We use high-level ab initio, up to RCCSD(T), and the density functional theory (DFT) method, B3LYP, to obtain the geometry, vibrational frequencies, and heats of formation of NaO3((X) over tilde B-2(1)) and NaO3+((X) over tilde (1)A(1)). In both cases, a C-2v, diamond structure is deduced. These values allow us also to derive the adiabatic ionization energy. We obtain the following values: DeltaH(f)[NaO3,0K] = -13 +/- 2 kcal mol(-1), DeltaH(f)[NaO3+,0K] = 167 +/- 2 kcal mol(-1), and AIE(NaO3) = 7.80 +/- 0.05 eV. In addition, it was found that the B3LYP functional performs very well for the O-3(-) species: both geometry and vibrational frequencies. For O-3, the method performed well for the geometry, but not so well for the vibrational frequencies. Comparison is made where appropriate to experimental data and to previous calculations. Finally, DeltaH(r) is calculated for a range of reactions that may contribute to the formation of NaO3 or NaO3+ in the atmosphere.