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Methane molecule confined in the small and large cages of structure I clathrate hydrate: Quantum six-dimensional calculations of the coupled translation-rotation eigenstates
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10.1063/1.3268623
/content/aip/journal/jcp/131/22/10.1063/1.3268623
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/22/10.1063/1.3268623

## Figures

FIG. 1.

Geometries of the small cage (top) and the large cage (bottom) of structure I clathrate hydrate. The Cartesian axes shown coincide with the principal axes of the cages.

FIG. 2.

One-dimensional cuts through the 6D intermolecular PESs of in the small (top) and large cage (bottom), along the Cartesian axes , which coincide with the principal axes of the cages. The potential profiles are obtained by minimizing the -cage interaction with respect to the three Euler angles of at every position of its cm.

FIG. 3.

Top: 3D isosurfaces at −1400, −1100, −700, 700, and for the 6D intermolecular PES of in the small cage. Bottom: 3D isosurfaces at −1300, −1000, −700, 700, and for the 6D intermolecular PES of in the large cage. The isosurfaces are obtained by minimizing the -cage interaction with respect to the three Euler angles of at every position of its cm.

FIG. 4.

3D isosurfaces of the RPD in the Cartesian coordinates of the 6D T-R states of in the large cage corresponding to the three translational fundamentals: (a) (1,0,0), (b) (0,1,0), and (c) (0,0,1). The isosurfaces are drawn at 20% of the maximum value of the density. The excitations energies shown are relative to the ground state, from Table VI.

FIG. 5.

3D isosurfaces of the RPD in the Cartesian coordinates of several 6D T-R states of in the large cage, with two or more quanta of excitation: (a) (1,0,1), (b) (0,1,1), (c) (0,0,2), (d) (2,0,1), and (e) (0,2,1). The isosurfaces are drawn at 20% of the maximum value of the density. The excitations energies shown are relative to the ground state.

## Tables

Table I.

Translational energy levels of in the small cavity of sI clathrate hydrate, from the quantum 3D calculations. The translational excitation energies are relative to the ground-state energy . The rms amplitudes , , and are in bohr. The quantum numbers and are those of the 3D isotropic HO.

Table II.

Translational energy levels of in the large cavity of sI clathrate hydrate, from the quantum 3D calculations. The translational excitation energies are relative to the ground-state energy . The rms amplitudes , , and are in bohr. The energy levels are assigned in terms of the Cartesian quantum numbers whenever possible, or as , where is the total number of quanta in the and modes. For additional explanation see the text.

Table III.

Rotational energy levels of inside the small cavity of sI clathrate hydrate, from the quantum 3D calculations for the cm of kept fixed at the cm of the cage. The rotational excitation energies are relative to the ground-state energy , and denotes the degeneracy of the levels. The columns labeled show the contributions of the corresponding rotational basis functions to the eigenstates.

Table IV.

Rotational energy levels of inside the large cavity of sI clathrate hydrate, from the quantum 3D calculations for the cm of kept fixed at the cm of the cage. The rotational excitation energies are relative to the ground-state energy , and denotes the degeneracy of the levels. The columns labeled show the contributions of the corresponding rotational basis functions to the eigenstates.

Table V.

Select T-R energy levels of in the small cavity of sI clathrate hydrate, from the quantum 6D calculations. The T-R excitation energies are relative to the ground-state energy . For the purely rotationally excited levels, those with up to , denotes their degeneracy. The rms amplitudes , , and are in bohr. The columns labeled show the contributions of the corresponding rotational basis functions to the eigenstates. The translational quantum numbers and are those of the 3D isotropic HO.

Table VI.

Select T-R energy levels of in the large cavity of sI clathrate hydrate, from the quantum 6D calculations. The T-R excitation energies are relative to the ground-state energy . For the purely rotationally excited levels, denotes their degeneracy. The rms amplitudes , , and are in bohr. The columns labeled show the contributions of the corresponding rotational basis functions to the eigenstates. The translational excitations are assigned in terms of the Cartesian quantum numbers whenever possible, or as , where is the total number of quanta in the and modes. For additional explanation see the text.

/content/aip/journal/jcp/131/22/10.1063/1.3268623
2009-12-09
2014-04-21

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