Melting temperatures of the noble gases from ab-initio Monte Carlo simulations : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University, Albany, New Zealand
This thesis describes simulations to determine the melting temperatures of
the noble gases based on rst-principles ab-initio methods.
The melting temperatures of bulk krypton, xenon, radon and oganesson are
determined using parallel-tempering Monte Carlo with the interaction potential
approximated by two- and three-body contributions. The employed
interaction potentials are obtained from relativistic coupled cluster theory
including spin-orbit coupling and are the most accurate ab-initio potentials
to this date. These potentials are tted to computationally e cient functions
utilized to calculate the interaction energy during the Monte Carlo melting
simulation. Two di erent techniques of obtaining the melting temperature
First, the melting temperature is studied by simulating nite clusters in a
canonical ensemble. The melting temperature is then deducted from extrapolation
of the nite cluster results to the bulk.
Second, the melting temperature is determined by direct sampling of the bulk
using cells with periodic boundary conditions in the isobaric-isothermal ensemble.
Upon correction for superheating, an excellent agreement to the
melting temperatures obtained from cluster simulations is obtained.
The numerically determined melting temperatures of krypton and xenon are
in close agreement with available experimental data. That is, for krypton a
melting temperature of 109.5 K and 111.7 K is obtained for cluster and periodic
simulations respectively, which is approximately 5 Kelvin lower than the
corresponding experimental value of 115.78 K. The melting point of xenon is
determined to be 156.1 K and 161.6 K respectively, which compares to the
experimental value of 161.40 K. The long debated value of the radon melting
temperature of 202 K is con rmed by our simulations (200 K for both techniques).
And nally, the melting point of oganesson is determined to be 330
K and therefore surprisingly high compared to the other rare gases. This implies
that oganesson is a solid at room temperature.
Furthermore, an analytical formula to compute the temperature of the solidliquid
phase transition based on the analytically expressed bulk modulus and
interaction potential is presented, and the superheating correction factor is