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…
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.
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Q1: How many stereoisomers can a molecule with multiple chiral centers have?
A molecule with n chiral centers has 2n possible configurations. For example, butane-2,3-diol with two chiral centers can have 2² = 4 possible configurations. However, not all configurations represent distinct stereoisomers because some may be superposable mirror images. Butane-2,3-diol actually has only three distinct stereoisomers despite four possible configurations.
Q2: What is a meso compound and how does it relate to molecular symmetry?
A meso compound is an achiral stereoisomer with multiple chiral centers that possesses a plane of symmetry or center of symmetry. These molecules are transformed into their mirror images by a 180° rotation, making them superposable on their mirror images. Meso-tartaric acid is a famous example of a meso compound with two chiral centers.
Q3: Why are RR and SS configurations of butane-2,3-diol enantiomers?
The RR and SS configurations are mirror images of each other because each chiral center's configuration is inverted. They cannot be superposed through any rotation, even when considering less energetically favorable but exactly mirrored conformations. This non-superposability makes them an enantiomeric pair.
Q4: How do RS and SR configurations differ from RR and SS in butane-2,3-diol?
RS and SR configurations are superposable after a 180° rotation, meaning they represent the same molecule rather than distinct stereoisomers. In contrast, RR and SS configurations cannot be superposed by any rotation. This distinction explains why butane-2,3-diol has only three distinct stereoisomers instead of four.
Q5: Why are molecules with only one chiral center always chiral?
A single chiral center precludes any symmetry in the molecule, preventing the existence of a plane of symmetry, center of symmetry, or improper axis of rotation. Without these symmetry elements, the molecule cannot be superposed on its mirror image, making it inherently chiral. This contrasts with molecules having multiple chiral centers, which may be achiral.
Q6: How does an improper axis of rotation make a molecule achiral?
An improper axis of rotation is an axis about which rotation creates a mirror image of the molecule in a plane perpendicular to that axis. When a molecule with multiple chiral centers lacks a plane or center of symmetry but possesses an improper axis, it remains achiral because it is still superposable on its mirror image through this rotational mechanism.
Q7: What determines whether a molecule with multiple chiral centers is chiral or achiral?
Chirality of molecules with multiple chiral centers depends on molecular symmetry evaluation. If the molecule has a plane of symmetry, center of symmetry, or improper axis of rotation, it is achiral. Without these symmetry elements, the molecule is chiral. Understanding isomerism constitutional isomers and stereoisomers is essential for determining overall molecular chirality.