In an important recent report, Coles and Hitchcock (Chem. Commun. 2005, 3165) have synthesized a unique compound of the form Li9O2(hpp)7, with an O2 unit encapsulated in the Li cluster. The group hpp is the bicyclic guanidinate 1,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidinate. Coles and Hitchcock raise the interesting possibility that the trapped species is the O2 dianion. We have theoretically investigated (with full geometry optimization) the structural, vibrational, and electronic properties of this fascinating system with 165 atoms. Every indication supports the qualitative conclusion that this system is best represented as an O2 dianion embedded in a Li cluster. Several smaller model systems, including replacement of the hpp ligands by Cl atoms, are also examined and provide some interesting comparisons.