Hydrogen Molecule in the Small Dodecahedral Cage of a Clathrate Hydrate:  Quantum Five-Dimensional Calculations of the Coupled Translation−Rotation Eigenstates

Abstract

We report quantum five-dimensional (5D) calculations of the energy levels and wave functions of the hydrogen molecule, para-H2 and ortho-H2, confined inside the small dodecahedral (H2O)20 cage of the sII clathrate hydrate. All three translational and the two rotational degrees of freedom of H2 are included explicitly, as fully coupled, while the cage is treated as rigid. The 5D potential energy surface (PES) of the H2-cage system is pairwise additive, based on the high-quality ab initio 5D (rigid monomer) PES for the H2-H2O complex. The bound state calculations involve no dynamical approximations and provide an accurate picture of the quantum 5D translation-rotation dynamics of H2 inside the cage. The energy levels are assigned with translational (Cartesian) and rotational quantum numbers, based on calculated root-mean-square displacements and probability density plots. The translational modes exhibit negative anharmonicity. It is found that j is a good rotational quantum number, while the threefold degeneracy of the j = 1 level is lifted completely. There is considerable translation-rotation coupling, particularly for excited translational states.

Quantum calculation of inelastic neutron scattering spectra of a hydrogen molecule inside a nanoscale cavity based on rigorous treatment of the coupled translation-rotation dynamics

“…This uniquely high degree of realism and detail in simulating the INS spectra is not achievable by the approaches in the literature. It is made possible by our ability to compute accurately the fully coupled quantum 5D T-R energy levels and wave functions of the entrapped molecule on the 5D intermolecular PES 11,12,15,16 and, as shown here, use them as input for calculating the spectra.…”

Mechanisms for thermal conduction in hydrogen hydrate

“…Bačić et al have studied these effects in much detail for hydrogen-containing clathrates [48][49][50][51][52][53][54], including explicit path-integral MD simulation [54]; based on these studies, it should be stressed that the classical MD results at 100 K and below reported in the present work needs to be interpreted with some caution due to the limitations of classical MD to describe accurately H 2 motion at low temperatures.…”

HD in C 60 : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

“…Besides H 2 @C 60 , the theoretical study of which will be reported shortly, this includes molecular hydrogen in clathrate hydrates [19,29,30], metal-organic frameworks [31][32][33][34][35] and zeolites [36,37], among others. Finally, methodological extensions are in progress in our group to the INS spectra of nanoconfined polyatomic molecules such as methane [38] and water [39].…”

“…Our approach to the rigorous calculation of the coupled five-dimensional T-R energy levels and wave functions of a hydrogen molecule inside fullerenes, applied in this study to HD@C 60 , has evolved in our group over a number of years, in the course of the theoretical investigations of the quantum T-R dynamics of H 2 and its isotopologues entrapped in the cages of clathrate hydrates [19][20][21], fullerenes C 60 and C 70 [2,5], and an open-cage derivative of C 60 (ATOCF) [22]. A detailed description of the quantum five-dimensional methodology is available in [18], and therefore only the salient features are given here.…”

“…the entrapped HD and the interior of C 60 , which is described below. The T-R energy levels and wave functions of the Hamiltonian in equation (2.1) are obtained utilizing the efficient computational methodology that originated in our group [19,24]. The final Hamiltonian matrix, its size drastically reduced by the sequential diagonalization and truncation procedure [25], is diagonalized, yielding the T-R eigenstates which are numerically exact for the five-dimensional PES used.…”