Point-Group Symmetry
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Dialog Box - called from: Symmetry Dialog

This is the simplest symmetry option for a molecule, provided the symmetry is crystallographic and atomic coordinates conform to standard orientations. It is not applicable if the symmetry is icosahedral, pentagonal or other non-crystallographic type; choose the Cartesian matrices symmetry option in any of these cases. If the symmetry is crystallographic, but the orientation is non-standard, it may be possible to use the Space group option.

To use this option, click on the point group symbol; symmetry operations will then be taken from a space group belonging to the given point group in the International Tables ; the space group chosen will have a primitive lattice, no screw axes or glide planes, and the standard orientation of axes. Usually, but not always, this is the one with superscript 1 on the Schoenflies symbol. In the case of monoclinic groups (2 - C2, m - Cs or 2/m - C2h), the first setting (unique axis parallel to c) is standard: this is different from the standard for settings of monoclinic crystals in the Title/Axes dialog in the Input1 menu, but when you select the point group the unique angle will be applied to the proper axes. For group mm2 - C2v the 2-fold axis is parallel to c. For groups with 3-, 4- or 6-fold axes, the unique axis is c, but there may be alternate orientations at 30 or 45 degrees from one another: see the Space group option for the standards and how to access the alternate orientations using space-group operations.
 
Coordinates of atoms in molecules are usually given in a Cartesian axial system. If the molecule has one 3-fold or 6-fold axis of symmetry, i.e. has trigonal or hexagonal symmetry ATOMS can either use reference axes which also have this symmetry, that is trigonal or hexagonal "crystal" axes (a1 and a2 axes at 120 degrees, c axis at 90 degrees to a1 and a2), or use unit Cartesian axes. The symmetry matrices for the standard point groups are actually stored in the form appropriate to hexagonal axes, and then converted to the Cartesian form during calculation if the structure axes are unit Cartesian.