Achiral molecules symmetry elements

Point groups of chiral and achiral molecules Chiral Achiral (identifying symmetry element)... 

Since the presence of a plane of symmetry in a molecule ensures that it will be achiral, one a q)ro h to classification of stereoisomers as chiral or achiral is to examine the molecule for symmetry elements. There are other elements of symmetry in addition to planes of symmetry that ensure that a molecule will be superimposable on its mirror image. The trans,cis,cis and tmns,trans,cis stereoisomers of l,3-dibromo-rranj-2,4-dimethylcyclobutaijte are illustrative. This molecule does not possess a plane of symmetry, but the mirror images are superimposable, as illustrated below. This molecule possesses a center of symmetry. A center of symmetry is a point from which any line drawn through the molecule encouniters an identical environment in either direction fiom the center of ixnimetry. 

Indicate which of the following molecules are chiral and which are achiral. For each molecule that is achiral, indicate the element of symmetry that is present in the molecule. 

Achiral molecules are characterised by the presence of symmetry elements of the second kind, for example, planes of symmetry, inversion centres or rotation-reflexion axes. 

Finally, reference must be made to the important and interesting chiral crystal structures. There are two classes of symmetry elements those, such as inversion centers and mirror planes, that can interrelate. enantiomeric chiral molecules, and those, like rotation axes, that cannot. If the space group of the crystal is one that has only symmetry elements of the latter type, then the structure is a chiral one and all the constituent molecules are homochiral the dissymmetry of the molecules may be difficult to detect but, in principle, it is present. In general, if one enantiomer of a chiral compound is crystallized, it must form a chiral structure. A racemic mixture may crystallize as a racemic compound, or it may spontaneously resolve to give separate crystals of each enantiomer. The chemical consequences of an achiral substance crystallizing in a homochiral molecular assembly are perhaps the most intriguing of the stereochemical aspects of solid-state chemistry. 

Systematic studies of topochemical reactions of organic solids have led to the possibility of asymmetric synthesis via reactions in chiral crystals. (A chiral crystal is one whose symmetry elements do not interrelate enantiomers.) (Green et al, 1979 Addadi et al, 1980). This essentially involves two steps (i) synthesis of achiral molecules that crystallize in chiral structures with suitable packing and orientation of reactive groups and (ii) performing a topochemical reaction such that chirality of crystals is transferred to products. The first step is essentially a part of the more general problem of crystal engineering. An example of such a system where almost quantitative asymmetric induction is achieved is the family of unsymmetrically substituted dienes ... 

A molecule that has a mirror image is also said to be dissymmetric while one that docs not (an achiral molecule) have an enantiomer is noiidissyiinnetric. The classification of a given structure as dissymmetric or nondissymmetric is based upon the presence (or lack) of symmetry elements (axes, planes) in the structure. 

The compound has two chirality centres and three pseudo chirality centres. There is however, only one (achiral) diastereomer of the compound shown in the question. The two isomers can be distinguished from one another solely on the relative position of the chlorine or bromine atoms which lie in a plane which also happens to be the plane of symmetry of the molecule (this is the only symmetry element present, therefore the symmetry point group is Cs). It is possible in this instance to specify the configuration unequivocally using the descriptors E and Z. However, in systematic nomenclature the complete configuration of all the stereogenic centres is specified. Thus the (so-called) Z isomer is (ls,3r,5 ,6r,7S)-l,6-dibromo-3,6-dichloroadamantane and the isomer is (ls,3r,5 ,6s,7S)-l,6-dibromo-3,6-dichloroadamantane, i.e. the two isomers can be distinguished simply by the descriptor used for position 6. 

Note that according to the foregoing definition, chirality occurs only in molecules that do not have a rotation/reflection axis. However, if the molecule has only ( ) an axis of rotation, it is chiral. For example, both trans-1,2-dibromocyclohexane (D in Figure 3.3) and the dibromosuccinic acid E have a two-fold axis of rotation (C2) as the only symmetry element. In spite of that, these compounds are chiral because the presence of an axis of rotation, in contrast to the presence of a rotation/reflection axis, is not a criterion for achirality. 

Chiral A geometric figure, or group of points is chiral if it is nonsuperimposable on its mirror image [82]. A chiral object lacks all of the second order (improper) symmetry elements, a mirror plane), i center of symmetry), and S rotation-reflection axis). In chemistry, the term is (properly) only applied to entire molecules, not to parts of molecules. A chiral compound may be either racemic or nonracemic. An object that has any of the second order symmetry elements i.e., that is superimposable on its mirror image) is achiral. It is inappropriate to use the adjective chiral to modify an abstract noun one cannot have a chiral opinion and one cannot execute a chiral resolution or synthesis. 

The methylene protons of propanoic acid (Fig. 4.37, structure c) are exchangeable by reflection through the plane of symmetry in the plane of the paper. There are no other symmetry elements. The protons are enantiotopes of each other and have the same chemical shift only in an achiral environment. Drawings and models of the molecule are indistinguishable by inspection before and after the operation. 

Various di- and polysubstituted cyclic compounds provide other examples of molecules having planes of symmetry. Since chirality depends on configuration, not conformation, cyclic molecules can be represented as planar structures to facilitate recognition of symmetry elements. These planar structures clearly convey the cis and trans relationships between substituents. Scheme 2.1 gives some examples of both chiral and achiral dimethylcycloalkanes. Note that in several of the compounds there is both a center and a plane of symmetry. Either element of symmetry ensures that the molecule is achiral. 

A chirality classification of crystal structures that distinguishes between homochiral (type A), heterochiral (type B), and achiral (type C) lattice types has been provided by Zorkii, Razumaeva, and Belsky [11] and expounded by Mason [12], In the type A structure, the molecules occupy a homochiral system, or a system of equivalent lattice positions. Secondary symmetry elements (e.g., inversion centers, mirror or glide planes, or higher-order inversion axes) are precluded in type A lattices. In the racemic type B lattice, the molecules occupy heterochiral systems of equivalent positions, and opposite enantiomers are related by secondary lattice symmetry operations. In type C structures, the molecules occupy achiral systems of equivalent positions, and each molecule is located on an inversion center, on a mirror plane, or on a special position of a higher-order inversion axis. If there are two or more independent sets of equivalent positions in a crystal lattice, the type D lattice becomes feasible. This structure consists of one set of type B and another of type C, but it is rare. Of the 5,000 crystal structures studied, 28.4% belong to type A, 55.6% are of type B, 15.7% belong to type C, and only 0.3% are considered as type D. 

In the context of chemistry, the term chirality usually refers to a pair of molecules that cannot be superimposed onto each other - also referred to as enantiomers or optical isomers. The main characteristic of chirality is the absence of an axis of improper rotation. The existence of such a symmetry element is implied by the presence of either a mirror plane through the central atom or a center of inversion if either of these elements is present, the molecule is achiral. The chiral sense of a molecule is specified by its absolute configuration (R/S, D/L, or A/A). Molecules may be present as enantiomeric mixtures, of which those with compositions 100 0 and 0 100%, described as enantiomerically pure or homochiral, and the equimolar one of 50 50% described as a racemate or racemic mixture are particularly important. 

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