Structural parameters, binding energies, and frequencies of the infrared- and Raman-active vibrations are calculated for an infinite zigzag chain of hydrogen fluoride molecules by ab initio crystal orbital theory with the analytical energy gradient scheme. The Becke-Lee-Yang-Parr (BLYP), Becke3-Lee-Yang-Parr (B3LYP), and Hartree-Fock (RHF) levels are used in conjunction with the 6-311++G(d,p) basis set. Molecular orbital calculations at the BLYP, B3LYP, RHF, and the second-order Moller-Plesset perturbation (MP2) levels with the same basis set are carried out on linear HF oligomers containing up to six molecules, to examine the chain-length dependence of the energetic and structural properties. The predicted chain-length dependence is found to be significantly smaller in the RHF results than in the BLYP and B3LYP results. The RHF level substantially underestimates the downward frequency shifts in the intramolecular H-F stretching modes on going from the monomer to the polymer, while the shifts calculated at the BLYP and B3LYP levels are much closer to the experimental findings, although they are slightly overestimated. The RHF level strongly underestimates the intramolecular H-F bond length and overestimates the intermolecular F ... H and F ... F distances of the HF polymer, while the structural parameters predicted at the BLYP and B3LYP levels are in good agreement with the experimental results. It is concluded that the RHF level seriously underestimates the cooperative binding effects of consecutive hydrogen bonds, whereas the BLYP and B3LYP levels slightly overestimate this behavior; but these latter levels provide much better description than the former. Vibrational assignment of Librational modes of HF crystals is reexamined on the basis of the calculated frequencies. The observed frequencies of the librational and pseudo-translational modes fall between the corresponding frequencies calculated at the RHF and density functional levels.