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Water proton configurations in structures I, II, and H clathrate hydrate unit cells
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10.1063/1.4795499
/content/aip/journal/jcp/138/12/10.1063/1.4795499
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4795499

Figures

Image of FIG. 1.
FIG. 1.

Positions of oxygen atoms of water molecules and hydrogen-bonding in sI hydrate unit cell. The dark green sphere at the lower back, left-hand corner of the unit cell is the origin of the coordinate system. The other spheres and solid lines are water molecules and hydrogen-bonding inside the unit cell. The color of spheres and lines show group of the assignment of protons in each water molecule (see Figure 2 ).

Image of FIG. 2.
FIG. 2.

Details of the assignment of proton positions of water molecules in a sI hydrate unit cell. (a) The yellow spheres and full lines show water molecules and hydrogen-bonding initially assigned as three independent hydrogen-bonded hexagonal rings; (b) the red spheres are secondary assigned water molecules that have two hydrogen bonds with the yellow water molecules, and two hydrogen bonds to other water types; (c) the blue spheres are the third group of water molecules that have one hydrogen bond with the yellow water molecule, two hydrogen bonds with the red water molecules, and one hydrogen bond to another blue molecule; (d) the green spheres are the fourth group of water molecules to be assigned proton positions. These waters have a hydrogen bond with a yellow water molecule, a hydrogen bond with the red water molecule, and two hydrogen bonds to other water molecules; (e) the purple spheres are last group of water molecules assigned proton positions. These water molecules have hydrogen bonds with a yellow, two green, and other purple colored water molecules. Every assignment of proton positions is performed based on the ice rules.

Image of FIG. 3.
FIG. 3.

Histogram of the net dipole moment of sI unit cell. The abscissa is in units of the TIP4P water molecule dipole moment 2.18 D.

Image of FIG. 4.
FIG. 4.

Histogram of the potential energy distribution of protons in the sI unit cell with a net zero dipole moment. The square point represents the configuration with lowest energy.

Image of FIG. 5.
FIG. 5.

Position of oxygen atoms of water molecules and hydrogen-bonding in the sII hydrate unit cell. The spheres and solid lines are water molecules and hydrogen-bonding inside the unit cell. The color of the spheres and lines show the groups of the assignment of protons in each water molecule (see Figure 6 ). The origin of the coordinate system is same as the sI (shown in Figure 1 ), the lower back, left-hand corner of the unit cell. In this figure, the origin coincides with one of the aqua colored water molecules.

Image of FIG. 6.
FIG. 6.

Details of the assignment of proton positions of water molecules in a sII hydrate unit cell. (a) The yellow spheres show water molecules that are initially assigned as six independent hydrogen-bonded hexagonal rings with almost zero dipole moment. (b) The red spheres are secondary assigned water molecules as three independent hydrogen-bonded hexagonal rings that have almost zero dipole moment. (c) The blue spheres are thirdly assigned water molecules that have hydrogen bonds with the yellow waters in hexagonal faces and the red waters in pentagonal faces. (d) The green spheres are fourthly assigned water molecules that have hydrogen bonds with the yellow and the red water molecules. Similarly, (e) purple, (f) orange, (g) magenta, and (h) aqua spheres are assigned to other water molecules that have hydrogen bonds with already assigned water molecules. All assignments of proton positions are performed based on the ice rules.

Image of FIG. 7.
FIG. 7.

The relationship between the net dipole moment and the unit cell potential energy of the sII hydrate. We adopted the proton configuration indicated by the square in this figure.

Tables

Generic image for table
Table I.

Cartesian coordinates of the 46 water molecules in sI hydrate unit cell for the lowest energy configuration with zero dipole moment.

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Table II.

Cartesian coordinates of the centers of the small and large cages in the sI hydrate unit cell.

Generic image for table
Table III.

Coulomb potential energies for a point charge placed at center of the each cage for sI hydrates.

Generic image for table
Table IV.

Cartesian coordinates of the 136 water molecules in the sII hydrate unit cell.

Generic image for table
Table V.

Cartesian coordinates of centers of the cages for initial placement of guest molecules in sII hydrate unit cell.

Generic image for table
Table VI.

Coulomb potential energies for a point charge placed at the center of the each cage for sII hydrates.

Generic image for table
Table VII.

Cartesian coordinates of 68 water molecules in two sH hydrates unit cells which are combined to form an orthorhombic cell as described in the text.

Generic image for table
Table VIII.

Cartesian coordinates of guest molecules in two sH hydrate unit cells.

Generic image for table
Table IX.

Coulomb potential energies for a point charge placed at center of the each cage for sH hydrates. Two hexagonal unit cells are combined to construct an orthorhombic cell. The even number cages are same cages as the odd number cages due to the periodicity.

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/content/aip/journal/jcp/138/12/10.1063/1.4795499
2013-03-27
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Water proton configurations in structures I, II, and H clathrate hydrate unit cells
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4795499
10.1063/1.4795499
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