The effect of the condensed-phase environment on the vibrational frequency shift of a hydrogen molecule inside clathrate hydrates.

We report a theoretical study of the frequency shift (redshift) of the stretching fundamental transition of an H molecule confined inside the small dodecahedral cage of the structure II clathrate hydrate and its dependence on the condensed-phase environment. In order to determine how much the hydrate water molecules beyond the confining small cage contribute to the vibrational frequency shift, quantum five-dimensional (5D) calculations of the coupled translation-rotation eigenstates are performed for H in the v=0 and v=1 vibrational states inside spherical clathrate hydrate domains of increasing radius and a growing number of water molecules, ranging from 20 for the isolated small cage to over 1900. In these calculations, both H and the water domains are treated as rigid. The 5D intermolecular potential energy surface (PES) of H inside a hydrate domain is assumed to be pairwise additive. The H-HO pair interaction, represented by the 5D (rigid monomer) PES that depends on the vibrational state of H, v=0 or v=1, is derived from the high-quality ab initio full-dimensional (9D) PES of the H-HO complex [P. Valiron et al., J. Chem. Phys. 129, 134306 (2008)]. The H vibrational frequency shift calculated for the largest clathrate domain considered, which mimics the condensed-phase environment, is about 10% larger in magnitude than that obtained by taking into account only the small cage. The calculated splittings of the translational fundamental of H change very little with the domain size, unlike the H j = 1 rotational splittings that decrease significantly as the domain size increases. The changes in both the vibrational frequency shift and the j = 1 rotational splitting due to the condensed-phase effects arise predominantly from the HO molecules in the first three complete hydration shells around H.