Can an ab initio three-body virial equation describe the mercury gas phase?

We report a sixth-order ab initio virial equation of state (EOS) for mercury. The virial coefficients were determined in the temperature range from 500 to 7750 K using a three-body approximation to the N-body interaction potential. The underlying two-body and three-body potentials were fitted to highly accurate Coupled-Cluster interaction energies of Hg2 (Pahl, E.; Figgen, D.; Thierfelder, C.; Peterson, K. A.; Calvo, F.; Schwerdtfeger, P. J. Chem. Phys. 2010, 132, 114301-1) and equilateral-triangular configurations of Hg3. We find the virial coefficients of order four and higher to be negative and to have large absolute values over the entire temperature range considered. The validity of our three-body, sixth-order EOS seems to be limited to small densities of about 1.5 g cm(-3) and somewhat higher densities at higher temperatures. Termwise analysis and comparison to experimental gas-phase data suggest a small convergence radius of the virial EOS itself as well as a failure of the three-body interaction model (i.e., poor convergence of the many-body expansion for mercury). We conjecture that the nth-order term of the virial EOS is to be evaluated from the full n-body interaction potential for a quantitative picture. Consequently, an ab initio three-body virial equation cannot describe the mercury gas phase.