Predicting the energy of the water exchange reaction and free energy of solvation for the uranyl ion in aqueous solution

The structures and vibrational frequencies of UO2(H2O)4(2+) and UO2(H2O)5(2+) have been calculated using density functional theory and are in reasonable agreement with experiment. The energies of various reactions were calculated at the density functional theory (DFT) and MP2 levels; the latter provides the best results. Self-consistent reaction field calculations in the PCM and SCIPCM approximations predicted the free energy of the water exchange reaction, UO2(H2O)4(2+) + H2O <--> UO2(H2O)5(2+). The calculated free energies of reaction are very sensitive to the choice of radii (O and H) and isodensity values in the PCM and SCIPCM models, respectively. Results consistent with the experimental HEXS value of -1.19 +/- 0.42 kcal/mol (within 1-3 kcal/mol) are obtained with small cavities. The structures and vibrational frequencies of the clusters with second solvation shell waters: UO2(H2O)4(H2O)8(2+), UO2(H2O)4(H2O)10(2+), UO2(H2O)4(H2O)11(2+), UO2(H2O)5(H2O)7(2+), and UO2(H2O)5(H2O)10(2+), were calculated and are in better agreement with experiment as compared to reactions involving only UO2(H2O)4(2+) and UO2(H2O)5(2+). The MP2 reaction energies for water exchange gave gas-phase results that agreed with experiment in the range -5.5 to +3.3 kcal/mol. The results were improved by inclusion of a standard PCM model with differences of -1.2 to +2.7 kcal/mol. Rearrangement reactions based on an intramolecular isomerization leading to a redistribution of water in the two shells provide good values in comparison to experiment with values of Delta G(exchange) from -2.2 to -0.5 kcal/mol so the inclusion of a second hydration sphere accounts for most solvation effects. Calculation of the free energy of solvation of the uranyl cation yielded an upper bound to the solvation energy of -410 +/- 5 kcal/mol, consistent with the best experimental value of -421 +/- 15 kcal/mol.