  We investigate theoretically the combination of first-order
quadrupole-quadrupole and second-order dipole-dipole effects on the long-range
electrostatic interactions between a ground-state homonuclear alkali-metal
dimer and an excited alkali-metal atom. As the electrostatic energy is
comparable to the dimer rotational structure, we develop a general description
of the long-range interactions which allows for couplings between the dimer
rotational levels. The resulting adiabatic potential energy curves, which
exhibit avoided crossings, cannot be expanded on the usual $1/R^{n}$ series. We
study in details the breakdown of this approximation in the particular case
Cs$_{2}+$Cs. Our results are found promising in the prospect of accomplishing
the photoassociation of ultracold trimers.
