  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.
