Point symmetry analysis

C30

1. Press Reset and then select File->Import, to import the file dat/molecule/symmetry/Ih_C30.xml.
2. Select Bond->Create, click on Length to create bonds using the length criterium, and press Ok. The C20 fullerene molecule is now clearly visible.
3. Select Molecule->Measure, change the Method to Symmetry and click on the molecule. The report produced shows that indeed the molecule has icosahedric symmetry Ih. The symmetry elements found include an inversion center, around 0.0000, 0.0000, 0.0000, 15 mirror planes, 31 normal axes (with orders 5, 3, 2) and 16 improper axes (with orders 10, 6). For each class of elements, they are ordered according to increasing errors, so more accurate elements are presented first.

   There are 24 C5 symmetry operations for 6 C5 axes only, because there are 4 operations for each axis: C15, C25, C35, C45. There are 20 C3 operations for 10 C3 axes only, because there are 2 operations for each axis: C13 and C23. There are only 15 C2 symmetry operations, as each C2 axis there is only one symmetry operation, C12.

4. Select again Molecule->Measure, set Method to Symmetry, but this time change Periodicity to Yes (Symmetry page), before clicking on the molecule. The report produced indicates that the molecule has cubic symmetry Th, because now only rotations 2,3,4,6 can be considered.

   The number of normal axes decreased to four C3, and three C2, the number of mirror planes decreased to 3, and the number of improper rotation axes decreased to four S6. It is important to understand why the restrictions on rotation operations afect also mirror and lower order normal and improper axes: for example, 5 mirror planes around a C5 axis cannot be considered simultaneously without violating the condition that symmetry of order 5 is absent, only one of the 5 planes can be considered.

   As a result, different groups of symmetry can be obtained in some cases. For example a C24v chemical group can be downgraded to totally different C4v or a C6v crystallographic groups, as the C4 symmetry operations are not a subset of the C6. When this happens, the GAMGI report shows the various options.

5. For this structure, most of the errors associated with the symmetry elements are between 1E-5 and 1E-4. Select again Molecule->Measure, set Method to Symmetry, but this time change Tolerance Initial and Final to 1E-4 (Symmetry page), so the less accurate elements are discarded. The symmetry group is now Undefined, as there is no group of symmetry that is compatible with the symmetry information found, after discarding all the elements with error above 1E-4.