Dynamics of benzene molecules situated in metal-organic frameworks

In this paper, we investigate the gyroscopic motion of a benzene molecule C₆H₆, which comprises an inner carbon ring and an outer hydrogen ring, and is suspended rigidly inside a metal-organic framework. The metal-organic framework provides a sterically unhindered environment and an electronic barrier for the benzene molecule. We model such gyroscopic motion from the inter-molecular interactions between the benzene ring and the metal-organic framework by both the Columbic force and the van der Waals force. We also capture additional molecular interactions, for example due to sterical compensations arising from the carboxylate ligands between the benzene molecule and the framework, by incorporating an extra empirical energy into the total molecular energy. To obtain a continuous approximation to the total energy of such a complicated atomic system, we assume that the atoms of the metal-organic framework can be smeared over the surface of a cylinder, while those for the benzene molecule are smeared over the contour line of the molecule. We then approximate the pairwise molecular energy between the molecules by performing line and surface integrals. We firstly investigate the freely suspended benzene molecule inside the framework and find that our theoretical results admit a two-fold flipping, with the possible maximum rotational frequency reaching the terahertz regime, and gigahertz frequencies at room temperature. We also show that the electrostatic interaction and the thermal energy dominate the gyroscopic motion of the benzene molecule, and we deduce that the extra energy term could possibly reduce the rotational frequency of the rigidly suspended benzene molecule from gigahertz to megahertz frequencies at room temperature, and even lower frequencies might be obtained when the strength of these interactions increases.