The results of an ab initio study of complexes with X−H···H−M dihydrogen bonds are presented. The proton donors include HCCH and its derivatives HCCF, HCCCl, and HCCCN; HCN and its derivatives HCNLi+ and HCNNa+; CNH, and H2O, and the proton acceptor is LiH. For comparison, selected complexes with NaH as the proton acceptor have also been investigated. The structures, binding energies and harmonic vibrational frequencies of all complexes were obtained at the MP2/aug‘-cc-pVTZ level of theory. The most stable complexes with C−H groups as proton donors are the cationic complexes NaNCH+:HLi and LiNCH+:HLi. These complexes exhibit very short H····H distances and are prototypical of dihydrogen-bonded complexes that may dissociate by eliminating H2. The calculated binding energies correlate with the H···H distance, the elongation of the C−H donor bond, the amount of charge transfer into the H····H bonding region, and the charge density at the H···H bond critical point. As in conventional hydrogen-bonded complexes, the elongation of the proton donor C−H group correlates with the strength of the interaction, and with the red shift of the C−H stretching frequency. Although changes in the Li−H bond length do not follow a simple pattern, the Li−H stretching frequency is blue-shifted in the complexes.