PATH-INTEGRAL CALCULATIONS OF THE FREE-ENERGIES OF HYDRATION OF HYDROGEN ISOTOPES (H, D, AND MU)

We have calculated the free energies of aqueous solvation of the hydro gen isotopes H, D, and Mu quantum mechanically, using path integral me thods, to understand the effect of equilibrium solvation on the rate c onstants for the addition of hydrogen atom isotopes to benzene in aque ous solution. Within a classical mechanical model, the free energy of solvation of the hydrogenic solute is independent of its isotopic mass . However, when treated quantum mechanically, these solvation free ene rgies can vary with solute isotopic mass. Our calculated Helmholtz fre e energies of solvation for the H and D isotopes are nearly the same, 2.53 +/- 0.31 and 2.44 +/- 0.29 kcal/mol, respectively, indicating tha t quantum effects on the solvation energetics are small for these syst ems. Similarly, our calculated Gibbs free energies of solvation for H and D are 3.23 +/- 0.32 and 3.29 +/- 0.35, respectively. The calculate d free energy of solvation of H is in qualitative agreement with the e xperimental estimate. We have also calculated the Helmholtz and Gibbs free energies of solvation at 300 K for the light hydrogenic isotope m uonium (Mu). (Muonium is a positive muon electron pair that behaves ch emically like hydrogen but has one-ninth the mass.) The calculated Hel mholtz and Gibbs free energies of solvation for Mu are much higher, ab out 3.83 +/- 0.71 and 4.23 +/- 1.23 kcal/mol, respectively. These valu es are used to evaluate the effect of equilibrium solvation on kinetic isotope effects for the addition reaction of hydrogen atom isotopes t o benzene. If classical mechanics is used for this reaction, the chang e in the free energy of activation upon solvation is independent of th e mass of the hydrogen atom isotope. Using our calculated free energy of solvation data, we conclude that the rate enhancement in solution c ompared to gas phase for hydrogen and deuterium atom addition to benze ne is well described by equilibrium solvation. This argument does not apply to muonium, indicating that details of the solvent dynamics will be important for the reaction of muonium with benzene in aqueous solu tion.