Stereochemistry, Symmetry and Molecular Chirality

Joseph AchiUe LeBel was one of the most important pupils and collaborators of Louis Pasteur. Both of than were interested in the salts of tartaric add (contained in wine), the tartarates. During the isolation of ammonium-sodium-tartarate, Pasteur and LeBel observed that two kinds of crystals appear (see figure bellow). Although these oystals are equal in shape they diffa in such a way as to be mirror picture of one anotha. 

VanCik, Basic Organic Chemistry for the Life Sciences, 103 

Besides the tetrahedral structure, the chirality of a molecule requires one additional condition all four substituents bound to the central carbon atom must be different. A carbon atom with four different substituents induces chirality of the entire molecule and is called a stereogenic, chiral or asymmetric center. If two or more substituents are identical the molecule and its mirror image can be superimposed and the molecule is not chiral. Some chiral and non-chiral molecules are represented bellow. 

Let us examine why only molecules with four different substituents are chiral What is the fundamental geometric property which the molecule, crystal or hand must possess in order to be chiral These phenomena can be examined within the theory of symmetry. Symmetry is the property which ensures that the figure or geometrical body remains unchanged under particular spatial operation, which is called a symmetry element. We say that the object is symmetric in relation to these symmetry elements. Some of the symmetry elements were already described in the 

The scheme above represents three symmetry elements symmetry plane, symmetry axis and the center of symmetry. We can recognize that the water molecule, methyl-chloride and formaldehyde all have symmetry planes. The water molecule and formaldehyde also possess one symmetry axis that leaves the molecule unchanged when rotated by 180°. The symmetry axis around which the object can be rotated by 180° angle and remain unchanged is called a second order 

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It is important to note that high molecular weight trans-isotactic poly(methy-lene-1,3-cyclopentane) contains no mirror or mirror glide planes of symmetry and is thus chiral by virtue of its main chain stereochemistry (it exhibits optical activity) this is in contrast to high molecular weight polypropylene and other poly(a-olefin)s, which contain an effective mirror plane perpendicular to the molecular axis in the middle of the molecule and are thus achiral [30,497],... 

A review of the older literature on compounds with a stereogenic axis is available22, as are reviews on planar chiral molecular structures 23, on the stereochemistry of twisted double bond systems 24, on helical molecules in organic chemistry 25, and on the synthesis and stereochemistry of chiral organic molecules with high symmetry 26. 

As the number of stereocenters in a molecule increases, the number of possible diastereomers increases. A molecule with four dissimilar stereocenters, for example, can exist as one of sixteen stereoisomers. Of these sixteen stereoisomers there are four pairs of enantiomers, and the remaining four pairs are diastereomers. Molecules with configurational diastereomers also arise from many systems other than those with stereocenters. One of the most common examples is a double bond that is substituted in such a way that diastereomers exist. Any combination of two or more molecular features that give rise to stereoisomers will always produce diastereomers, whereas sources of chirality are needed to produce enantiomers. Because stereochemistry can have a high impact on molecular properties, diastereomers generally have easily discernable differences in their physical and chemical behaviors. Some molecules possess greater than or equal to two tetrahedral stereocenters and are nonetheless achiral. These are called meso stereoisomers. These occur when the internal symmetry of the molecule makes it superimposable on its mirror image. 

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