An ab initio computational study of the properties of four linear dihydrogen-bonded complexes formed between the first compound with an Ar-C chemical bond (FArCCH) and HBeX (X = H, F, Cl, and Br) molecules was undertaken at the MP2/6-311++G(2d,2p) level of theory. The calculated complexation energy at MP2 and G2(MP2) levels decreases in the order (HBeHHCCArF)-H-... > (BrBeHHCCArF)-H-... > (ClBeHHCCArF)-H-... > (FBeHHCCArF)-H-.... The intermolecular stretching frequency, and shifts within the monomers, are compared with the energetic strength of complexation.