Redox potentials in electrochemistry are specified relative to the standard free energy of the normal hydrogen electrode (NHE). The NHE reaction consists of the oxidation of a gas-phase hydrogen molecule to aqueous protons. Computing the free energy of this reaction in a molecular dynamics simulation is challenge as it involves the insertion of a proton in water. We have developed such a method using a combination of density functional based molecular dynamics (DFTMD) and free energy perturbation methods. In this talk we will outline how this method works and discuss the application to the computation of the NHE potentials of the reduction of some simple aqueous radical species to their anions, namely OH, Cl and SH, OOH and O2. In particular the OH , OOH and O2 reduction are of great importance because they are steps in the reduction of dioxygen to water (or the reverse reaction the oxidation of water). Unfortunately, common density functionals as used in DFTMD are for radical species not nearly as accurate as for closed shell species. The NHE reduction potentials computed by our method can be directly compared to experiment and can therefore be used to quantify the problem which is currently holding the application of DFT to electrochemical energy conversion in fuel and photocatalytic cells.