An ab initio computational study of the properties of four linear dihydrogen-bonded complexes pairing MH2 (M = Zn, Cd) with HCCRgF (Rg = Ar, Kr) was undertaken at the MP2/DGDZVP level of theory. The calculated complexation energies of the linear complexes vary between 6.5 kJ/mol for M = Zn to 8.5 kJ/mol for M = Cd. Equilibrium interatomic (HH)-H-... distances are roughly 2.07.8. for all four complexes. The red shifts of the H-C stretching frequency of HCCRgF correlate nicely with the interaction energies.