Computing topological indices for simplified CaCO3 polymorphs 


  1. Open the database CaCO3_c generated in Module 4 and open an ADS window for the first record (Aragonite).

  2. Specify the ADS Topology options as shown in the picture below. All Common options may be unchecked.

    To classify atomic nets in crystals ToposPro uses the following conventional topological descriptors:

    Coordination sequence (CS) {Nk}, k=1–n, is a sequence of numbers N1, N2, N3,… counting the atoms in the 1st, 2nd, 3rd etc. coordination shells of any given atom in the net. The length of CS to be computed, n, has to be specified as Coord. Seq. parameter.

    Point symbol lists the numbers (amount) and sizes of shortest circuits (closed chains of connected nodes) starting from any non-equivalent node in the net. A Total Point Symbol for net (TS) summarizes all the point symbols for the non equivalent nodes 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. To compute point symbols, TS and ES, check the Point Symbol option.

    Vertex symbol (VS) gives similar information as ES, but only for rings (circuits without shortcuts). Specify Max. Ring parameter more than zero to find the shortest rings or no more than Max. Ring size.

    These descriptors for all non-equivalent atoms are collected in the binary .ttd (TOPOS Topological Database) files that form the TTD collection to be considered below.

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

    Coordination sequences
    ZA1: 1 2 3 4 5 6 7 8 9 10
    Num 6 18 42 74 114 162 222 290 366 450
    Cum 7 25 67 141 255 417 639 929 1295 1745
    ZB1: 1 2 3 4 5 6 7 8 9 10
    Num 6 20 42 74 114 164 222 290 366 452
    Cum 7 27 69 143 257 421 643 933 1299 1751
    Vertex symbols for selected sublattice
    ZA1 Point symbol:{4^9;6^6}
    Extended point symbol:[]
    Vertex symbol: []
    ZB1 Point symbol:{4^12;6^3}
    Extended point symbol:[]
    Vertex symbol: [* .*.*]
    ATTENTION! Some rings * are bigger than 10, so likely no rings are contained in that angle
    Point symbol for net: {4^12;6^3}{4^9;6^6}
    6-c net; 2-nodal net
    Database with topological types was not loaded. Check 'Classification' flag.
    Elapsed time: 3.14 sec.

    The following topological parameters have been computed here:
    Num – Nk values;
    Cum – cumulative numbers of the coordination sequence including the central atom;
    TD10 – topological density, TD10, a round averaged Cum10 for all central atoms in the asymmetric unit;
    Point symbol – the record like {4^9;6^6} corresponds to the point symbol (4966), i.e. nine angles at Ca atom contain the shortest 4-circuits and six angles contain 6-circuits;
    Extended point symbol – ES; thus, for the ZA (Ca) atom ES looks like [], i.e. eight 6-circuits meet in any of the six angles, in three other angles two 4-circuits meet and other angles are occupied by one 4-circuit;
    Vertex symbol – VS; thus, for the ZB atom (carbonate ion centroid) VS = [∞.∞.∞], i.e. three angles contain no rings of size 10 or smaller. Remember that the rings were computed up to size 10 (Max. Ring = 10). So possibly larger rings may exist - ToposPro does not know this!
    Point symbol for net – TS; {4^12;6^3}{4^9;6^6} summarizes point symbols {4^12;6^3} and {4^9;6^6} for two non-equivalent 6-coordinated nodes contained in the net with equal ratio.
    6-c net – the net is 6-connected or 6-coordinated (all vertices are of degree 6);
    2-nodal net – the net is binodal (contains two topologically inequivalent nodes; they have different CS+ES+VS sets).

    The last message remind the user that topological classification of the net will not be provided – for this purpose one has to check the Classification flag (see the next example).

  4. Save the results in a textual CaCO3_c.ado file (Data/Save). Close the ADS window.

  5. Repeat the procedure for the remaining two records in a batch mode. Select them, open an ADS window and set Options/Continuous/Central Atoms = El. Run ADS.

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