A generalized scheme for characterizing orientational correlations in condensed phases of high symmetry molecules: SF$_6$ and C$_{60}$

Abstract

The orientational correlation scheme introduced earlier for tetrahedral molecules is extended for being able to classify orientational correlations between pairs of high symmetry molecules. While in the original algorithm a given orientation of a pair of tetrahedral molecules is characterized unambiguously by the number of ligand atoms that can be found between two planes that contain each centre and perpendicular to the centre-centre connecting line, in the generalized algorithm, the planes are replaced by cones, whose apex angles are set according to the symmetry of each molecule. To demonstrate the applicability of the method, the octahedral-shaped SF$_6$ molecule is studied in a wide range of phases (gaseous, supercritical fluid, liquid and plastic crystalline) using classical molecular dynamics. By analyzing the orientational correlations, a close-contact region in the first coordination shell and a medium-range order behaviour are identified in the non-crystalline phases. While the former is invariant to changes of the density, the latter showed longer-ranged correlations as density is raised. In the plastic crystalline state, fluorine atoms are oriented along the lattice directions with higher probability. To test the method for icosahedral symmetries, the crystalline structures of room temperature C$_{60}$ is generated by three sets of potentials that produce different local arrangements. The novel analysis provided quantitative result on preferred arrangements.