Molecular Classification Using Symmetry Operations

The fact that molecules have a three-dimensional structure and shape was shown by Louis Pasteur in 1848 in some critical experiments on crystalline salts of tartaric acid that formed part of his doctoral studies. Tartaric acid is a naturally occurring compound that is extracted from grape juice and sometimes crystallizes as potassium bitartrate from solution in wine. Pasteur concentrated on the related compound sodium ammonium tartrate. The two forms of tartrate were chemically identical, but a solution of potassium bitartrate would rotate the plane of polarization of plane polarized light to the right whereas a solution of sodium ammonium tartrate would not. Pasteur studied the crystal structures of tartaric acid salts and found the crystallites themselves were chiral, i.e. the facets of the crystals occur in two forms that are mirror images of one another, so that the two crystallite forms cannot be superimposed. In the pure potassium bitartrate, only right-handed facets were 

Molecular Symmetry David J. Willock ( ) 2009 John Wiley Sons, Ltd 

This was the first example of classification based on molecular shape and gave some indication of the physical properties of molecules that were classified as symmetric compared with those that were labelled asymmetric. However, chirality is not the only manifestation of molecular symmetry, and so a more complete classification of molecular shape has been developed the system of point groups. To classify the symmetry of a molecule we derive its point group, which carries much more geometric information than Pasteur s symmetric or asymmetric designation. 

---

Linear molecules fit into the above classification by using the designation for the molecular axis, implying that a rotation of any angle whatever is a symmetry operation. Thus, we have C for a molecule with no centre of inversion (examples being CO and N20) and D if there is an inversion center (examples being N2 and C02), the presence of such a center implying also that there are dihedral axes. 

The PI group operations are defined by their effect on the space-fixed coordinates of the atomic nuclei and electrons. Since our molecular wavefunctions are written in terms of the vibrational coordinates, the Euler angles and the angle p, we must first determine the effect of the PI group operations on these variables. In the case of inversion this can lead to certain problems both in the understanding of the concepts of molecular symmetry and in the proper use of group theoretical methods in the classification of the states of ammonia. 

---