Point Groups

Point groups are a method of classifying the shapes of molecules according to their symmetry elements.

The proper axis of symmetry is an imaginary line through a compound. Rotation of the compound by an integral fraction of a circle around this axis (1/2, 1/3, etc.) brings the compound to superposition on itself. An axis of symmetry is represented by C_n, where n is the integral fraction. All shapes have at least a C₁ axis (the identity axis).

Compounds in the C class can be C_s, C_i, C_n, C_nv, or C_nh, where n is an integer.

Compounds in the C_s point group have a plane of symmetry and nothing more.

Compounds in the C₁ point group have only the identity axis; in other words, they have no symmetry. Most compounds have C₁ symmetry.

Linear molecules with conical symmetry (CO, ClC≡CH) are classified in the C_∞v point group.

Compounds in the D_n point group have no additional elements of symmetry. Compounds in this point group are always chiral. This point group is not common. Examples.

Linear molecules with cylindrical symmetry (N₂, HC≡CH) are classified in the D_∞h point group.

Compounds in the S class are S_n, where n is an even integer. Compounds in the S class contain a S_n axis plus a C_n/2 axis coinciding with it.

Compounds in the T (tetrahedral) class can be T, T_d, or T_h. Compounds in the T class contain four C₃ axes and three C₂ axes.

Compounds in the T point group have no additional elements of symmetry. Compounds in this point group are always chiral. This point group is not common. The compound C(X_S)₄, where X_S is a group with a stereocenter with the (S) configuration, is in this point group.

Compounds in the O (octahedral) and I (icosahedral) classes have even higher symmetry. These point groups are not common. PF₆ – is in the O_h point group, and C₆₀ is in the I_h point group.

You should also remember that most compounds are conformationally mobile (i.e., constantly changing their shape), and, as a result, the point group of a compound can depend on the time scale. For example, at a very short time scale, 1-propyne (HC≡CCH₃) is in the C_3v point group, but at longer time scales, rapid rotation about the C–CH₃ bond puts it in the C_∞v point group. Cyclohexane is in the D_3d point group at short time scales, when it is in a single chair form, but at longer time scales, at which it is in rapid equilibrium between its two chair forms, it is in the D_6h point group.

Additional vocabulary help

You might want to look at some definitions of stereoisomers.

Or you might want to look at the stereochemical glossary.

Or you might want to look at a flow chart showing how to determine the isomeric relationship between two structures.