Ab initio calculations at the MP2 and CCSD(T) levels of theory have disclosed the conceivable existence of fluorine-coordinated complexes of HHeF with alkali-metal ions and molecules M+ (M+=Li+–Cs+), M+–OH2, M+–NH3 (M+=Li+, Na+), and MX (M=Li, Na; X=F, Cl, Br). All these ligands L induce a shortening of the HHe distance and a lengthening of the HeF distance accompanied by consistent blue- and redshifts, respectively, of the HHe and HeF stretching modes. These structural effects are qualitatively similar to those predicted for other investigated complexes of the noble gas hydrides HNgY, but are quantitatively more pronounced. For example, the blueshifts of the HHe stretching mode are exceptionally large, ranging between around 750 and 1000 cm−1. The interactions of HHeF with the ligands investigated herein also enhance the (HHe)+F− dipole character and produce large complexation energies of around 20–60 kcal mol−1. Most of the HHeF–L complexes are indeed so stable that the three-body dissociation of HHeF into H+He+F, exothermic by around 25–30 kcal mol−1, becomes endothermic. This effect is, however, accompanied by a strong decrease in the HHeF bending barrier. The complexation energies, ΔE, and the bending barriers, E*, are, in particular, related by the inverse relationship E*(kcal mol−1)=6.9exp[−0.041ΔE(kcal mol−1)]. Therefore the HHeFL complexes, which are definitely stable with respect to H+He+F+L (ΔE≈25–30 kcal mol−1), are predicted to have bending barriers of only 0.5–2 kcal mol−1. Overall, our calculations cast doubt on the conceivable stabilization of HHeF by complexation.