The bond length alternation (BLA), the highest-occupied-lowest-unoccupied (HO-LU) orbital energy gap, and the corresponding excitation energy are determined for trans-polyacetylene (PA) and polyyne (PY) using density functional theory. Results from the Coulomb-attenuated CAM-B3LYP functional are compared with those from the conventional BHHLYP and B3LYP hybrid functionals. BLA values and HO-LU gaps are determined using both finite oligomer and infinite chain calculations, subject to periodic boundary conditions. TDDFT excitation energies are determined for the oligomers. The oligomer excitation energies and HO-LU gaps are then used, in conjunction with the infinite chain HO-LU gap, to estimate the infinite chain excitation energy. Overall, BHHLYP and CAM-B3LYP give BLA values and excitation energies that are larger and more accurate than those obtained using B3LYP. The results highlight the degree to which excitation energies can be approximated using the HO-LU gaps-at the infinite limit, this approximation works well for B3LYP, but not for the other functionals, where the HO-LU gap is significantly larger. The study provides further evidence for the high-quality theoretical predictions that can be obtained from the CAM-B3LYP functional.