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 <i>N</i>-body interaction potential. The underlying two-body and three-body potentials were fitted to highly accurate Coupled-Cluster interaction energies of Hg<sub>2</sub> (Pahl, E.; Figgen, D.; Thierfelder, C.; Peterson, K. A.; Calvo, F.; Schwerdtfeger, P.<i> J. Chem. Phys</i>. <b>2010</b>, <i>132</i>, 114301-1) and equilateral-triangular configurations of Hg<sub>3</sub>. 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<sup>–3</sup> 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 <i>n</i>th-order term of the virial EOS is to be evaluated from the full <i>n</i>-body interaction potential for a quantitative picture. Consequently, an ab initio three-body virial equation cannot describe the mercury gas phase.