Point Symmetry analysis

Point symmetry characterization is extremely important in describing atomic structures, particularly in molecular spectroscopy and crystallography. GAMGI supports both the (infinite) unrestricted chemical groups of symmetry, and the 32 crystallographic groups with 2,3,4,6 rotations only.

To exemplify the method, we create first a water molecule and measure its symmetry (C2v), then we import a C30 fullerene molecule and measure its chemical, unrestricted (Ih) and crystallographic, restricted (Th) point symmetry.


  1. Press Atom->Create, set Element to O, set X, Y, Z to 0, 0, 0, and press Ok, to create the O atom.
  2. Set Element to H, set X, Y, Z to 0.6, 0.7749, 0, and press Ok, to create the first H atom. To create the second, set Element to H, and X, Y, Z to 0.6, -0.7749, 0, before pressing Ok.
  3. Select Molecule->Create, write a name for the molecule, for example water, and press Ok. The new molecule has no contents yet, so the dialog Molecule->Link replaces automatically the previous one. Press the mouse over one of the atoms and press Ok, to link it to the molecule. Repeat for the other two atoms.
  4. Select Bond->Create and click over the O and a H atom to create a bond. Repeat with the other H atom. To see the object hierarchy, select for example Molecule->Select.
  5. To confirm that the water molecule has the proper geometry, select Molecule->Measure, and click on the molecule. The report produced shows that there are two OH bond lengths with the value 0.98 and one HOH bond angle with the value 104.5 degrees.
  6. Select again Molecule->Measure, but this time change the Method to Symmetry, before clicking on the molecule. The report produced shows that the molecule belongs to the group C2v and its symmetry elements are two mirror planes and one C2 rotation axis. The error associated with each symmetry element is reported, plus unit vectors normal to the planes, 0.0000, -1.0000, 0.0000 and 0.0000, 0.0000, 1.0000, and paralell to the axis 1.0000, 0.0000, 0.0000. Try to understand the orientation of the planes and axis, considering that the x direction points to the right, the y direction to the top and the z direction to the user. To get a detailed explanation of the information shown on the report, press Help->Current.