Using first-principles calculations based on the density-functional theory, we perform a detailed study of the dihydrogen (H-2) binding in cis- and trans-polyacetylene decorated with transition metal atoms. First, we investigate the origin of metal-dihydrogen bonding and observe the hybridization of e(g) (t(2g)) orbitals of the Ti atom with the sigma (sigma(*)) orbitals of the H-2 molecules in octahedral geometries, which is consistent with the Kubas model. Second, using a statistical model parametrized by the results of ab initio calculations and experimental data, the adsorption and desorption of molecular hydrogens are calculated at ambient temperature and pressure. We find that the usable capacity at ambient conditions is dramatically reduced from the maximum capacity, the zero-point energy affects the storage capacity significantly, and the optimal binding energy of H-2 molecules under practical conditions is similar to 0.3 eV/H-2. Third, we examine the effects of the aggregation and intercalation of the Ti atoms on H-2 adsorption.