Calculations of long-range three-body interactions for Li($2\,^2S$)-Li($2\,^2S$)-Li$^{+}$($1\,^{1}S$)

Using perturbation theory for energies, we evaluate the additive and nonadditive interaction coefficients $C_4$, $C_6$, $C_7$, $C_8$ and $C_9$ for the Li($2\,^2S$)-Li($2\,^2S$)-Li$^{+}$($1\,^{1}S$) system. The obtained coefficients $C_n$ are evaluated with highly accurate variationally-generated nonrelativistic wave functions in Hylleraas coordinates. The nonadditive interaction coefficients depend on the geometrical configurations of this three-body system and on the different positions of the ion for each configuration. Our calculations may be of interest for the study of three-body recombination and for constructing precise potential energy surfaces.