Definition of Chirality

Before defining the symmetry point groups for achiral and chiral molecules, we will hypothesize that the positions of their atoms may vary in a continuous manner. In this 

We will now examine the point groups of achiral and chiral molecules. 

Procedure for finding the point symmetry group of a molecular unit (reproduced with permission from reference 

Some examples of chiral organometallic compounds 2.6-2.11 with different symmetry point groups. 

We hypothesized that all the possible conformations are iso-energetic, but this situation is not general. In certain cases some particular conformations are more stable than others. These conformations, which become configurational isomers, can sometimes be separated by energy barriers that are sufficient for them to be isolated at a given temperature. This type of isomerism is known as atropisomerism. 

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Although the term prochirality is frequently used, especially by biochemists, it suffers from a limitation which arises from a corresponding limitation in the definition of chirality. Molecules may display purely stereochemical differences without being chiral cis-tram isomers of olefins and certain achiral cis-trans isomers of cyclanes are examples. Thus (Fig. 2) (Z)- and ( )-1,2-dichloroethylene (4, 5) are achiral diastereomers, as are cis- and /rtww-1,3-dibromocyclobutanes (6, 7) being devoid of chirality these compounds have no chiral centers (or other chiral elements). Thus it is inappropriate to associate stereoisomerism with the occurrence of chiral... 

We have encountered a number of different definitions of chirality. In the spirit of making everything as simple as possible, but not simpler, 126 we suggest a concise and at the same time general definition for a chiroid (and hence of chirality) whose very simplicity makes it broadly applicable in geometry and topology, as well as in the natural sciences ... 

L. L. Whyte extended the definition of chirality Three-dimensional forms (point arrangements, structures, displacements, and other processes) which possess non-superposable mirror images... 

The definition of chirality and its measurement are described in great detail in a number cf texts (3) however, a brief introduction to the key issues is given in this section. Specifically, chirality is a term referring to a property cf a molecule that is nonsuperimposableon its mirror image as shown in Fig. 18.1, where such a molecule is chiral. 

The definitions of chiral and the associated terms homochiral and heterochiral made their first appearance in a footnote of a lecture, entitled The Molecular Tactics of a Crystal, that Sir William Thomson, who had been elevated to Lord Kelvin in 1892, delivered to the Oxford University Junior Scientific Club on May 16, 1893. The famous footnote reads ... 

One definition of chirality is that the molecule be nonsuperimposablc on its mirror image. An equivalent criterion is that it not possess an improper axis of rotation (page 52). The absence of a mirror plane does not insure optical activity because a molecule may have no mirror plane, yet may possess an improper rotational axis. We can, hpv/ever, be sure that the molecule with a mirror plane will be optically inactive. 

Whyte [2-37] extended the definition of chirality as follows Three-dimensional forms (point arrangements, structures, displacements, and other processes) which possess non-superposable mirror images are called chiral . A chiral process consists of successive states, all of which are chiral. The two main classes of chiral forms are screws and skews. Screws may be conical or cylindrical and are ordered with respect to a line. Examples of the latter are the left-handed and right-handed helices in Figure 2-50. The skews, on the other hand, are ordered around their center. Examples are chiral molecules having point-group symmetry. 

Barron, L. D.. Am. Chem. Soc. 1986, 108, 5539 noted that there is a difference between the words dissymmetry and chirality, since dissymmetry is the absence of certain symmetry elements, while chirality is the presence of the attribute of handedness. However, Mislow defined chirality as the "absence of reflection symmetry" and investigated the quantification of chirality Buda, A. B. Auf der Heyde, T. Mislow, K. Angew. Chem. Int. Ed. Engl. 1992, 31, 989. Zabrodsky, H. Peleg, S. Avnir, D. /. Am. Chem. Soc. 1993,115, 8278 treated symmetry as a continuous and quantifiable property rather than as a "yes or no" condition. Zabrodsky, H. Avnir, D. /. Am. Chem. Soc. 1995, 117, 462 gave a quantitative definition of chirality. also the discussion in reference 22, pp. 241-256. 

So far, we have considered only nonchiral molecules, which have a plane of mirror symmetry, so the molecule is equal to its mirror image. However, there are molecules that are not symmetric when reflected, and they are called chiral. The first studies of the molecular chirality are dated back to the Ph.D. work of Louis Pasteur in 1848, when he observed the chiral separation of the crystals of tartaric and paratartaric acids in the sediments of fermenting wines. However, the definition of chiral objects was given first by Lord Kelvin only in 1893 "An object is chiral, if it cannot be superimposed on its mirror image."... 

The structural chirality of large, random supramolecular structures, spiral diffusion-limited aggregates, was analyzed by the CCM approach. It was found that classical definitions and terminologies of chirality are too restrictive for the description of such complex objects. A refined methodology and a conceptual vocabulary were developed, along with a generalized definition of chirality which takes care of supramolecular structures. The statistical significance of symmetry and chirality were defined, and applied on many examples. 

Based on the definition of chiral in Model 4, explain why an sp carbon with four different groups attached must be chiral. 

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