Internal mirror plane

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. 

However, 5 and 8 are identical. Although there are two chiral centers in 5 (and 8), the molecule itself is achiral because it contains an internal mirror plane. Thus it has a plane of symmetry. Structure 8 is superimposable on 5 by a 180°... 

Internal mirror plane, cis-1,2-Dichlorocyclopentane has an internal mirror plane of symmetry. 

The converse is not true, however. When we cannot find a mirror plane of symmetry, that does not necessarily mean that the molecule must be chiral. The following example has no internal mirror plane of symmetry, yet the mirror image is superimposable on the original molecule. You may need to make models to show that these mirror images are just two drawings of the same compound. 

Using what we know about mirror planes of symmetry, we can see why a chiral (asymmetric) carbon atom is special. Figure 5-4 showed that an asymmetric carbon has a mirror image that is nonsuperimposable on the original structure it has no internal mirror plane of symmetry. If a carbon atom has only three different kinds of substituents, however, it has an internal mirror plane of symmetry (Figure 5-9). Therefore, it cannot contribute to chirality in a molecule. 

For each compound, determine whether the molecule has an internal mirror plane of symmetry. If it does, draw the mirror plane on a three-dimensional drawing of the molecule. If the molecule does not have an internal mirror plane, determine whether or not the structure is chiral, (a) methane (b) cis-1,2-dibromocyclobutane... 

Let s consider whether cis-l, 2-dibromocyclohexane is chiral. If we did not know about chair conformations, we might draw a flat cyclohexane ring. With a flat ring, the molecule has an internal mirror plane of symmetry (cr), and it is achiral. 

Cis-trans isomerism is also possible when there is a ring present. Cis- and trans-1,2-dimethylcyclopentane are geometric isomers, and they are also diastereomers. The trans diastereomer has an enantiomer, but the cis diastereomer has an internal mirror plane of symmetry, so it is achiral. 

A meso compound with two chirality centers will be (R,S) or (S,R) because the chirality centers must be mirror images of each other, reflected across the internal mirror plane. 

To distinguish among the other four protons, notice that cyclobutanol has an internal mirror plane of symmetry. Protons Hc are cis to the hydroxyl group, while protons Hd are trans. Therefore, protons Hc are diastereotopic to protons Hd and the two sets of protons absorb at different magnetic fields and are capable of splitting each other. 

It was mentioned above that tris(chelate) complexes of the type [Colenlj] lack an improper axis of rotation. As a result, such complexes can exist in either of two enantiomeric forms (or a racemic mixture of the two). Figure 12.20 illustrates the complex ions [ 0(00)3] and [Crioxlj] ", each of which is chiral with Dj symmetry. It is not necessary to have three chelate rings present. The cation dichloro-bis(ethylenediamine)cobaIt(III) exists as two geometric isomers, cis and trans. The trans isomer has approximate Dj, symmetry (Fig. 12.21b). Because it has three internal mirror planes, it is achiral. The cis isomer has C, symmetry and is chiral (Fig. 12.2la). Since the two chloride ions replace two nitrogen atoms from an eth-... 

A molecule can be chiral without having a chiral center if it has a chiral shape such as a propeller or helix. A molecule is not chiral if it contains an internal mirror plane. A compound can contain chiral centers and not be chiral if there is an internal mirror plane. Whenever you are uncertain, build the model of the compound and try to superimpose it on a model of its mirror image. See the Appendix for how to name chiral compounds. 

If a compound has two identical chiral centers, then the RS and SR compounds can be superimposed they are identical and are called a meso compound. Meso compounds can usually be recognized by having an internal mirror plane, and are not chiral. 

A meso compound is achiral by virtue of the fact that it contains an internal mirror plane of symmetry, so the molecule is superimposable on its mirror image and hence does not have an enantiomer. Use a dashed line to show the internal plane of symmetry present in the structure of ds-l,2-cyclohexanediol (6). 

From this example, we can make this generalization about meso compounds They have an internal mirror plane (or center of symmetry). Commonly, there are two chiral centers, each with the same four groups one is R the other, S. 

In addition, when a chiral molecule is subjected to any improper rotation, it is converted into its enantiomer. Since the simplest improper axis to use is an S, the a plane (see many of our examples above), most chemists first look for an internal mirror plane in a molecule to decide if it is chiral or not. If the molecule possesses an internal mirror plane in any readily acce.ssible conformation, then the molecule is achiral. For those familiar with point groups, it is a simple matter to show that all chiral molecules fall into one of five point groups C, D, T, O, or I. All other point groups contain an S axis. 

The experimental observations are consistent with the intermediacy of a non-classical carbocation called the norbornyl cation (see Figure 11.10), a structure primarily attributed to Winstein. The non-classical structure possesses an internal mirror plane of symmetry, and the endo face of the compound is protected by the bridging interaction. This, at the time, was a highly novel proposal, and it was not universally accepted. The experimental observations could alternatively be explained by invoking two classical carbocations rapidly equilibrating via carbon shifts (Eq. 11.38). The biggest proponent of this explanation was Brown. The distinction between these two possibilities is an important issue to discuss. 

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