Explicitly correlated coupled cluster theory at the CCSD(T)-F12x level (T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106, 2007) has been employed to study structures and vibrations of complexes of type c-C3H3+center dot L and H2C3H+center dot L (L = Ne, Ar, N-2, CO2, and O-2). Both cations have different binding sites, allowing for the formation of weak to moderately strong hydrogen bonds as well as "C-bound'' or "pi-bound'' structures. In contrast to previous expectations, the energetically most favourable structures of all H2C3H+center dot L complexes investigated are "C-bound'', with the ligand bound to the methylenic carbon atom. The theoretical predictions enable a more detailed interpretation of infrared photodissociation (IRPD) spectra than was possible hitherto. In particular, the bands observed in the range 3238-3245 cm(-1) (D. Roth and O. Dopfer, Phys. Chem. Chem. Phys. 4, 4855, 2002) are assigned to essentially free acetylenic CH stretching vibrations of the propargyl cation in "C-bound'' H2C3H+center dot L complexes.