Symmetry arguments in chemistry

Abstract

The use (and misuse) of symmetry arguments in constructing molecular models and in the interpretation of experimental observations bearing on molecular structure (spectroscopy, diffraction, etc.) is discussed. Examples include the development of point groups and space groups for describing the external and internal symmetry of crystals, the derivation of molecular symmetry by counting isomers (the benzene structure), molecular chirality, the connection between macroscopic and molecular chirality, pseudorotation, the symmetry group of nonrigid molecules, and the use of orbital symmetry arguments in discussing aspects of chemical reactivity.

Figure 1

Relationships among the chloro-substituted benzenes, C₆H_6-nCl_n, n = 0–6.

Figure 2

Isomers of chloro-substituted benzenes, C₆H_6-nCl_n, n = 0–6, based on hexagonal symmetry of the benzene molecule.

Figure 3

Structure of benzene that satisfies the quadrivalency of carbon. Kekulé assumed that the single and double bonds interchange rapidly.

Figure 4

Axial and equatorial isomers expected of a monosubstituted cyclohexane with a nonplanar carbon skeleton with bond angles close to the tetrahedral angle of 109.47°. Ring inversion interchanges the axial and equatorial positions.

Figure 5

A set of 18 isometric structures of the ethane molecule, obtained by symmetry operations of the D₃ point group and by rotation of one methyl group with respect to the other. There is a matching set of 18 isometric enantiomorphic structures, so the order of the isometric group is 36.

Figure 6

Molecular orbitals of butadiene, built from the AOs of the four carbon atoms.

Figure 7

Conrotatory and disrotatory motions leading to different cyclization products of a disubstituted butadiene.