Click here to see a lecture on this topic . Introduction A Point Group describes all the symmetry operations that can be performed on a molecule that result in a conformation indistinguishable from the original. Point groups are used in Group Theory, the mathematical analysis of groups, to determine properties such as a molecule's molecular orbitals. Assigning Point Groups While a point group contains all of the symmetry operations that can be performed on a given molecule, it is not necessary to identify all of these operations to determine the molecule's overall point group. Instead, a molecule's point group can be determined by following a set of steps which analyze the presence (or absence) of particular symmetry elements. Steps for assigning a molecule's point group: Determine if the molecule is of high or low symmetry. If not, find the highest order rotation axis, C n . Determine whether the molecule has any C 2 axes perpendicular to the principal C n axis. If so, then there are n such C 2 axes, and the molecule is in the D set of point groups. If not, it is in either the C or S set of point groups. Determine whether the molecule has a horizontal mirror plane (σ h ) perpendicular to the principal C n axis. If so, the molecule is either in the C nh or D nh set of point groups. Determine whether the molecule has a vertical mirror plane (σ v ) containing the principal C n axis. If so, the molecule is either in the C nv or D nd set of point groups. If not, and if the molecule has n perpendicular C 2 axes, then it is part of the D n set of point groups. Determine whether there is an improper rotation axis, S 2n , collinear with the principal C n axis. If so, the molecule is in the S 2n point group. If not, the molecule is in the C n point group. Example \(\PageIndex{1}\) Find the point group of benzene (C 6 H 6 ). Answer Solution 1. Benzene is neither high nor low symmetry 2. Highest order rotation axis: C 6 3. There are 6 C 2 axes perpendicular to the principal axis 4. There is a horizontal mirror plane (σ h ) Benzene is in the D 6h point group. See Also Symmetry Gallery