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.