Quantitative structure-activity relationships (QSARs) for prediction of the reaction rate constants of phenols and phenolates with three photochemically produced oxidants, singlet oxygen, carbonate radical, and triplet excited state sensitizers/organic matter, are developed. The predictive variable is the one-electron oxidation potential (E), which is calculated for each species using density functional theory. The reaction rate constants are obtained from the literature, and for singlet oxygen, are augmented with new experimental data. Calculated E values have a mean unsigned error compared to literature values of 0.04-0.06 V. For singlet oxygen, a single linear QSAR that includes both phenols and phenolates is developed that predicts experimental rate constants, on average, to within a factor of three. Predictions for only 6 out of 87 compounds are off by more than a factor of 10. A more limited data set for carbonate radical reactions with phenols and phenolates also gives a single linear QSAR with prediction of rate constant being accurate to within a factor of three. The data for the reactions of phenols with triplet state sensitizers demonstrate that two sensitizers, 2-acetonaphthone and methylene blue, most closely predict the reactivity trend of triplet excited state organic matter with phenols. Using sensitizers with stronger reduction potentials could lead to overestimation of rate constants and thus underestimation of phenolic pollutant persistence.

Within a basis set of one-electron functions that form linearly independent products (LIPs), it is always possible to construct a unique local (multiplicative) real-space potential that is precisely equivalent to an arbitrary given operator. Although standard basis sets of quantum chemistry rarely form LIPs in a numerical sense, occupied and low-lying virtual canonical Kohn–Sham orbitals often do so, at least for small atoms and molecules. Using these principles, we construct atomic and molecular exchange–correlation potentials from their matrix representations in LIP basis sets of occupied canonical Kohn–Sham orbitals. The reconstructions are found to imitate the original potentials in a consistent but exaggerated way. Since the original and reconstructed potentials produce the same ground-state electron density and energy within the associated LIP basis set, the procedure may be regarded as a rigorous solution to the Kohn–Sham inversion problem within the subspace spanned by the occupied Kohn–Sham orbitals.