The thermochemical constants for the oxidation of tyrosine and tryptophan through proton coupled electron transfer in aqueous solution have been computed applying a recently developed density functional theory (DFT) based molecular dynamics method for reversible elimination of protons and electrons. This method enables us to estimate the solvation free energy of a proton (H(+)) in a periodic model system from the free energy for the deprotonation of an aqueous hydronium ion (H(3)O(+)). Using the computed solvation free energy of H(+) as reference, the deprotonation and oxidation free energies of an aqueous species can be converted to pK(a) and normal hydrogen electrode (NHE) potentials. This conversion requires certain thermochemical corrections which were first presented in a similar study of the oxidation of hydrobenzoquinone [J. Cheng, M. Sulpizi, and M. Sprik, J. Chem. Phys. 131, 154504 (2009)]. Taking a different view of the thermodynamic status of the hydronium ion, these thermochemical corrections are revised in the present work. The key difference with the previous scheme is that the hydronium is now treated as an intermediate in the transfer of the proton from solution to the gas-phase. The accuracy of the method is assessed by a detailed comparison of the computed pK(a), NHE potentials and dehydrogenation free energies to experiment. As a further application of the technique, we have analyzed the role of the solvent in the oxidation of tyrosine by the tryptophan radical. The free energy change computed for this hydrogen atom transfer reaction is very similar to the gas-phase value, in agreement with experiment. The molecular dynamics results however, show that the minimal solvent effect on the reaction free energy is accompanied by a significant reorganization of the solvent.