The electronic structures and vibrational frequencies of dimethyl-substituted carbonyl oxide and its cyclic isomer dimethyldioxirane have been investigated using high-level ab initio quantum mechanical techniques with large basis sets. The equilibrium geometries have been optimized at the self-consistent field (SCF), the single and double excitation configuration interaction (CISD), the coupled cluster with single and double excitation (CCSD), and the CCSD with connected triple excitations [CCSD(T)] levels of theory. The absolute and relative energies of carbonyl oxide, dimethyldioxirane, and the transition state between them have also been compared. At the highest level of theory employed in this study, TZP CCSD(T), dimethyldioxirane is predicted to be lower in energy than the carbonyl oxide by 23.2 kcal/mol with the inclusion of zero-point vibrational energy (ZPVE) corrections. The energy barrier for the cyclization of carbonyl oxide becomes 19.5 kcal/mol at the same level of theory. Harmonic vibrational frequencies and infrared (IR) intensities are determined at the DZP SCF and TZP SCF levels of theory for the dimethyl-substituted carbonyl oxide and the transition state, and at correlated levels (CISD and CCSD) with DZP and TZP basis sets for dimethyldioxirane. The experimental vibrational frequencies of dimethyldioxirane are assigned using the present theoretical predictions. It is hoped that the theoretical frequencies for the dimethyl carbonyl oxide isomer will stimulate new experiments.