Diastereomers — Organic Chemistry Notes

Two stereoisomers can be mirror images of each other: enantiomers. Once a molecule has two stereocenters, a second relationship appears. Two stereoisomers can match at one center and differ at the other, and then neither is the mirror image of the other. Unlike a pair of enantiomers, such a pair has different melting points, boiling points and spectra.

The definition

Take 3-bromobutan-2-ol, CH₃–CH(OH)–CH(Br)–CH₃. It has two stereocenters: C2, which carries the OH, and C3, which carries the Br. The figure draws two of its stereoisomers. C2 is R in both of them, while C3 is R in the first and S in the second.

The skeleton and the OH wedge are identical. Only the Br bond differs: a wedge on the left, a hash on the right.

These two are stereoisomers: the same atoms, joined in the same order, arranged differently in space. They are not the same molecule. Turning a drawing over changes every wedge to a hash at once, so no rotation can change the Br bond alone. They are not mirror images either. A mirror image inverts every stereocenter, so the mirror image of (2R,3R) is (2S,3S), not (2R,3S).

Two stereoisomers related like this are diastereomers: stereoisomers that are not mirror images of each other. The definition says what diastereomers are not. Enantiomers are the mirror-image case, and every other pair of stereoisomers is a pair of diastereomers.

Two stereocenters, four stereoisomers

Each stereocenter of 3-bromobutan-2-ol can be R or S independently of the other. That gives 2 × 2 = 4 combinations: (2R,3R), (2S,3S), (2R,3S) and (2S,3R). This is the 2ⁿ rule from Stereocenters, with n = 2: two stereocenters give at most four stereoisomers, and here all four exist. The figure draws all four on the same zigzag, so the only thing that changes from one to the next is which bonds are wedges and which are hashes.

Across each row every wedge has become a hash, so both centers are inverted. Down a column or along a diagonal, only one bond has changed.

Same or different, center by center

The grid follows one rule. Invert both stereocenters and you get the enantiomer, the complete mirror image. Invert only one and you get a diastereomer, with the same configuration at one center and the opposite configuration at the other.

Worked example — every pairing of the four

Four stereoisomers can be paired in six ways. For each pair, ask whether both centers are inverted or only one.

(2R,3R) with (2S,3S): both centers are inverted, so the two are enantiomers. (2R,3S) with (2S,3R): again both are inverted, so this is the second enantiomeric pair.

The other four pairings, such as (2R,3R) with (2R,3S), or (2S,3S) with (2R,3S), invert only one center. Each of them is a pair of diastereomers.

So the four compounds form two enantiomeric pairs and four diastereomeric pairs, and each compound has exactly one enantiomer and two diastereomers.

The rule works for any number of stereocenters. Take a compound with three stereocenters, (2R,3R,4S). Inverting all three gives (2S,3S,4R), its enantiomer. Inverting one or two of them, as in (2R,3S,4S), gives a diastereomer.

When you have only the names, compare the descriptors one stereocenter at a time. If every letter differs, the two are enantiomers; if only some differ, they are diastereomers. One exception is covered next, in Meso compounds: when a molecule is its own mirror image, inverting every center gives back the same compound.

Diastereomers from double bonds and rings

Stereocenters are not the only source of diastereomers. Take but-2-ene, CH₃–CH=CH–CH₃, which older books call 2-butene. Its two methyls can sit on the same side of the double bond, in cis-but-2-ene, or on opposite sides, in trans-but-2-ene. A double bond cannot rotate without breaking, so the two do not interconvert at room temperature. Neither molecule has a stereocenter.

The arrows under each molecule are its two C–CH₃ bond dipoles, redrawn from one point so their sum can be read off.

The two are stereoisomers, and neither is the mirror image of the other: each molecule is flat, so its mirror image is itself. That makes them diastereomers. A part of a molecule that gives rise to stereoisomers is called a stereogenic unit, as Stereocenters noted. A stereocenter is one kind, and a double bond with two different groups on each of its carbons is another.

The two isomers differ just as diastereomers should. cis-But-2-ene boils at 3.7 °C and has a dipole moment of 0.33 D. trans-But-2-ene boils at 0.9 °C, and its dipole moment is zero, because its two C–CH₃ bond dipoles point in exactly opposite directions and cancel. The trans isomer is also about 1 kcal/mol more stable, because its methyl groups are farther apart.

A ring gives diastereomers in the same way. Moving a group from one face of a ring to the other would mean breaking a bond, so each arrangement is a separate compound. In 1,2-dimethylcyclohexane the two methyls can be on the same face (cis) or on opposite faces (trans). Here C1 and C2 are stereocenters, and the figure labels each one.

Compare the labels beside C1 and C2 in the two drawings.

Going from cis to trans inverts C2 and leaves C1 alone. Only one of the two centers is inverted, so cis- and trans-1,2-dimethylcyclohexane are diastereomers. As Alkanes & Conformations showed, they differ in energy by about 2 kcal/mol, and they can be separated. The cis isomer has no enantiomer at all, even though it has two stereocenters; the next section, Meso compounds, explains why.

So the source of the stereoisomerism does not matter. Whether it is a stereocenter, a double bond or a ring, any two stereoisomers that are not mirror images are diastereomers.

Two warnings about the words cis and trans are worth making now. Both come up again in Cis/trans and E/Z, later in this chapter. The first is about alkenes. Cis and trans work cleanly only while each carbon of the double bond carries one hydrogen. In 3-methylpent-2-ene, C3 carries a methyl and an ethyl group and no hydrogen, so the words become ambiguous: each isomer is cis by one pairing of groups and trans by another.

C2 carries H and CH₃; C3 carries CH₃ and CH₂CH₃.

3-Methylpent-2-ene still exists as two diastereomers. The CIP priority rules you used for R/S tell them apart, and they give the labels E and Z in place of cis and trans.

The second warning is about rings. On a ring, cis and trans describe faces: the same face or opposite faces. A ring flip swaps every axial position for an equatorial one, but it never moves a group to the other face. So cis and trans survive a ring flip, while axial and equatorial do not.

Why diastereomers have different physical properties

In an achiral environment, enantiomers have identical physical properties; only the direction in which they rotate plane-polarized light differs. Every distance and angle inside one is matched exactly in its mirror image, so the two have the same energy. Diastereomers have no such match. To see this, put (2R,3S)- and (2R,3R)-3-bromobutan-2-ol in the same conformation and look straight down the C2–C3 bond, with the two methyls pointing opposite ways.

Both molecules are in the same conformation, with the two methyls anti. The OH and the Br still end up in different places relative to each other.

In (2R,3S) the OH and the Br end up anti, 180° apart. In (2R,3R) they end up gauche, only 60° apart. Rotating about the bond does not remove the difference. Whichever conformation you compare, the two molecules place their groups differently. So they differ in shape, in dipole moment, in how they pack in a crystal, and in energy.

The consequences are practical. Diastereomers have different melting points, boiling points, densities, solubilities, polarities, NMR spectra and reactivities. This means ordinary methods can separate them: distillation, recrystallization or standard column chromatography. None of these methods can separate enantiomers. It is also why resolution works, as Enantiomers described: it temporarily turns a pair of enantiomers into a pair of diastereomers, separates those, and then turns them back.

"Diastereomer" is a relationship, not a kind of molecule. No compound is "a diastereomer" on its own; it is a diastereomer of some other stereoisomer. A question about "the relationship between A and B" is asking about a pair, and a property of one molecule does not answer it.

Epimers and anomers

Two more names come from sugar chemistry. Compare D-glucose with D-mannose and D-galactose, drawn below as Fischer projections. (The D says which of two mirror-image families a sugar belongs to.) In a Fischer projection the carbon chain runs down the page, and at each crossing the horizontal bonds point toward you and the vertical bonds point away. Fischer projections, two sections from here, teaches the notation and the D properly.

Read each shaded row against the same row of glucose in the middle. Every other row matches.

Glucose and mannose differ only at C2. Glucose and galactose differ only at C4. Diastereomers that differ at exactly one stereocenter are called epimers, so mannose is the C2 epimer of glucose and galactose is its C4 epimer. Mannose and galactose differ at two centers, so they are diastereomers but not epimers.

A sugar can also close into a ring. When glucose does, C1, the aldehyde carbon, becomes a new stereocenter bonded to two oxygens, and its OH can end up on either face of the ring. The two ring forms are called anomers and are labeled α and β. They differ only at that new stereocenter, so anomers are a special kind of epimer. The figure draws each ring flat, as seen from above, with wedges and hashes.

Four of the five ring stereocenters match. Only C1, the carbon bonded to two oxygens, differs.

The difference between α- and β-glucose looks small, but it is the difference between starch, which is built from α-glucose, and cellulose, which is built from β-glucose. Biomolecules shows how the ring forms and draws it as a Haworth projection, the usual way to draw a sugar ring.

Absolute and relative configuration

Look back at the grid of four. (2R,3R) and (2S,3S) are different compounds, but in both of them the OH and the Br sit on the same kind of bond: two wedges in one, two hashes in the other. Their two centers relate to each other in the same way. R and S give the absolute configuration, since each label describes one stereocenter completely, on its own. The relative configuration describes only how the centers sit with respect to each other. Enantiomers share a relative configuration, and diastereomers do not.

Relative configuration is often all a reaction controls. A reaction that starts from achiral compounds, with achiral reagents, catalysts and solvent, has no way to favor one enantiomer over the other. It can still be completely selective about which diastereomer forms. The product is then a single diastereomer. If that diastereomer is chiral, it forms as a racemate, a 50:50 mixture of its two enantiomers; if it is meso, it is a single compound. Nearly every stereochemical result later in the course takes one of these two forms.

Additions to a double bond show how this works. The flat C=C of cyclohexene has two faces, one above the ring and one below. When two new groups add to the same face, the addition is syn. When they add to opposite faces, it is anti. The figure adds two OH groups each way.

Cyclohexene is drawn tilted, with its C=C along the front edge. In the flat drawings its top face is the face toward you, so an OH that arrived from the top sits on a wedge.

On a ring, the product shows the faces directly: syn addition gives the cis diol, and anti addition gives the trans diol. The trans diol forms as a racemate, because the first OH is as likely to arrive from the top face as from the bottom. In both cases the reaction fixes only the relative configuration.

An open-chain alkene needs one more piece of information. Anti addition to cis-but-2-ene and anti addition to trans-but-2-ene give different diastereomers, so the outcome depends on the alkene's geometry as well as on syn or anti. Meso compounds works through this case with bromine, and Alkenes & Alkynes covers the rest.

Chemists also need to name the relative configuration of a finished chain, and two systems are in use. The figure shows both on 3-bromobutan-2-ol, each compound drawn once as a Fischer projection and once as a zigzag.

Each column is one compound drawn two ways, and the R/S labels match within a column. The same-side relationship in the Fischer projection becomes opposite sides in the zigzag, and the reverse.

The current system uses the zigzag. Draw the main chain as a zigzag in the plane of the page. If two neighboring groups are both on wedges, or both on hashes, the pair is syn. If one is on a wedge and the other on a hash, the pair is anti. So (2R,3R)-3-bromobutan-2-ol is syn, and (2R,3S) is anti.

The older system uses a Fischer projection with the main chain vertical. A compound is erythro when the two non-hydrogen groups on neighboring carbons (here OH and Br) sit on the same side, and threo when they sit on opposite sides. The names come from two sugars, erythrose and threose. So (2R,3S) is erythro, and (2R,3R) is threo.

For neighboring stereocenters the two systems read opposite ways. A Fischer projection draws the C2–C3 bond with its groups eclipsed, while the zigzag stretches the chain out, which turns C3 by 180° relative to C2. That turn moves one group to the other side, so erythro becomes anti in the zigzag and threo becomes syn. Always check which drawing a label refers to. Syn/anti has largely replaced erythro/threo, which survives mainly in older papers and in sugar names.

Notice that syn and anti now have two jobs. For an addition they name the faces the two groups arrived from. For a finished zigzag they name the wedges and hashes. The two need not match. Anti addition of bromine to cis-but-2-ene gives (2R,3R)- and (2S,3S)-2,3-dibromobutane, which are threo, and so syn in the zigzag.

Why this matters for reactions

Diastereomers differ in energy, and so do the paths that lead to them. So a reaction that can form two diastereomers usually forms them in unequal amounts. Favoring one diastereomer over another is called diastereoselectivity, and it is the basis of nearly all control of stereochemistry in synthesis.

Enantiomers behave differently. When the starting materials, reagents, catalysts and solvent are all achiral, the paths to two enantiomers are mirror images with identical energies, so the enantiomers form in exactly equal amounts. A chiral catalyst or reagent removes that symmetry, which is how asymmetric synthesis makes one enantiomer in excess.

You will meet diastereoselectivity again and again. Anti addition of bromine to an alkene gives one diastereomer and not the other. Hydroboration, a reaction in Alkenes & Alkynes, adds its two new groups syn, so it also gives a specific diastereomer. And when a molecule that already has a stereocenter contains a C=O group, new groups add to one face of that C=O more often than to the other.

What carries forward

From here on, every stereochemical result is reported in terms of enantiomers and diastereomers. The next section, Meso compounds, covers the case where internal symmetry makes one of the expected stereoisomers achiral. The two sections after it, Fischer projections and Cis/trans and E/Z, give you the notation to name and draw stereoisomers without ambiguity.