# 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:

1name 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
1au20           # Result file name
2Au 20          # Symbols
3D2d 2 2 2      # Structure types
410             # Maximal number of calculations
5>>>>
6copy $inp$ $out$
7>>>>


For Linux users, the content should be:

au20.inp
1au20           # Result file name
2Au 20          # Symbols
3D2d 2 2 2      # Structure types
410             # Maximal number of calculations
5>>>>
6cp $inp$ $out$
7>>>>


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
1b6n6             # Result file name
2B 6 N 6          # Symbols
3C3h 1 1 1 plane  # Structure types
410               # Maximal number of calculations
5>>>>
6./runxTB.sh $inp$ $out$ $xxx$
7>>>>


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
1Reordered from low to high energy:
2===============================================================
3    #          Energy      Match-RMSD
4===============================================================
5    3    -25.18133725      0.00000000
6    2    -24.84570255      1.31315189
7    0    -24.79607559      1.04903840
8    1    -24.49640410      0.99841844
9===============================================================


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!