Advanced oxidation processes that utilize highly oxidative radicals are widely used in water reuse treatment. In recent years, the application of sulfate radical (SO4˙-) as a promising oxidant for water treatment has gained increasing attention. To understand the efficiency of SO4˙- in the degradation of organic contaminants in wastewater effluent, it is important to be able to predict the reaction kinetics of various SO4˙--driven oxidation reactions. In this study, we utilize density functional theory (DFT) and high-level wavefunction-based methods (including computationally-intensive coupled cluster methods), to explore the activation energies of SO4˙--driven oxidation reactions on a series of benzene-derived contaminants. These high-level calculations encompass a wide set of reactions including 110 forward/reverse reactions and 5 different computational methods in total. Based on the high-level coupled-cluster quantum calculations, we find that the popular M06-2X DFT functional is significantly more accurate for OH- additions than for SO4˙- reactions. Most importantly, we highlight some of the limitations and deficiencies of other computational methods, and we recommend the use of high-level quantum calculations to spot-check environmental chemistry reactions that may lie outside the training set of the M06-2X functional, particularly for water oxidation reactions that involve SO4˙- and other inorganic species.