Construction of a composite-sphere model for molecules of tetrahedral symmetry

Abstract

We propose a ‘composite sphere’ model for molecules of tetrahedral symmetry. In particular, we choose as an example the hydrocarbon neopentane. We disassemble the molecule into five moieties: four methyl groups (species A) and one carbon atom (species B). By imparting pair potentials of spherical symmetry to the A–A (hard sphere type), B–B (hard sphere type), and A–B (square-well type) pairs, we are able to reconstitute the pentamer structure via Monte Carlo simulation. This is demonstrated for four density states: ρσ 3 = 0.03, 0.10, 0.15, and 0.20. We apply two criteria in assessing the per cent formation of pentamers: namely the proximity rule and the energy rule. The proximity rule gives 57% formation of pentamers, while the energy rule is able to give 99% pentamers. The structures are also calculated via the spherical Ornstein-Zernike integral equations with the Percus-Yevick (PY) closure. It is found that the PY closure is inadequate for predicting quantitatively the MC radial distribution functions. The root cause of the lack of agreement is attributed to the improper application of the isotropic version of the Ornstein-Zernike integral equations to a fluid that has become anisotropic.