The one-electron reduction of quinones is important not only in electrochemistry but also in biochemical energy storage, energy utilization, and organic chemcial reactions. Thermodynamic cycles are investigated to estimate aqueous one-electron reduction potentials for the redox indicators p-benzoquinone and p-duroquinone, as well as chloro-substituted p-benzoquinones. Gas-phase reduction free energy differences are approximated from electron affinities calculated by using the hybrid Hartree-Fock/density-functional B3LYP method, a semiempirical quantum chemical method that expresses a molecule's exchange-correlation energy as a weighted sum of Hartree-Fock, local, and gradient-corrected density-functional energies. Free energy perturbation theory was used with molecular dynamics simulations (at constant temperature, pressure, and number of atoms) to estimate hydration free energy differences. Calculated one-electron reduction potentials for the quinones are within 10-190 meV of experimental values. An exceptionally accurate reduction potential was calculated for p-benzoquinone (E 0 calc ) 4.51 eV and E 0 expt ) 4.52 to 4.54 eV) and least accuracy was obtained for p-duroquinone (E 0 calc ) 3.99 eV and E 0 expt ) 4.18-4.21 eV). Radial distribution functions show that more hydrogens contact the oxygens of the p-benzosemiquinone anions than the oxygen atoms of the neutral quinones. The strengths and numbers of water hydrogen bonds to the semiquinone anions also correlate with hydration free energy differences between the quinones and their semiquinone anions, implying that models of water solvation designed to reproduce hydration free energy differences or reduction potentials should somehow incorporate the effects of specific solute-water interactions.