4.6: Molecules with Multiple Chiral Centers
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