Point Group Symmetry

Point Group Symmetry

Point group symmetry is a significant property of molecules extensively used in several branches of chemistry: spectroscopy, quantum chemistry and crystallography.
An entity point group is characterizing through a set of symmetry operations:

• E - the individuality operation
• C_n - rotation by 2π/n angle *
• S_n - improper rotation (rotation by 2π/n angle and indication in the plane perpendicular to the axis)
• σ_h - horizontal reflection plane (perpendicular to the principal axis) **
• σ_v - vertical reflection plane (encloses the principal axis)
• σ_d - diagonal reflection plane (encloses the principal axis and bisect the angle among two C₂ axes perpendicular to the principal axis)

* - n is an integer
** - principal axis is a C_n axis with the largest n.

Molecule belongs to a symmetry point group if it is untouched under all the symmetry operations of this group.