Symmetry, Pseudosymmetry, Spectroscopy, and Molecular Structure

There are a number of goals for this article on symmetry. The first and foremost is to illustrate that there is an intimate relationship between the environment surrounding a molecule and its three-dimensional spatial structure. Another goal is to stress the difference between genuine symmetry and apparent symmetry (nonmathematical symmetry) which is known as pseudosymmetry. While genuine symmetry is an ideal state, pseudosymmetry represents a continuum of distortion from the ideal to the asymmetric state. It will be shown that symmetry in molecular structure manifests itself by affording degenerate frequency spectroscopic and diffraction signals from equivalent molecular subunits. While the above mentioned are primary goals, a strong foundation will be provided for understanding molecular symmetry in terms of both its principles and its modern nomenclature. As part of the building of such groundwork, the basic principles of chiroptical phenomena, pulse nuclear magnetic resonance spectroscopy, and X-ray crystallography will be presented.