We present a two-dimensional collinear, adiabatic model to describe the motion of a proton in between two hydrogen molecules which adjust their elongation to trace a minimum-energy path. Together with bound states, the predissociative, vibrationally excited states involved in the electric dipole transitions are characterized. The main qualitative features of the infrared spectra of H${}_{5}{}^{+}$ and its deuterated variant are discussed, and the effect of the temperature of the clusters is analyzed.