Reactions with ozone transform organic and inorganic molecules in water treatment systems as well as in atmospheric chemistry, either in the aqueous phase, at gas/particle interfaces, or in the gas phase. Computed thermokinetic data can be used to estimate the reactivities of molecules toward ozone in cases where no experimental data are available. Although the gas-phase reactivity of olefins with ozone has been characterized extensively in the literature, this is not the case for the richer chemistry of ozone with polar molecules, which occurs in the aqueous phase or in microhydrated environments. Here, we selected a number of model reactions with small molecules (ethene, ethyne, hydrogen cyanide, hydrogen chloride, ammonia, bromide, and trimethylamine) to study the accuracy of different quantum chemical methods for describing the reactivities of these molecules with ozone. We calculated benchmark electronic energies of gas-phase reactions of these systems with single reference coupled cluster (CC) theory. These benchmark results for the binding energy in the van der Waals complex, the energy of the transition structure, and the reaction energy were estimated to be accurate within 1-2 kcal mol(-1). Singlet oxygen (O-1(2)) is a common product of ozone reactions. Coupled cluster calculations with up to perturbative quadruples (CCSDT(Q)) were needed to obtain reaction energies accurate within 1 kcal mol(-1) when this species was involved. In (micro)hydrated environments or at interfaces, coupled cluster methods are prohibitively expensive in most cases. We tested the suitability of some contemporary density functional theory (DFT) methods to reproduce the benchmark electronic energy differences. Range-separated functionals were found to be promising candidates to estimate forward barrier heights, with LC-omega PBE rivaling the accuracy of CCSD(T). For energies of reaction, however, DFT methods exhibited large systematic errors, depending on their fraction of orbital exchange. This was found to worsen when O-1(2) is a product, and no safe recommendation can be given for DFT reaction energies in such cases.