# Can an Ab Initio Three-Body Virial Equation Describe the Mercury Gas Phase?

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posted on 27.03.2014, 00:00 by J. Wiebke, M. Wormit, R. Hellmann, E. Pahl, P. SchwerdtfegerWe 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 Hg_{2}(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 Hg_{3}. 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*n*th-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.