Symmetry¶
Non-Scalar Structural
Point Group¶
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.
Space Group¶
Non-Scalar Structural
In crystallography, space groups 4 5 represent a description of the symmetry of the crystal structure, generated by the symmetric repetition of an atomic grouping which, by itself, may or may not be symmetrical. There are 230 space groups in total, and each crystal structure existent in nature belongs to one of them.
In its simplest form, a space group may be derived from translational symmetry. It can be developed further by incorporating additional more complex symmetry elements, such as mirror planes, rotations, screw axes and glide planes.
Notation¶
Space Groups are labelled by a distinctive notation convention, as tabulated in Ref. 6. For example, the space group of the cubic-diamond crystal structure, which silicon, germanium and carbon (diamond) share in common, is labelled by the symbol "Fd-3m".
Schema¶
The JSON schema and an example representation for this property can be found here.