Point symmetry analysis
C30
- Press Reset and then select File->Import, to import
the file dat/molecule/symmetry/Ih_C30.xml.
- Select Bond->Create, click on Length to create bonds
using the length criterium, and press Ok. The C20 fullerene
molecule is now clearly visible.
- 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.
- 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.
- 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.