Achiral Molecules with Two Stereogenic Centers

The situation is the same when the two stereogenic centers are present in a ring. There are four stereoisomeric l-bromo-2-chlorocyclopropanes a pair of enantiomers in which the halogens are trans and a pair in which they are cis. The cis compounds are diastereomers of the trans. 

A molecule framed in green Is a diastereomer of one framed in red or blue. 

A molecule framed in black is an enantiomer of a greenframed one. Both are diastereomers of their red or blue-framed stereoisomers. 

Now think about a molecule, such as 2,3-butanediol, which has two stereogenic centers that are equivalently substituted. 

FIGURE 7.11 Stereo-isomeric 2,3-butanediols shown in their eclipsed conformations for convenience. Stereoisomers (a) and (b) are enantiomers of each other. Structure (c) is a diastereo-mer of (a) and (b), and is achiral. It is called meso-2,3-butanediol. 

---

Meso stereoisomer (Section 7.11) An achiral molecule that has stereogenic centers. The most common kind of meso compound is a molecule with two stereogenic centers and a plane of symmetry. 

To summarize, a molecule with a stereogenic center (in our examples, the stereogenic center is a carbon atom with four different groups attached to it) can exist in two stereoisomeric forms, that is, as a pair of enantiomers. Such a molecule does not have a symmetry plane. Compounds with a symmetry plane are achiral. 

The reason that the third stereoisomer is achiral is that the substituents on the two asymmetric carbons are located with respect to each other in such a way that a molecular plane of symmetry exists. Compounds that incorporate asymmetric atoms but are nevertheless achiral are called meso forms. This situation occurs whenever pairs of stereogenic centers are disposed in the molecule in such a way as to create a plane of symmetry. A... 

Chirality is due to the fact that the stereogenic center, also called the chiral center, has four different substitutions. These molecules are called asymmetrical and have a Q symmetry. When a chiral compound is synthesized in an achiral environment, the compound is generated as a 50 50 equimolar mixture of the two enantiomers and is called racemic mixture. This is because, in an achiral environment, enantiomers are energetically degenerate and interact in an identical way with the environment. In a similar way, enantiomers can be differentiated from each other only in a chiral environment provided under... 

Any object that cannot be superimposed on its mirror image is called chiral, that is, it has the property of being right-handed or left-handed. Molecules (or other objects) that are not chiral are described as being achiral, which is the opposite of chiral. Tetrahedral atoms with four nonidentical substituents, then, give rise to two stereoisomers. Such atoms are called stereogenic centers, sometimes shortened to stereocenters. An older term applied specifically to carbon is asymmetric carbon. 

More elaborate molecules can also have a plane of symmetry. For example, there are only three stereoisomers of tartaric acid (2,3-dihydroxybutanedioic acid). Two of these are chiral but the third is achiral. In the achiral stereoisomer, the substituents are located with respect to each other in such a way as to generate a plane of symmetry. Compounds that contain two or more stereogenic centers but have a plane of symmetry are called meso forms. Because they are achiral, they do not rotate plane polarized light. Note that the Fischer projection structure of meio-tartaric acid reveals the plane of symmetry. 

This peculiar chirality was generated by the directionality of the cone calix[6] arene wheel which upon threading with 12a differentiates the two benzylic units around the ammonium center (Scheme 30.3) [29]. It is here worth noting that while beautiful examples of dissymmetric supramolecules assembled from achiral molecules are known [31], to the best of our knowledge, this is the first example of a chiral supramolecule in which an atomic stereogenic center is generated supramolecularly. 

I.I.3.8. Chirality without Stereocenters Not only does a plane of symmetry, which divides a molecule into two exactly identical halves, guarantee achirality, but there are also other elements of symmetry that will make a molecule with stereogenic centers optically inactive. For example, a center of symmetry, a point at which aU the straight lines joining identical points in the molecule cross each other, will be responsible that such molecules do not show an enantio-merism and therefore are not optically active (Figure 1.21). 

---