TTD, TTO, and TTR collections 

The TTD collection

To classify atomic nets in crystals ToposPro uses the following conventional topological descriptors (see for more details: “Vertex-, face-, point-, Schläfli-, and Delaney-symbols in nets, polyhedra and tilings: recommended terminology”. Blatov V.A., O’Keeffe M., Proserpio D. M. CrystEngComm, 2010, 12, 44-48):

Coordination sequence (CS) {Nk} is a sequence of numbers N1, N2, N3,… counting the atoms in the 1st, 2nd, 3rd etc. coordination spheres of any given atom in the net.

Point Symbol lists the numbers and sizes of shortest circuits (closed chains of connected atoms) starting from every angle of every non-equivalent atom in the net. A Total Point Symbol for net (TS) summarizes all the Point Symbols for the non-equivalent atoms with their relation/weight. The terminology “Schläfli Symbol” SHOULD BE ABANDONED because of the use of this term in mathematics with a different definition.

Extended Point symbol (ES) lists all shortest circuits for each angle for any non-equivalent atom.

Vertex symbol (VS) gives similar information as ES, but only for rings (circuits without shortcuts).

These descriptors for all non-equivalent atoms are collected in the binary .ttd (TOPOS Topological Database) files. The following structure corresponds to the .ttd file, and is realized in the textual .nnt (New Net Topology) file:

An NNT and TTD entry example: TiO2, Rutile, rtl topological type

'3 14 19 62 51 144 99 254 163 400',
'6 10 38 34 102 74 198 130 326 202',

Detailed description:
'$TiO2', Name of the record with the ‘$’ prefix
'{4;6^2}2{4^2;6^10;8^3}', TS, Total point symbol for the whole net: {4.62}2{42.610.83}.
In this case the numbers of the two non-equivalent nodes (O and Ti) relate as 2:1
'3 14 19 62 51 144 99 254 163 400', CS, Coordination sequence {Nk} for the first non-equivalent node (oxygen atom); k=1–10
'[4.6(2).6(2)]', ES, Extended point symbol: [4.62.62] for the first non-equivalent node
'[4.6(2).6(2)]', VS, Vertex symbol for the first non-equivalent node (here coincides with the Extended point symbol)
'6 10 38 34 102 74 198 130 326 202',Similar triples for other non-equivalent nodes (Ti atom) “*” means that there are no rings for this angle: [*.*.*]
(alternatively to * the ∞ symbol could be used in the Vertex symbol notation)

The TTO Collection

Beside the classification of a net via the TTD collection, starting from December 2007 a new collection is being created – TTO (Topological Types Observed).
In short, TTO collection matches topological types of abstract nets with examples of real crystal structures.
TTO files contain the records of the following format:

RefCode – the Reference Code of a particular structure;
Dimen – dimensionality of the underlying net;
Z – number of nets;
TopType – topology of the net (its code in TTD collection);
ReprType – code of representation type of the structure.

The correspondences between ReprType codes and the description of representations are given in the textual file TTOReprTypes.txt. Having TTO collection the user may now perform the following operations:

  1. Find all topologies for all representations of a particular crystal structure.
  2. Find all structures with a particular topology of underlying net.
  3. Find all structures with a particular topology in a given database.

All .ttd and .tto files have to be copied into separate subdirectories (/TTD and /TTO by default) within the ToposPro folder. TTOReprTypes.txt file has to be copied into /TTO directory. In alternative, the paths to TTD and TTO collections can be changed in System/TOPOS Parameters/Paths.

The TTR Collection

Starting from April 2011, ToposPro includes the TTR collection (Topological Types Relations). This collection is based on the TTO collection and lists all ways of transformation from one net to another that are realized in crystal structures. If for a given crystal structure there are at least two possible representations in the TTO collection, and these representations have different topology, a pair of the corresponding nets appears in the TTR collection. In other words, these nets can be transformed to each other if the structure groups are chosen in different ways in the initial crystal structure. For example a diamond (dia) net can be transformed to a srs net by an appropriate choice of dimers (edges) in dia and matching them to srs vertices.

The TTR collection consists of .ttr files that are allocated in the /TTO directory.

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