Quantum Dynamics of Carbon Dioxide Encapsulated in the Cages of the sI Clathrate Hydrate: Structural Guest Distributions and Cage Occupation

Abstract

We perform quantum multiconfiguration time-dependent Hartree calculations for the two cages of the sI CO2 clathrate hydrate, and we report, for first time, results on the translational, rotational, and vibrational states. The potential surface is constructed by the semiempirical SPC/E water model and pairwise additive interactions between the CO2 molecule and all water molecules forming each cage, while a spectroscopic-determined potential is used for the CO2 monomer. The exact kinetic energy operator is derived for the linear CO2 in the cage, and the potential energy operator is adapted to combined mode schemes, chosen adequately in order to obtain the desired product representation. The rotational ability of the CO2 is hindered in the small cavities (512), while in the large cage (51262) translational and rotational degrees of freedom are highly coupled. By analyzing the corresponding T-R eigenstates, we established a connection with experimental X-ray measurements on the orientation of the CO2 molecule in the two cages. Further, vibrational excitations of the fundamental symmetric and antisymmetric stretch modes, their overtones, and combination bands are computed from 7D quantum calculations. We found significant frequency shifts, which are comparable to those observed in the double-peak profile of the experimentally recorded infrared spectra, for the CO2 molecule trapped in the small and large cages of the sI clathrate hydrate. Such good agreement, with the data from recent spectroscopic studies of carbon dioxide clathrate hydrate at low temperatures, indicates a single occupancy of the sI structure cages, allowing an assessment of the theoretical approaches employed.