The tendency for mixed-isotope O₂ fragments to exhibit different stretching frequencies in asymmetric environments is examined with various levels of electronic structure theory for simple peroxides and peroxyl radicals, as well as for a variety of monocopper–O₂ complexes. The study of the monocopper species is motivated by their relevance to the active site of galactose oxidase. Extensive theoretical work with an experimental model characterized by Jazdzewski et al. (J. Biol. Inorg. Chem. 8:381–393, 2003) suggests that the failure to observe a splitting between ¹⁶O¹⁸O and ¹⁸O¹⁶O isotopomers cannot be taken as evidence against end-on O₂ coordination. Conformational analysis on an energetic basis, however, is complicated by biradical character inherent in all of the copper–O₂ singlet structures.