Computing the natural tiling for the zeolite LTA, visualizing tiles and storing the information for the 3dt program 


Algorithm:

1. Open the database LTA_SOD and open an ADS window for the first record (Si framework for the zeolite LTA). Specify the ADS options in Common, Topology and Tiling tabs as shown below. The options Write Data to .tnt and Essential Rings for 3dt provide the information for visualizing tiles in IsoCryst and 3dt, respectively. The information will be stored in the files LTA_SOD_t.tnt and LTA_SOD_3dt.cgd, respectively. The option All Rings ensures that all rings up to size Max. Ring, not only the shortest, will be found. In the Tiling tab specify first the maximal number of tile faces (Max. Tile Size = 200 is sufficient for most of nets), then check Natural Tiles. Other options to obey the natural tiling rules will be checked automatically.



The rules (a)-(d) and the algorithm for computing natural tiles are described by Blatov V.A., Delgado-Friedrichs O., O’Keeffe M., Proserpio D. M. (Acta Cryst. (2007), A63, 418–425):

(a) the tiling must have the symmetry of the net (be proper);
(b) the faces of tiles must be locally strong rings (no tile has one face larger than the rest);
(c) a tile does not have non-face strong rings that do not intersect other such rings;
(d) when rules (a)–(c) result in multiple tilings because of intersecting strong rings, we use only the smaller of a pair if the intersecting rings are unequal in size and reject both if the intersecting rings are equal in size.

2. Run ADS and select all atoms in the Choose Central Atoms window. You will get the following output:





The line All rings (up to 12) means that not only 4-, 6- or 8-rings, but also larger 12-rings meet at the same angle of the node. The all ring VS could be reported as: [(4,6).(6,123).(4,6).(6,123).(4,6,122).8]. Moreover, 6- and 12-rings are not all equivalent by symmetry, ToposPro distinguishes them in the line All rings with types by uniting in equivalent groups. The groups are designated by one or more letters: a-z, aa-az, ba-bz, etc, e.g. 4a, 12ab, 20xaz. As a result, an all-ring labelled VS is calculated. Here there are two inequivalent 6-rings, 6a and 6b, and two inequivalent 12-rings, 12a and 12b.
Not all rings are essential, i.e. are tile faces. In this case the whole tiling is constructed of four kinds of rings: 4a, 4b, 6b and 8. There are three kinds of tiles in the natural tiling: [46], [46.68] and [412.68.86]. The line corresponding to each tile contains the following information on the tile:



8/6 – number of vertices/faces;
[4^6] – face symbol, [46];
[4a^2.4b^4] – face symbol with ring types;
Centroid – coordinates of the center of gravity;
Volume – volume, Å3;
G3 – normalized second moment of inertia, G3.

The line Tiling shows the formula of the tiling: the stoichiometric ratio [46]:[46.68]:[412.68.86] = 3:1:1.
Transitivity give the transitivity of the tiling pqrs, where p, q, r and s are numbers of inequivalent vertices, edges, faces and tiles in the tiling.
Some other features of the tiling are indicated, in particular, this tiling is simple.
The table consolidates the main data on all possible proper tilings, the NT label indicates natural tiling.

3. Perform Image command to invoke IsoCryst.



4. Grow the net several times until the PPT label in the Tint file data window becomes bold. This means that all vertices of the tiles are shown in the picture.

5. Go to the Tint file data window, expand the tiling tree, select a tile and click Apply button. You will get the main cavity (α-cage) in the LTA framework.



6. Expand the tiling tree. Hold down the “ctrl” and choose all tiles and click Apply again. All tiles will be shown.



7. Check that all atoms were not selected. Grow up a structure (2 clicks). In the Tint window select the option Hide none (all the tiles must still be selected). In IsoCryst three tiles will be selected. Use a magic wand and change the color of the selected atoms.



Further, use Cylinder model . Then deselect all atoms. Three types of tiles will show as green.



8. Close the IsoCryst and ADS windows and run the 3dt program (http://www.gavrog.org). Use the LTA_SOD_3dt.cgd file to draw the tiling.



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