GAMGI Interfaces: Cluster Measure

# Cluster Measure

- Type
- Symmetry
- Voronoi
- Tolerance
- View

Select here the parameters to measure the point symmetry.

### Periodicity

When the No option is chosen (the default), all elements of symmetry are taken into account, and the chemical point group is determined. When the Yes option is chosen, all elements of symmetry related with rotations of order different from 6, 4, 3, 2 are ignored. The reported crystallographic point group is thus the maximum point symmetry that could be achieved in the center of this aggregate, if it was in a periodic crystal.

For example, a C5v chemical group becomes a Cs crystallographic point group because after discarding the C5 axis, only one of the five mirror planes can be considered as a true element of symmetry in a periodic system. A chemical Ih becomes a Th crystallographic group, because after discarding the C5 axes, the remaining planes and axes form five different sets of cubic Th symmetry, although only one can be considered at a time.

Everytime the chemical group is found, the crystallographic group can also be determined. Usually this crystallographic group is not unique. For example, a D12h chemical group can be either a D4h or a D6h crystallographic group. GAMGI shows the various crystallographic groups that cover all the possible operations of symmetry, in sequence, with their symmetry operations and symmetry elements. In particular, chemical C0v becomes C4v or C6v, chemical D0h becomes D4h or D6h and chemical Kh becomes D4h or D6h or Oh crystallographic groups respectively.

### Tolerance

The elements of symmetry of a cluster depend entirely of the tolerance applied to the operations of symmetry. GAMGI uses the same tolerance for all operations: the maximum distance that is tolerated between initial and transformed coordinates.

GAMGI tries to find all the symmetry elements independently, and in general each of these elements requires a different tolerance. Thus, for a given tolerance, some elements may be recognized and others may go missing, resulting in an inconsistent set of symmetry elements. When this happens, the group is reported Undefined. The solution is to increase the tolerance (so valid elements might be found) or to decrease it (so fake elements might be discarded).

When the transformed coordinates for a given symmetry element are closer than the Initial tolerance, GAMGI attempts to optimize the symmetry element, to get transformed coordinates closer than the Final tolerance. When the transformed coordinates do not pass the Initial tolerance or when the optimization fails, the attempted element is discarded. When the transformed coordinates pass the Final tolerance, the element is accepted.

During optimization, GAMGI will never attempt to change the atoms, only the symmetry elements. To disable optimization, just set Initial equal to Final tolerance.
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