Density functional theory calculations on melatonin, metabolites and synthetic derivatives thereof, and a range of other biological antioxidant molecules are presented, with a view to understanding the antioxidant ability of these molecules. After testing of the necessary calculations, we show that melatonin lies close to vitamin E on a donor-acceptor map, indicating that it should be an excellent electron donor but a poor acceptor. The neutral radical metabolite of melatonin is predicted to be an even better donor, whereas other metabolites and synthetic derivatives should retain antioxidant ability but are less powerful than the parent. QSAR models of antioxidant activity, measured in two different assays, are presented. We show that octanol-water partition coefficient is an excellent predictor of activity in lipophilic media, while properties related to electron donor/acceptor power give good fits against activity in aqueous media.