Point Group¶
Non-Scalar Structural
In geometry, point groups 1 represent a description of the symmetry of the geometry when one point is kept fixed in space. Point groups can be used to describe the symmetry of a molecular structure.2 Generally the symmetry of a molecular structure can be used to categorize molecules due to the point groups ability to predict and explain a molecules chemical properties.
There are 31 common point groups that tend to be applied to molecules.2 For example, benzene (C6H6) is categorized as D6h as it has a 6-fold symmetry around the center of the structure. Five types of symmetry elements are used to classify the a molecule by its point group: 1. Symmetry Axis: An axis around which a rotation by 360o/n results in an indistinguishable structure from the original. 2. Plane of Symmetry: A plane of reflection which generates an identical copy of the original. 3. Inversion Center: Idential atoms exist at points (x, y, z) and (-x, -y, -z) when the molecule is plotted in 3-dimensional space. 4. Rotation-reflection Axis: An axis in which a rotation by 360o/n, followed by a reflection in a plane perpendicular to the axis results in an indistinguishable copy of the original. 5. Identity: No change in the structure results in the same structure. This operation is the equivalent of multiplying the coordinates of the structure by 1 (unity).
Notation¶
Point Groups are labelled using Schoenflies notation3, and examples include D6h, C2v, and Td.
Schema¶
The JSON schema and an example representation for this property can be found here.