Shape and Geometry

A molecule is not simply a collection of its constituent atoms. It is kept together by interactions among these atoms. Thus, for some purposes it is better to consider the molecule as consisting of the nuclei of its constituent atoms and its electron density distribution. Generally, it is the geometry and symmetry of the arrangement of the atomic nuclei that is considered to be the geometry and symmetry of the molecule itself. 

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. On the other hand, severe restrictions apply to the symmetries of crystals, as will be seen later (Section 9.3). In fact, molecules occupy a more fundamental level in the hierarchy of structures than do crystals. Many crystals themselves are built from molecules (see. Section 9.6). 

Molecules in the gas phase are considered to be free. They are so far apart that they are unperturbed by interactions with other molecules. 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 to be 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, gaseous molecules, and also 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, 

Symmetry considerations are fundamental in any description of molecular vibrations, as will be seen later in detail (Chapter 5). First, however, we will discuss the molecular symmetries, ignoring entirely the motion of the molecules. Various molecular symmetries will be illustrated by examples from outside chemistry. 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 and 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. 

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Electronic structure theory describes the motions of the electrons and produces energy surfaces and wavefiinctions. The shapes and geometries of molecules, their electronic, vibrational and rotational energy levels, as well as the interactions of these states with electromagnetic fields lie within the realm of quantum stnicture theory. 

Vendor information (available materials, their composition, properties and applications available sizes, shapes and geometry availability, delivery schedule, cost and performance data)... 

In this group of disperse systems we will focus on particles, which could be solid, liquid or gaseous, dispersed in a liquid medium. The particle size may be a few nanometres up to a few micrometres. Above this size the chemical nature of the particles rapidly becomes unimportant and the hydrodynamic interactions, particle shape and geometry dominate the flow. This is also our starting point for particles within the colloidal domain although we will see that interparticle forces are of great importance. 

In situ (Latin for in the place ) polymerization means the fabrication of a polymer network directly in the finally desired shape and geometry. In the context of monolithic separation columns, the term in situ is referred to the polymerization in the confines of a HPLC column or a capillary as mold. 

Anions require receptors of greater size than cations and they occur in a range of shapes and geometries. Anions have high free energies of solvation and hence anion hosts must compete more effectively with the surrounding medium. Many anions exist only in a relatively narrow pH window and are usually coordinatively saturated. 

The valence shell electron pair repulsion theory states the all electrons in a molecule mutually repel each other and achieve a geometry so that the bonding pairs and lone pairs of electrons are as far apart in space as possible. This theory allows one to predict the shape and geometry of a molecule. 

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