# Molecules with Several Chirality Centers and Meso Compounds

## Molecules with Several Chirality Centers

A molecule may contain not only one, but several chirality centers. Compounds with n chirality centers may form up to $2 n$ stereoisomers, as each asymmetric carbon can represent two different absolute configurations. According to the CIP nomenclature, these configurations are termed (R) and (S). A molecule that contains two asymmetric carbons can, for instance, form up to $2 2$ = 4 stereoisomers; a molecule with three asymmetric carbons can form up to eight stereoisomers.

The maximum number of combinations of absolute configurations in a molecule, containing a certain number of chirality centers, can be calculated, regardless of the structure.

Example: Which combinations of absolute configurations are possible in a molecule with three chirality centers?

Tab.1
Combinations of absolute configuration of three chirality centers
 RRR all R RRS, RSR, SRR two R, one S SSR, SRS, RSS one R, two S SSS all S

### The four stereoisomers of 2,3-dibromopentane

Let us further go into the combinations of absolute configurations with a simple example, 2,3-dibromopentane.

2,3-Dibromopentane contains two asymmetric carbons, namely C2 and C3. As a result, the possible combinations of absolute configurations are (2S,3S), (2R3R), (2S,3R), and( 2R,3S). From these combinations, four different structures, that cannot become superimposable by conformational changes such as single bond rotations, are derived. They are therefore stereoisomers. All 2,3-dibromopentane stereoisomers are optically active. Nevertheless, they are not a quartet of enantiomers, as an image always has no more than one mirror image. Rather, they are two pairs of entantiomers. Molecules I and II are one pair of enantiomers and molecules III and IV are the other pair.

Fig.1
Pair of enantiomers A.
Fig.2
Pair of enantiomers B.

Which relationship exists among the A and B pairs of enantiomers? They are not enantiomeric, because they have no mirror-image relationship. However, they are stereoisomeric, because they have the same empirical formula and they do show the same connectivity.

Definition
Stereoisomers which have no mirror-image relationship are called diastereomers.

Molecule III is therefore enantiomeric to molecule IV, but it is diastereomeric to molecules I and II. The relationship among the four stereoisomers is shown in the illustration below. Use the decision tree to ascertain the isomeric relationship between two molecules with the same empirical formula.

Fig.3

Isomeric relationship of the 2,3-dibromopentane stereoisomers.

Fig.4

Decision tree for the differentiation between the types of isomerism.

Try to discover the isomeric relationship of the two erythrose stereoisomers shown in the interactive molecular models below by manipulating their orientation with your mouse.

Fig.5
Fig.6
Fig.7

Enantiomers differ only in their interaction with other chiral compounds and plane-polarized light. That is, they rotate the plane of polarized light by equal amounts in opposite directions. Diastereomers, however, depict different physical properties such as melting points, boiling points, and different, though usually not opposite, optical rotations.

Hint
In certain cases, the maximum number ($2 n$) of combinations of absolute configurations of a molecule is higher than the number of possible stereoisomers. This is because some of the stereoisomers are identical compounds, though they do have different combinations of absolute configurations. These identical compounds are called meso compounds.

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