Intermolecular Three-Body Forces and Third Virial Coefficients

Nonadditivity corrections to the third virial coefficients $C\left(T\right)\mathrm{}$ of the noble gases have been calculated for the three-body exchange interactions in the first and second orders of perturbation theory using approximate formulas of Jansen based on the Gaussian model. Denoting these corrections by $\Delta C_1$ and $\Delta C_2$, respectively, and the correction for the triple dipole interaction by $\Delta C_3$, it is found that $\Delta C_1<0\mathrm{}$, $\Delta C_2>0\mathrm{}$, $\Delta C_3>0\mathrm{}$, $\Delta C_1+\Delta C_2<0\mathrm{}$, and the total nonadditivity correction ($\Delta C_1+\Delta C_2+\Delta C_3$) is small because of cancellations. The values of $\Delta C_1$ and $\Delta C_2$ are somewhat inaccurate, principally because of uncertainty in the Gaussian-density width parameter. Qualitatively, the results provide support for the additivity hypothesis, and do not help to explain existing discrepancies with experiment.