The effect of classical and quantum dynamics on vibrational frequency shifts of H₂ in clathrate hydrates

Vibrational frequency shifts of H₂ in clathrate hydrates are important to understand the properties and elucidate details of the clathrate structure. Experimental spectra of H₂ in clathrate hydrates have been measured for different clathrate compositions, temperatures, and pressures. In order to establish reliable relationships between the clathrate structure, dynamics, and observed frequencies, calculations of vibrational frequency shifts in different clathrate environments are required. In this study, a combination of classical molecular dynamics simulations, electronic structure calculations, and quantum dynamical simulation is used to calculate relative vibrational frequencies of H₂ in clathrate hydrates. This approach allows us to assess dynamical effects and simulate the change of vibrational frequencies with temperature and pressure. The frequency distributions of the H₂ vibrations in the different clathrate cage types agree favorably with experiment. Also, the simulations demonstrate that H₂ in the 5¹² cage is more sensitive to the details of the environment and to quantum dynamical effects, in particular when the cage is doubly occupied. We show that for the 5¹² cage quantum effects lead to frequency increases and double occupation is unlikely. This is different for the 5¹²6⁴ cages for which higher occupation numbers than one H₂ per cage are likely.