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

Abstract

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.

Intramolecular stretching vibrational states and frequency shifts of (H2)2 confined inside the large cage of clathrate hydrate from an eight-dimensional quantum treatment using small basis sets

“…First, both the ground-state energy and the frequency of the intramolecular stretch fundamental decrease with increasing N H 2 O , although the decrease for the latter is very small. This behavior matches that which has previously been observed in computational studies 38,47 of one H 2 in the small cage of the sII clathrate hydrate. It is readily rationalized in that the H 2 -H 2 O interactions relevant to the hydrate inclusion compounds tend to be predominantly attractive, and such as to lower the H 2 intramolecular fundamental frequency.…”

“…An analogous angular anisotropy decrease with N H 2 O (as reflected in a decrease in the magnitude of the H 2 j = 1 rotational-level splitting) was also found to hold for H 2 in the small cage. 38,47 The trend is easily understood once one recognizes that the angular anisotropy in the H 2 -cage interaction is due to the asymmetry in the spatial distribution of H-atoms in the hydrogen-bond framework of the hydrate. The effects of such asymmetry tend to get averaged away as more layers of water moieties are included in the larger hydrate domains.…”

“…Recently, Powers et al 38 have calculated the frequency shift of H 2 inside the small cage of the sII hydrate, isolated and surrounded by spherical hydrate domains of increasing size, allowing the investigation of the effects of the condensed-phase environment. The approach employed was that developed earlier by Bačić and co-workers for the purpose of computing the HF stretch frequency shift in Ar n HF clusters.…”

“…It was suggested that improving further the agreement with experiment may require including many-body interactions, three-body in particular, missing from the pairwise-additive intermolecular PES employed. 38 Motivated in part by this suggestion, as well as by other considerations, Qu and Bowman 44 have performed diffusion Monte Carlo (DMC) calculations of the vibrational frequency shift of H 2 encapsulated in the (rigid) small cage of the sII hydrate, without and with surrounding water molecules, for the PES that included ab initio 3-body H 2 -H 2 O-H 2 O interactions, in addition to the 2-body H 2 -H 2 O interactions. For the largest hydrate domain considered, the inclusion of the 3-body interactions resulted in the shift of −40 ± 4 cm −1 , in good agreement with experiment.…”

Does cage quantum delocalisation influence the translation–rotational bound states of molecular hydrogen in clathrate hydrate?

“…The best agreement with the experimental data thus far was obtained using the empirical simple point charge model SPC/E. The most recent calculations, using an ab initio potential computed with pairwise water-hydrogen dimer potential, V08 24 , have shown to overestimate angular anisotropy 25 . One interest of those theoretical studies is to use spectroscopy as a probe of the possible multiple occupancy of hydrogen in those clathrate structure.…”