Symmetry in Achiral Structures

Sample Solution (a) The hydroxyl-bearing carbon in 2-cyclopentenol is a chirality center. There is no chirality center in 3-cyclopentenol, because the sequence of atoms 1 2- 3 4 5is equivalent regardless of whether one proceeds clockwise or counterclockwise. 

Even isotopes qualify as different substituents at a chirality center. The stereochemistry of biological oxidation of a derivative of ethane that is chiral because of deuterium (D = H) and tritium (T = H) atoms at carbon, has been studied and shown to proceed as follows  

The stereochemical relationship between the reactant and the product, revealed by the isotopic labeling, shows that oxygen becomes bonded to carbon on the same side from which H is lost. As you will see in this and the chapters to come, determining the three-dimensional aspects of a chemical or biochemical transformation can be a subtle, yet powerful, tool for increasing our understanding of how these reactions occur. 

One final, very important point Everything we have said in this section concerns molecules that have one and only one chirality center molecules with more than one chirality center may or may not be chiral. Molecules that have more than one chirality center will be discussed in Sections 7.11 through 7.14. 

Certain structural features can sometimes help us determine by inspection whether a molecule is chiral or achiral. For example, a molecule that has a plane of symmetry or a center of symmetry is superimposable on its mirror image and is achiral. 

A plane of symmetry defined by the atoms H—C—Cl divides chlorodifluoromethane into two mirror-image halves. Note that the Cl and H atoms lie within the plane and reflect upon themselves. 

Locate any planes of symmetry in each of the following compounds. Which of the compounds are chiral Which are achiral  

Sample Solution (a) ( )-l,2-Dichloroethene is planar. The molecular plane is a plane of symmetry. Identifying a plane of symmetry tells us the molecule is achiral. 

A point in the center of a molecule is a center of symmetry if any line drawn from it to some element of the structure will, when extended an equal distance in the opposite direction, encounter an identical element. rran5-l,3-cyclobutanediol has a plane of symmetry as well as a center of symmetry. The center of symmetry is the center of the molecule. A line starting at one of the hydroxyl groups and drawn through the center of the molecule encounters the equidistant hydroxyl group on the opposite side. Mirror images A and B are superimposable, and fran.y-l,3-cyclobutanediol is achiral. 

Furthermore, (E)-1,2-dichloroethene has a center of symmetry located at the midpoint of the carbon-carbon double bond. It is achiral. 

A plane of symmetry bisects a molecnle so that one half of the molecnle is the mirror image of the other half. The achiral molecule chlorodifluoromethane, for example, has the plane of symmetry shown in Fignre 7.3. 

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Multiple Chiral Centers. The number of stereoisomers increases rapidly with an increase in the number of chiral centers in a molecule. A molecule possessing two chiral atoms should have four optical isomers, that is, four structures consisting of two pairs of enantiomers. However, if a compound has two chiral centers but both centers have the same four substituents attached, the total number of isomers is three rather than four. One isomer of such a compound is not chiral because it is identical with its mirror image it has an internal mirror plane. This is an example of a diaster-eomer. The achiral structure is denoted as a meso compound. Diastereomers have different physical and chemical properties from the optically active enantiomers. Recognition of a plane of symmetry is usually the easiest way to detect a meso compound. The stereoisomers of tartaric acid are examples of compounds with multiple chiral centers (see Fig. 1.14), and one of its isomers is a meso compound. 

We start with some elementary information about anisotropic intermolec-ular interactions in liquid crystals and molecular factors that influence the smectic behaviour. The various types of molecular models and commonly accepted concepts reproducing the smectic behaviour are evaluated. Then we discuss in more detail the breaking of head-to-tail inversion symmetry in smectic layers formed by polar and (or) sterically asymmetric molecules and formation of particular phases with one and two dimensional periodicity. We then proceed with the description of the structure and phase behaviour of terminally fluorinated and polyphilic mesogens and specific polar properties of the achiral chevron structures. Finally, different possibilities for bridging the gap between smectic and columnar phases are considered. 

It is now instructive to ask why the achiral calamitic SmC a (or SmC) is not antiferroelectric. Cladis and Brand propose a possible ferroelectric state of such a phase in which the tails on both sides of the core tilt in the same direction, with the cores along the layer normal. Empirically this type of conformational ferroelectric minimum on the free-energy hypersurface does not exist in known calamitic LCs. Another type of ferroelectric structure deriving from the SmCA is indicated in Figure 8.13. Suppose the calamitic molecules in the phase were able to bend in the middle to a collective free-energy minimum structure with C2v symmetry. In this ferroelectric state the polar axis is in the plane of the page. 

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. 

In the envelope conformation (A) the peroxide bond and the two carbon atoms are all coplanar (with the C-O-O-C dihedral angle being close to 0°) while the ethereal oxygen atom can be displaced by as much as 0.65 A to either side of this plane. In conformation B the peroxide bond straddles the plane of the remaining three atoms and this dihedral is around 50°. While conformation A is achiral, B has C.y symmetry. Usually ozonides crystallize in chiral space groups however, both enantiomorphic forms of B are usually encountered in the crystal lattice. Furthermore, disorder of the peroxide oxygen atoms over several occupancies is frequent, and in recent analyses, due mostly to improvement in the structure refinement algorithms, this disorder could be taken into account and suitably refined models could be built from the diffraction data. 

The crystallization of achiral molecules in chiral space groups, while rare and unpredictable, is well documented. Molecules with a C2 symmetry axis tend to crystallize in chiral structures, according to Jacques and coworkers, but despite impressive work on crystal engineering, predictions of a correlation between crystal symmetry and molecular structures are still hard to make [6]. 

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. 

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