Chiral object, defined

Using the concept of chirality as defined above, we follow the program stated in our introduction and now aim to provide a quantitative, objective means for expressing the chirality of an ensemble of molecules. The fundamental notion is that of a chemically achiral ensemble of molecules ... 

In Fig. 3.1, we have represented a comparison of chiral objects based on their sizes. If we define an object whose mirror image is nonsuperposable with it as chiral, almost all objects of our life are chiral a perfect macroscopic achiral object does not exist. But usually, we use the term chiral in the sense that its mirror image... 

FIGURE 14.1. The importance of lack of mirror symmetry in defining a chiral object, (a) Right and left hands, and (b) two chiral molecules [B(ADEF)] are shown. One is the mirror image of the other, but they cannot be superimposed on each other. E and F, which are out of the plane of the page, cannot be superimposed on the mirror image of B(ADEF) by a rotation about A-B. F will lie on E, and E will lie on F after such a rotation. 

Two general classes of chirality measures have been recognized in the first, the degree of chirality expresses the extent to which a chiral object differs from an achiral reference object, while in the second it expresses the extent to which two enantio-morphs differ from each other [Buda et al., 1992]. The continuous chirality measure (CCM) recently proposed [Zabrodsky and Avnir, 1995] is an example of chirality measure belonging to the first class and is based on the general definition of continuous symmetry measure defined as ... 

Before we attempt to answer the above questions, we need to examine briefly the terminology relevant to a discussion of chiral drugs. Specifically, the definition and usage of two important terms need to be clarified. Chiral was defined in one recent leading monograph on stereochemistry as follows Not superposable. .. with its mirror image, as applied to molecules, conformations, as well as macroscopic objects, such as crystals [3]. Mislow gave a shorter but essentially equivalent definition An object is chiral if and only if it is not superposable on its mir-... 

We have just seen that a chiral object is defined in a three-dimensional space. However, it is possible to reduce the space to two dimensions and to define chiral objects in a plane. To say that a molecule is two-dimensional appears at first sight to be an abuse of language. In effect, no molecule, even benzene, can be reduced to a plane. We will nevertheless treat molecules such as benzene and ethylene as two-dimensional molecules. These molecules are achiral in three-dimensional space since they possess at least the plane of symmetry in which they lie (Figure 2.15). 

In Chapter 2 we saw that, while in three dimensions a chiral object is defined by the fact of being nonsuperimposable with its mirror image, in two-dimensional space the... 

We define as (pro) -chiral (p>0) any finite, achiral object that can be desymmetrized into a chiral object by at most p stepwise replacements of a point by a differently labeled one and as (pro) -chirality the corresponding property of an achiral object. ... 

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. 

One example of a quantitative measure of molecular chirality is the continuous chirality measure (CCM) [39, 40]. It was developed in the broader context of continuous symmetry measures. A chital object can be defined as an object that lacks improper elements of symmetry (mirror plane, center of inversion, or improper rotation axes). The farther it is from a situation in which it would have an improper element of symmetry, the higher its continuous chirality measure. 

Lord Kelvin lla> recognized that the term asymmetry does not reflect the essential features, and he introduced the concept of chiralty. He defined a geometrical object as chiral, if it is not superimposable onto its mirror image by rigid motions (rotation and translation). Chirality requires the absence of symmetry elements of the second kind (a- and Sn-operations) lu>>. In the gaseous or liquid state an optically active compound has always chiral molecules, but the reverse is not necessarily true. 

One of the most important features of these analogues is their ability to be further cross-linked. The feasibility of the post-polymerization was demonstrated by the application of UV light induced polymerisation of the diynoic galactonamide 32b, which resulted in polymers retaining the superstructure of the surfactant aggregates.167 Similar observations were made for the dodecyl galactonamides 32a, which open up a route to the construction of pre-defined chiral nano-objects, which can be then stablized after assembly. 

It has been recognized147 that chirality measures can be subdivided into two types those that gauge the extent to which a chiroid differs from an achiral reference object (measures of the first kind) and those that gauge the extent to which two enantiomorphs differ from one another (measures of the second kind). In chirality measures of the first kind, the question to be answered is How dissimilar are the chiroid and its achiral reference object In chirality measures of the second kind, the question is How dissimilar are the two enantiomorphs of a chiroid In both cases the underlying concept is that of a distance, measured either between a chiral and an achiral object or between two enantiomorphous chiroids. That is, the degree of chirality of a chiroid X is defined in relation to another, chiral or achiral, reference object Xref The less these two objects match, the more chiral is X. 

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