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

Abstract

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 are presented. 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 evaluated.