5.4. Clusters with Specific Point Group Symmetry

5.4.1. Point Group Input

ABCluster can generate atomic clusters with specific point group symmetry. This can be done by just changing the third line of isomer input by point group descriptions. The grammar is:

name x y z plane(optionally for Cnh, Dn, Dnh, Dnd)

Here, name is the point group name, like C2v, Oh (See below for a full list). x y z are three real numbers. They control the shape of the cluster. For example, 2 2 2 may result a cluster having close length, width, and height, and 5 5 1 may result an elongate cluster. For C _nh, D _n, D _nh, and D _nd, you can add a word plane, then isomer will only generate planar clusters under the point group symmetry!

Point group	Note
`Cn`	Like `C3` or `C12`. `C1` is not allowed.
`Cnh`	Like `C2h` or `C11h`. `C1h` is not allowed: use `Cs` instead.
`Cnv`	Like `C4v` or `C9v`. `C1v` is not allowed: use `Cs` instead.
`Sn`	Like `S2` or `S8`. `S2` is not allowed: use `Ci` instead. Plus, `n` must be even.
`Dn`	Like `D5` or `D6`. `D1` is not allowed.
`Dnh`	Like `D4h` or `D7h`. `D1h` is not allowed.
`Dnd`	Like `D3d` or `D6d`. `D1d` is not allowed.
`Cs`	The $\mathrm{HClO}$ symmetry.
`Ci`	The inversion symmetry.
`T`	A symmetry weaker than $\mathrm{CH}_4$.
`Th`	A symmetry weaker than $\mathrm{CH}_4$.
`Td`	The $\mathrm{CH}_4$ symmetry.
`O`	A symmetry weaker than $\mathrm{SF}_6$.
`Oh`	The $\mathrm{SF}_6$ symmetry.
`I`	A symmetry weaker than $\mathrm{C}_{60}$.
`Ih`	The $\mathrm{C}_{60}$ symmetry.

5.4.2. Example: Au20 under Point Group Symmetries

Tip

The sample input and output files can be found in testfiles/isomer/5-pointgroup.

We want to build clusters of $\mathrm{Au}_{20}$. If you just use cube to do global optimization, it may take you 100 steps to find the famous T _d symmetry global minimum. Using point group grammar, you can quickly get a lot clusters with the assigned symmetry.

Prepare the following file au20.inp to generate $\mathrm{Au}_{20}$ of D _2d symmetry.

For Windows users, the content should be:

au20.inp

au20           # Result file name
Au 20          # Symbols
D2d 2 2 2      # Structure types
10             # Maximal number of calculations
>>>>
copy $inp$ $out$
>>>>

For Linux users, the content should be:

au20.inp

au20           # Result file name
Au 20          # Symbols
D2d 2 2 2      # Structure types
10             # Maximal number of calculations
>>>>
cp $inp$ $out$
>>>>

Here, copy $inp$ $out$ or cp $inp$ $out$ means just guess cluster structures without further optimization. Of course, you can change them to use Gaussian or xTB or others for optimization. Just run this:

isomer au20.inp > au20.out

In au20-LM, you will find that all structures have D _2d symmetry!

You can also try the following commands:

C5v 2 2 2 Generate clusters under C _5v symmetry.
C5h 2 2 2 Generate clusters under C _5h symmetry.
C5h 2 2 2 plane Generate planar clusters under C _5h symmetry.
Td 2 2 2 Generate clusters under T _d symmetry.
Oh 2 2 2 Generate clusters under O _h symmetry.

For each of the point groups given above, we show an example here:

5.4.3. Example: B6N6

Tip

The sample input and output files can be found in testfiles/isomer/6-b6n6-xTB.

We want to know what a planar $\mathrm{B}_{6}\mathrm{N}_{6}$ looks like in a C _3h symmetry? This can be done easily with xTB and isomer. Prepare the following input:

b6n6.inp

b6n6             # Result file name
B 6 N 6          # Symbols
C3h 1 1 1 plane  # Structure types
10               # Maximal number of calculations
>>>>
./runxTB.sh $inp$ $out$ $xxx$
>>>>

Make sure that in runxTB.sh the command line is: --chrg 0 --gfn 2. Run the global optimization:

isomer b6n6.inp > b6n6.out

In the output file b6n6.out, you can find the following output:

b6n6.out

Reordered from low to high energy:
===============================================================
    #          Energy      Match-RMSD
===============================================================
    3    -25.18133725      0.00000000
    2    -24.84570255      1.31315189
    0    -24.79607559      1.04903840
    1    -24.49640410      0.99841844
===============================================================

All the 4 isomers are shown below:

Of course, the global minimum of $\mathrm{B}_{6}\mathrm{N}_{6}$ may not be even planar, but here we demonstrate that you can control the cluster symmetry flexibly with ABCluster!