Electrode potentials are computed theoretically for quinones by using a combination of statistical and quantum mechanics. The calculations, which incorporate the all-important influence of solvent, can achieve an accuracy of about 25 mV. The most stable conformation in solution has been determined by running constrained molecular dynamics to sample predetermined conformations. The most stable conformations may be used to calculate theoretical electrode potentials in aqueous solution, which are in very good agreement with experiment. The results show that the method is likely to be very useful in the design of bioreductive anticancer agents whose activity is determined by their electrode potential. Studies on the effect of the torsional constraints on the changes in the free energy of hydration illustrate the sensitivity of the free energy perturbation results to the torsional parameters.