Investigating CH₄ Thermal Activation in Clathrate Nanocages

Abstract : The energy levels of methane molecule trapped, at low temperature, in small (s) and large (l) nano-cages of cubic sI clathrates are calculated in the Born-Oppenheimer approximation using the Extended Lakhlifi-Dahoo model based on pairwise atom-atom effective interaction potentials. In the s cage, the center of mass of CH4 exhibits a slightly asymmetrical 3D oscillation motion with small amplitude around the cage center. Two methods were used to calculate the frequencies of such a motion: a 3D harmonic treatment and a 1D Discrete Variable Representation (DVR) treatment in the X, Y and Z directions. They give approximately the same values of, respectively, 133 cm-1, 108 cm-1 and 120 cm-1. In the l cage, the oscillations are anharmonic and characterized by large amplitude motions with frequencies of 63 cm-1, 52 cm-1 and 47 cm-1. In the s and l nano-cages, the molecule exhibits strongly perturbed rotational motion. The rotational level schemes are quite different from that of the molecular free rotational motion, and for each nano-cage, the obtained levels are described as combination of the free rotation levels.