An exploration of the antioxidant power of curcumin, demethoxycurcumin, and bisdemethoxycurcumin, three natural antioxidants found in Curcuma longa, is reported in this work. We exhaust all structural possibilities leading to intramolecular hydrogen bonding and evaluate 15 isomers in total. Calculations were carried out in the gas phase and in the presence of solvents (water, to mimic biological media, and ethanol, to reproduce experimental assays) following the hydrogen atom transfer (HAT) and single electron transfer (SET) mechanisms. CH3OH-O hydrogen bonds are directly related to the antioxidant power via both mechanisms. We provide evidence to explain the experimental observations and to understand the fundamental factors driving antioxidant activity from a molecular perspective. Noticeably, the solvent enhances the antioxidant power in every case. All structures considered here are predicted to have better antioxidant abilities than phenol, and come very close to or surpass vitamin E.