise non-additive triple-dipole interaction between atoms first studied by Muto and by Axilrod and Teller. A second category of dispersion interactions, which depends on molecular hyperpolarizability tensors that also occur in the theory of the linear electro-optic effect, is non-vanishing only when at least one of the molecules has a permanent electric multipole moment. This category of interactions has pairwise non-additive as well as pairwise additive components and has not previously been considered in the literature. The third category of dispersion interactions is a generalization to asymmetric molecules of the two-body interactions between spherical molecules studied by Chan and Dalgarno. A comparison of interaction energies derived from third-order perturbation theory with energies from first- and second-order perturbation theory is given for two linear molecules.