Third-order dispersion energy from response functions

In the second order of perturbation theory, the dispersion component of the interaction energy of two atoms or molecules can be expressed as an integral of frequency-dependent response functions of monomers. An analogous formula is derived here for the third-order dispersion energies. The general formula involves a nonstandard response function, but for atoms in asymptotic expansion the expression involves only the standard dynamic hyperpolarizabilities.