Mirror image concept

One of the fundamental concepts of structural chemistry is that of molecular asymmetry or chirality. The most typical example is that of a tetrahedral carbon atom with four different substituents, C(abcd), which can produce two different arrangements, which are nonsuperimposable mirror images of one another. Such a carbon atom is usually called asymmetric or chiral. In contrast, when two of the substituents are alike, as in C(abc2), the system is usually termed symmetrical or achiral, except for a special class of compounds... 

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. 

According to the classical concept of van t Hoff one would need two operations for the conversion of 18 into its mirror image, namely the inversion of both asymmetric C-atoms. These two examples demonstrate the advantages of the present procedure for enumerating the chirality elements of molecules. 

The most important type of stereoisomerism is that which arises when molecules possess two structures that are not identical and also are mirror images of one another. This is not a difficult or unfamiliar concept. Many things around us, such as our hands, and pairs of shoes, are not identical and also are mirror images of one another. In the same way, nonidentical molecules exist in which the only distinction between them is that one is the mirror image of the other. A common statement is that such isomers are mirror images of one another, but these images are not superimposable. A simple example of this type of... 

An important approach to stereochemical problems is to make use of the concept of chirality. Chirality (7), namely, the phenomenon that a chiral object and its mirror image cannot be superimposed, has been classified according to different elements of chirality. Chiral molecules may contain chiral centers, axes, and/or planes (2, 3). 

Note that this differs from Lord Kelvin s notion in that it involves the observation conditions and the intramolecular motions that can occur under those conditions. It is known, for example, that under suitable conditions, some molecules which cannot be superimposed on their mirror image by any combination of rotations and translations may nevertheless convert to their mirror image by intramolecular motions alone such molecules cannot be observed as chiral under the stated conditions. In particular, this definition of chemical chirality gives meaning to the concept... 

The breadth in scope of this definition comes at the cost of requiring flexibility and judgment in the interpretation of object, superposable, and mirror image. The model must suit the occasion of its use. Chirality, with respect to an isolated molecule, is a quantum-mechanically undefined concept, but, because we... 

The noncovalent helicity induction and chiral memory concept is versatile enough to produce and maintain either a right- or left-handed helix because the helix-sense is predetermined by the chirality of the enantiomeric amines used. Consequently, the opposite enantiomeric helicity induction and the memory requires the opposite enantiomeric amine, followed by replacement with achiral amines. However, both mirror-image enantiomeric helices can be produced with a high efficiency from a helical poly(phenylacetylene) induced by a single enantiomer (Fig. 26) [129]. This dual memory of enantiomeric... 

Let us also visualize the important concept of chirality. Only molecules that differ from their mirror image have enantiomers. Molecules of this type are called chiral. For anything to be chiral, that is, non-superimposable on its mirror—there is a necessary and sufficient condition it is the absence of an intramolecular rotation/reflection axis. What s that, you say See the next paragraph. 

Chirality is a concept well known to organic chemists and to all chemists concerned in any way with structure. The geometric property that is responsible for the nonidentity of an object with its mirror image is called chirality. A chiral object may exist in two enantiomorphic forms that are mirror images of one another. Such forms lack inverse symmetry elements, that is, a center, a plane, and an improper axis of symmetry. Objects that possess one or more of these inverse symmetry elements are superimposable on their mirror images they are achiral. All objects belong to one of these categories. 

The molecular basis for the left- and right-handedness of distinct crystals of the same chemical substance and the associated differences in optical rotation was developed from the hypothesis of Paterno (1869) and Kekule that the geometry about a carbon atom bound to four ligands is tetrahedral. Based on the concept of tetrahedral geometry, Van t Hoff and LeBel concluded that when four different groups or atoms are bound to a carbon atom, two distinct tetrahedral molecular forms are possible, and these bear a non-superimposable mirror-image relationship to one another (Fig. 3). This hypothesis provided the link between three-dimensional molecular structure and optical activity, and as such represents the foundation of stereoisomerism and stereochemistry. 

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