Molecules with Two Stereocentres: Diastereomers

Introduction

A molecule with one stereocentre exists as a single pair of enantiomers. Add a second stereocentre and the picture becomes richer: there are now four possible combinations of configurations, and some pairs of these are mirror images while others are not. Stereoisomers that are not mirror images are called diastereomers . Unlike enantiomers, diastereomers have different melting points, boiling points, solubilities and reaction rates, which makes them both easier to separate and hugely important in biology, where natural sugars and amino acids often carry several stereocentres.

Core explanation

The 2^n rule. Each stereocentre can adopt one of two configurations, R or S. With n stereocentres there are 2 × 2 × ... = 2^n combinations, so a molecule has at most 2^n stereoisomers. One stereocentre gives 2; two give 4; three give 8. The word "at most" matters, because internal symmetry can reduce the number, as the next topic on meso compounds shows.

A worked set: 2-bromo-3-chlorobutane. CH₃–CHBr–CHCl–CH₃ has stereocentres at C2 and C3. The four stereoisomers are (2R,3R), (2S,3S), (2R,3S) and (2S,3R).

Finding enantiomers. The mirror image of a molecule has every stereocentre inverted. So (2R,3R) and (2S,3S) are enantiomers, and (2R,3S) and (2S,3R) are enantiomers. There are two enantiomeric pairs.

Finding diastereomers. Any two stereoisomers that are not enantiomers are diastereomers. If two structures differ at some, but not all, stereocentres, they are diastereomers. (2R,3R) is a diastereomer of both (2R,3S) and (2S,3R). Each stereoisomer therefore has one enantiomer and two diastereomers in this set.

Why diastereomers have different properties. Enantiomers are related by reflection, so every distance between atoms and every intramolecular interaction is identical in both. Diastereomers are not related by any symmetry operation. The distances between groups on C2 and groups on C3 differ, dipole moments differ, and the molecules pack differently in crystals. Consequently diastereomers have different melting points, boiling points, densities, NMR spectra and reactivity, just like constitutional isomers.

Epimers. When a molecule has several stereocentres, two diastereomers that differ at only one of them are called epimers. D-glucose and D-galactose are epimers at C4; D-glucose and D-mannose are epimers at C2.

Natural examples. The amino acid threonine has two stereocentres. Natural L-threonine is (2S,3R); its diastereomer (2S,3S) is called allo-threonine. Ephedrine (1R,2S) and pseudoephedrine (1S,2S) are diastereomers with different melting points and pharmacological profiles.

Step-by-step reasoning

To classify a pair of stereoisomers with two stereocentres:

1. Confirm they have the same constitution. 2. Assign R or S at every stereocentre in both structures. 3. If every centre is inverted, they are enantiomers. 4. If every centre is the same, they are the same compound. 5. If some centres differ and others do not, they are diastereomers.

Visual explanation

Draw the four stereoisomers at the corners of a square. Place (2R,3R) and (2S,3S) at opposite corners, joined by a diagonal labelled "enantiomers", and do the same for (2R,3S) and (2S,3R). The four sides of the square, each joining structures that differ at one centre, are labelled "diastereomers". Every corner has one diagonal partner and two side partners.

Real-world analogy

Think of a pair of gloves worn on hands. A left glove on the left hand and a right glove on the right hand are mirror images of each other as a combination. A left glove on the right hand is a different combination altogether: it is not the mirror image of the correct pairing, and it fits differently. That mismatch is like a diastereomer.

Real-world example

Ephedrine and pseudoephedrine are diastereomers found in plants of the genus Ephedra. They have the same atoms and bonds, differing at only one stereocentre, yet they differ in melting point and in how strongly they act on the body; pseudoephedrine is the one widely used as a nasal decongestant.

Why?

Why is the maximum 2^n and not some other number? The configuration of each stereocentre is an independent binary choice. Combining n independent two-way choices gives 2^n arrangements, exactly as n coin tosses give 2^n sequences of heads and tails.

Common misconception

"Any two stereoisomers that are not identical must be enantiomers." Only stereoisomers that are non-superimposable mirror images are enantiomers. With two or more stereocentres, most pairs of stereoisomers are diastereomers.

Worked example

Question: A compound has three stereocentres. Its natural form is (2R,3S,4R). Give its enantiomer, one of its epimers, and the maximum number of stereoisomers.

Reasoning: Inverting every centre gives the enantiomer. Inverting only one centre gives an epimer. With n = 3, the maximum is 2³.

Answer: Enantiomer (2S,3R,4S); an epimer such as (2S,3S,4R); at most 8 stereoisomers.

Quick check

1. Are (2R,3S)-2,3-dihydroxybutanal and (2R,3R)-2,3-dihydroxybutanal enantiomers or diastereomers? Answer: Diastereomers, because only one of the two stereocentres differs between them.

Exam focus

Be able to draw all stereoisomers of a molecule with two stereocentres, label each with R/S, and state which pairs are enantiomers and which are diastereomers. Remember the key contrast: enantiomers share physical properties in an achiral environment; diastereomers do not.

Advanced insight

Because diastereomers have different energies, reactions that create a second stereocentre in a molecule already containing one usually give unequal amounts of the possible diastereomers. The ratio, reported as the diastereomeric ratio (dr), reflects the difference in transition-state energies. This principle, called substrate control, underpins much of modern stereoselective synthesis, where an existing stereocentre guides the formation of the next.

Summary

A molecule with n stereocentres has at most 2^n stereoisomers. Stereoisomers related by inversion of every stereocentre are enantiomers; those differing at some but not all centres are diastereomers. Diastereomers are not mirror images, so they have different physical properties and reactivities. Epimers are diastereomers that differ at a single stereocentre.

Practice questions

1. What is the maximum number of stereoisomers of a compound with four stereocentres? Answer: 2⁴ = 16 stereoisomers. 2. State the enantiomer of (2S,3S)-2-bromo-3-chlorobutane and name one of its diastereomers. Answer: The enantiomer is (2R,3R); a diastereomer is (2R,3S) or (2S,3R). 3. Explain why two diastereomers can be separated by distillation, whereas two enantiomers cannot. Answer: Diastereomers are not mirror images, so their intermolecular forces and boiling points differ, whereas enantiomers have identical boiling points. 4. D-glucose and D-mannose differ only in the configuration at C2. What term describes this relationship? Answer: They are epimers, a special kind of diastereomer differing at one stereocentre.