Hydration of Kr(aq) in dilute and concentrated solutions

Molecular dynamics simulations of water with both multi-Kr and single Kr atomic solutes are carried out to implement quasi-chemical theory evaluation of the hydration free energy of Kr(aq). This approach obtains free energy differences reflecting Kr-Kr interactions at higher concentrations. Those differences are negative changes in hydration free energies with increasing concentrations at constant pressure. The changes are due to a slight reduction of packing contributions in the higher concentration case. The observed Kr-Kr distributions, analyzed with the extrapolation procedure of Kr\"{u}ger, \emph{et al.}, yield a modestly attractive osmotic second virial coefficient, $B_2\approx -60~\mathrm{cm}^3$/mol. The thermodynamic analysis interconnecting these two approaches shows that they are closely consistent with each other, providing support for both.