Equilibrium geometries and harmonic vibrational frequencies of three substituted dioxiranes, CO2FOF, CO2NF, End CO2(NH)(2), which have not been previously investigated, are reported. Results are based on second-order Moller-Plesset (MP2) and quadratic configuration interaction through single and double excitation (QCISD) calculations using 6-31G(d) and 6-311G(d,p) basis sets. Molecular geometric characteristics, vibrational frequencies, dipole moments, as well as local atomic charges, are compared with those of known dioxiranes (CO2H2, CO2F2, CO2N2, CO4). It is found that bond lengths and angles of the dioxirane ring are sensitive to the electropositivity of the central carbon. Hydrazodioxirane, CO2(NH)(2), is found to be a high-energy density molecule; whereas fluorofluoroxydioxirane (CO2FOF) may be of further interest as a powerful oxidizer. Equilibrium geometries and vibrational frequencies of the previously uncharacterized energetically low-lying 1(3)B(1) and 1(3)B(2) triplet states of CO2F2 and the ground state of its cation, CO2F2+(1(2)A(2)), are predicted and analyzed.