Simulating Relaxation Channels of CO₂ in Clathrate Nano-cages

Abstract : The energy levels of CO₂ in the small (s) and large (l) nano-cages of cubic sI clathrates are calculated in the Born-Oppenheimer approximation using pairwise atom-atom interaction potentials. In the s cage, the centre of mass of CO₂ oscillates with small amplitudes, asymmetrically about the cage center with harmonic frequencies around 100 cm^-1. In the l cage, oscillations are anharmonic with large amplitude motions in a plane parallel to the hexagonal faces of the cage and the corresponding frequencies are calculated to be 55 cm^-1 and 30 cm^-1. Librational harmonic frequencies are calculated at 101.7 cm^-1 and 56.0 cm^-1 in the s cage and at 27.9 cm^-1 and 46.4 cm^-1 in the l cage. Results show that the coupling between the CO₂ molecule and the nano-cage is quite different for the low frequency translational, rotational or librational modes and the high frequency vibrational modes, which consequently leads to different relaxation channels.