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 HBeH···HCCArF > BrBeH···HCCArF > ClBeH···HCCArF > FBeH···HCCArF. The intermolecular stretching frequency, and shifts within the monomers, are compared with the energetic strength of complexation.