Recent experiments on the UV and electron beam irradiation of solid O2 reveals a series of IR features near the valence antisymmetric vibration band of O3 which are frequently interpreted as the formation of unusual On allotropes in the forms of weak complexes or covalently bound molecules. In order to elucidate the question of the nature of the irradiation products, the structure, relative energies, and vibrational frequencies of various forms of On (n = 1−6) in the singlet, triplet, and, in some cases, quintet states were studied using the CCSD(T) method up to the CCSD(T,full)/cc-pCVTZ and CCSD(T,FC)/aug-cc-pVTZ levels. The results of calculations demonstrate the existence of stable highly symmetric structures O4(D3h), O4 (D2d), and O6 (D3d) as well as the intermolecular complexes O2·O2, O2·O3, and O3·O3 in different conformations. The calculations show that the local minimum corresponding to the O3···O complex is quite shallow and cannot explain the ν3 band features close to 1040 cm−1, as was proposed previously. For the ozone dimer, a new conformer was found which is more stable than the structure known to date. The effect of the ozone dimer on the registered IR spectra is discussed.