Molecular Shape and Geometry

Hargittai, I. Hargittai, Symmetry through the Eyes of a Chemist, 3rd ed., 

Molecules are finite figures with at least one singular point in their symmetry description. Thus, point groups are applicable to them. There is no inherent limitation on the available symmetries for molecules. Molecules in the gas phase are considered to be free. They are so far apart that they are unperturbed by interactions from other molecules and thus can be considered isolated from each other. On the other hand, intermolecular interactions may occur between the molecules in condensed phases, i.e., in liquids, melts, amorphous solids, or crystals. In the present discussion all molecules will be assumed unperturbed by their environment, regardless of the phase or state of matter in which they exist. 

Molecules are never motionless. They are performing vibrations all the time. In addition, the gaseous molecules, and also the molecules in liquids, are performing rotational and translational motion as well. Molecular vibrations constitute relative displacements of the atomic nuclei with respect to their equilibrium positions and occur in all phases, including the crystalline state, and even at the lowest possible temperatures. The magnitude of molecular vibrations is relatively large, amounting to several percent of the intemuclear distances. Typically, there are about 1012-1014 vibrations per second. 

Symmetry considerations are fundamental in any description of molecular vibrations, as will be seen later in detail (Chapter 5). First, however, the molecular symmetries will be discussed, ignoring entirely the motion of the molecules. Various molecular symmetries will be illustrated by examples. A simple model will also be discussed to gain some insight into the origins of the various shapes and symmetries in the world of molecules. Our considerations will be restricted, however, to relatively simple, thus rather symmetrical systems. The importance and consequences of intramolecular motion involving relatively large amplitudes, will be commented upon in the final section of this chapter. 

The empirical formula, or sum formula, of a chemical compound expresses its composition. For example C2H4O2 indicates that the molecule consists of two carbon, four hydrogen and two oxygen atoms. This formulation, however, provides no information on the 

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