In order to elucidate the experimental results on the UV and electron beam irradiation of solid O2 at the cryogenic temperatures, the structures, relative energies and vibrational frequencies of known and hypothetical oxygen allotropes On (n=1-6) in the singlet, triplet, and quintet states were studied using the CCSD(T,full)/cc–pCVTZ and CCSD(T,fc)/aug-cc–pVTZ theory levels. The results of the quantum chemical calculations demonstrate the existence of several unusual highly symmetric covalently bound structures as well as the intermolecular complexes which were described here for the first time. See Oleg B. Gadzhiev, Stanislav K. Ignatov, Mikhail Yu.Kulikov, Alexander M. Feigin, Alexey G.Razuvaev, Peter G. Sennikov, Otto Schrems; DOI: 10.1021/ct3006584