Overview
Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are superposable mirror images of each other and, accordingly, represent the same molecule. For instance, butane-2,3-diol with its two chiral centers can have 22, i.e., four possible configurations. While RR and SS are mirror images of each other, they are not superposable and hence are chiral. However, RS and SR are also mirror images of each other but are superposable and the same molecule. Therefore, butane-2,3-diol has only three distinct stereoisomers of the potential four.
In this context, the understanding of a chiral center vis-à-vis a chiral molecule is vital. This is fundamentally dependent on molecular symmetry – be it a plane or center of symmetry or an improper axis of rotational symmetry. Molecules with a plane of symmetry or a center of symmetry possess superposable mirror images and are hence achiral. However, when both are absent, the molecule is still achiral if the object's rotation about an axis creates a mirror image of the molecule in a plane perpendicular to the axis. Such an axis is known as an improper axis of rotation.
A single chiral center precludes the possibility of any symmetry in the molecule, and hence molecules with only one chiral center are always chiral. Asserting the chirality of a molecule with multiple chiral centers can only be done after evaluating the symmetry of the molecular structure. Molecules with multiple chiral centers and an achiral configuration are referred to as meso compounds. A famous example is the meso-tartaric acid shown in Figure 1(c).
Figure 1: Fischer projection skeletal structures of tartaric acid enantiomers - (a) ʟ-tartaric acid, (b) ᴅ-tartaric acid, and (c) meso-tartaric acid
Procedure
Recall that a chiral center in a molecule, such as in (R)-2-butanol, is a tetrahedral atom with four different substituents. Some molecules, such as butane-2,3-diol, have multiple chiral centers.
While molecules with only one chiral center are always chiral, molecules with multiple chiral centers may have achiral configurations.
A molecule with n chiral centers has 2n possible configurations. If any configuration can be superposed on another, those two configurations represent the same molecule. Thus, there may be fewer distinct stereoisomers than possible configurations.
For example, butane-2,3-diol has two chiral centers and four possible configurations. The RR and SS configurations are mirror images of each other, as each chiral center’s configuration is inverted.
Although their lowest-energy conformations do not appear to be mirror images overall, each chiral center is still the mirror image of its partner.
Here, there is no way to rotate the RR and SS configurations to make them superposable, even in their less energetically favorable but exactly mirrored conformations. Thus, they are an enantiomeric pair.
The other pair of configurations, RS and SR, are superposable after a 180° rotation; that is, they are the same molecule. Hence, butane-2,3-diol has only three distinct stereoisomers, one of which is achiral. This achiral stereoisomer is called a meso compound.
Nearly all meso compounds have a plane of symmetry or a center of symmetry. Such molecules are transformed into their mirror images by a 180° rotation.
However, a molecule with multiple chiral centers that lacks those elements still may be superposable on its mirror image by a rotation of less than 180°. If any such rotation exists, both configurations represent the same meso compound.