Chapter 7 — Stereoisomerism: Chirality, Enantiomers, and Diastereomers

"I call any geometrical figure, or group of points, chiral, and say it has chirality, if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself." — Lord Kelvin (1894)

Part I built the two-dimensional picture — structures drawn on paper, connectivity, functional groups. Chapter 7 begins the three-dimensional picture: molecules as objects in space, with shapes that matter.

The central concept is chirality — the property some molecules have of being non-superimposable on their mirror images. Two "mirror image" molecules — called enantiomers — have identical bonds, identical lengths, identical masses, identical nearly-everything. What they do not have identical is biology. A receptor protein, built from $L$-amino acids, distinguishes one enantiomer from the other with exquisite precision. This is why one enantiomer of thalidomide sedates and the other causes birth defects; why (S)-ibuprofen relieves pain and (R)-ibuprofen is a biological bystander; why levothyroxine (the $L$ form) is a thyroid hormone and dextrothyroxine is a lipid-lowering drug.

By the end of Chapter 7 you should be able to:

• Identify a chiral center (stereocenter) in any molecule.
• Assign R or S configuration using the Cahn-Ingold-Prelog priority rules.
• Distinguish enantiomers from diastereomers and recognize meso compounds.
• Predict the number of stereoisomers for a molecule with multiple stereocenters.
• Interpret (R), (S), (E), (Z) designations in molecule names.
• Understand optical activity and the distinction between a racemic mixture and a pure enantiomer.
• Apply chirality concepts to drug examples and pharmaceutical applications.

7.1 Constitutional isomers vs. stereoisomers

Isomers are different compounds with the same molecular formula. Two broad categories:

• Constitutional isomers (also called structural isomers) — different connectivity of atoms. $n$-butane and isobutane are constitutional isomers of $C_4H_{10}$ because the carbons are bonded differently.

• Stereoisomers — same connectivity, different arrangement of atoms in space. This is our subject.

Two types of stereoisomers:

• Enantiomers — mirror images of each other. Non-superimposable.
• Diastereomers — stereoisomers that are not mirror images. (A specific subcase: cis/trans isomers of alkenes and rings.)

Key distinction: enantiomers have identical physical properties (mp, bp, density, IR, NMR in achiral solvent) — they only differ in optical rotation and in interactions with other chiral things (other enantiomers, biological receptors, chiral catalysts). Diastereomers are different compounds with different physical properties; they can be separated by ordinary means.

Figure 7.1 — Categorization of isomers. Two compounds with the same molecular formula are either constitutional (different connectivity) or stereoisomers (same connectivity). Stereoisomers are either enantiomers (mirror images) or diastereomers (not mirror images — includes cis/trans cases).

Conformational isomers — a quick caveat

Recall from Chapter 5: the staggered and eclipsed forms of ethane are different conformations, accessible by single-bond rotation. They are conformational isomers (or rotamers, or conformers), not stereoisomers. The term "stereoisomer" implies that two structures cannot be interconverted by bond rotation alone — at least one bond must break and reform.

Some textbooks blur the line. We will use stereoisomer strictly: two compounds that differ in 3D arrangement and cannot be interconverted by rotation alone.

7.2 Chirality and the chiral center

A chiral molecule is one whose mirror image is not superimposable on itself.

The simplest and most common source of chirality is a chiral center (or stereocenter): a tetrahedral ($sp^3$) carbon with four different substituents. Such a carbon's four bonds can be arranged in two mirror-image ways that are not superimposable. Each arrangement is a different stereoisomer.

Example: 2-butanol ($CH_3CH(OH)CH_2CH_3$). The C2 carbon has four different substituents: $H$, $OH$, $CH_3$, $CH_2CH_3$. 2-butanol exists as two enantiomers.

A molecule can have more than one chiral center. With $n$ independent chiral centers, the maximum number of distinct stereoisomers is $2^n$.

Spotting chiral centers

Look for any $sp^3$ carbon with four different groups. Some tips:

• A carbon bonded to two of the same thing (like $CH_3-CH_2-CH(CH_3)_2$, where the central carbon bears two methyls) is NOT chiral.
• A $sp^2$ or $sp$ carbon (with three or two bonds) is NOT chiral because it cannot have four different substituents.
• A nitrogen with three different groups plus a lone pair would be chiral in principle, but amines invert rapidly (umbrella-like flipping at ~10⁴ Hz at room temperature) and don't have long-lived chirality. Exception: quaternary ammonium with four different substituents — chiral and configurationally stable.
• Sulfur, phosphorus, and silicon can also be stereocenters when bonded to four different groups (sulfoxides, phosphines, silanes — all configurationally stable).

Beyond the chiral center: other sources of chirality

Some molecules are chiral without having a traditional stereocenter:

• Atropisomerism (rotational chirality): a hindered single bond gives different "twists" that are configurationally stable. Example: 1,1'-binaphthyl (two naphthalenes linked by a single bond; restricted rotation due to steric clash).
• Axial chirality: in allenes (R₂C=C=CR₂) where the two end groups can differ, the allene's two ends are perpendicular, creating chirality without a stereocenter.
• Planar chirality: certain "stacked" chiral systems (e.g., certain cyclophanes; ferrocene with substituent).
• Helical chirality: helical structures (DNA, proteins, helicenes) have inherent handedness even without classical stereocenters.

These are encountered later (Ch 19 allenes; Ch 33 proteins; Ch 32 DNA).

Cahn-Ingold-Prelog priority rules

To name which of two enantiomers you are looking at, we use the R/S system (also called CIP after Cahn, Ingold, Prelog, who developed the rules in the 1950s).

The procedure:

1. Identify the stereocenter and its four substituents.
2. Assign priorities to the four substituents: - Rule 1: Higher atomic number = higher priority. (At first point of difference.) - Rule 2: Isotopes — heavier = higher. ($D$ > $H$; $^{13}C$ > $^{12}C$.) - Rule 3: In case of ties at the attached atom, move out to the next atoms and compare at the first point of difference. Treat as the attached atom + the three substituents (other than the stereocenter direction). - Rule 4: Double/triple bonds counted as duplicate atoms. A $C=O$ counts as carbon bonded to two oxygens for priority. A $C\equiv N$ counts as carbon bonded to three nitrogens.
3. Orient the molecule with the lowest-priority group pointing AWAY from you.
4. Look at the remaining three groups in the order 1 → 2 → 3: - Clockwise = R (rectus, right) - Counterclockwise = S (sinister, left)

Figure 7.2 — Assigning R/S to the stereocenter of (R)-2-butanol. Step 1: identify the four groups — $OH$, $CH_2CH_3$, $CH_3$, $H$. Step 2: priority order = $OH > CH_2CH_3 > CH_3 > H$ (oxygen beats all; at C, two-carbon chain beats one-carbon; hydrogen is last). Step 3: orient with H (lowest) pointing back. Step 4: the path $OH → CH_2CH_3 → CH_3$ traces clockwise → R configuration.

Detailed CIP rules with examples

Rule 1 (atomic number): F > O > N > C > H. Higher Z wins at the first comparison.

Rule 3 (proceeding outward): When two atoms attached to the stereocenter are the same (e.g., two carbons), look at what each carbon is bonded to. Compare the highest of the three other atoms on each. Tiebreak as needed.

Example: at a stereocenter, you have two C neighbors: one is -CH₂CH₃ (attached to C, H, H, H) and the other is -CH₂Cl (attached to Cl, H, H). The -CH₂Cl carbon has Cl > C, so -CH₂Cl > -CH₂CH₃.

Rule 4 (multiple bonds): a C=O is treated as a carbon bonded to two oxygens. So an aldehyde carbon (-CHO) is treated as C(O,O,H). A C≡N is treated as C(N,N,N). A C=CR₂ is treated as C(C,C,...).

Worked Problem 7.1 — Assign R/S to (S)-alanine

Alanine is $H_2N-CH(CH_3)-COOH$. The stereocenter is the central carbon, with substituents $NH_2$, $CH_3$, $COOH$, and $H$.

Priority by atomic number at the attached atom: N (from NH₂), C (from COOH), C (from CH₃), H. So N > C,C > H. The two C's need a tiebreaker.

For the $COOH$ carbon: bonded to O, O, O (double-bond-to-O counts as two Os; plus the -OH oxygen is the third O). For the $CH_3$ carbon: bonded to H, H, H.

So $COOH$ > $CH_3$. Final priority: $NH_2 > COOH > CH_3 > H$.

Orient with H pointing back. Trace $NH_2 → COOH → CH_3$. If that is counterclockwise, we have $S$-alanine (the natural protein-building form).

Worked Problem 7.2 — Multiple stereocenters: 2,3-dibromobutane

2,3-dibromobutane has two stereocenters (at C2 and C3). Each can be R or S, giving four combinations: - (2R,3R): one enantiomer - (2S,3S): the mirror image of (2R,3R), the other enantiomer - (2R,3S): a meso compound (has internal mirror plane) - (2S,3R): identical to (2R,3S) (same molecule, different naming)

So there are 3 distinct stereoisomers: (2R,3R), (2S,3S), and meso (2R,3S = 2S,3R). The (R,R) and (S,S) are enantiomers; meso is its own pair (not chiral overall).

R and S are not + and −

A common mistake: assuming (R) is always dextrorotatory and (S) levorotatory (see Section 7.4). There is no such correspondence. The R/S designation is a structural label. Optical rotation (+/-) is an experimental measurement. A single compound can be (R,+) or (R,-) depending on the molecule.

For example: (S)-alanine is (S,+) (rotates light to the right). (S)-2-bromobutane is (S,+) too. But (S)-leucine is (S,-) — same configuration, opposite rotation.

7.3 Diastereomers and meso compounds

When a molecule has more than one stereocenter, not all stereoisomer pairs are enantiomers. Two stereoisomers that are NOT mirror images are diastereomers.

Example: 2,3-dihydroxybutanedioic acid (tartaric acid, $(HOOC-CH(OH)-CH(OH)-COOH)$) has two stereocenters. The possible configurations are:

• (2R,3R) — natural form found in grapes
• (2S,3S) — mirror image of (2R,3R), also a possibility
• (2R,3S) — a meso form (see below)
• (2S,3R) — identical to (2R,3S) because of symmetry

The (2R,3R) and (2S,3S) are enantiomers of each other. They have identical physical properties (melting point, solubility, etc.) and opposite optical rotations.

The (2R,3S) form has an internal mirror plane that makes it identical to its mirror image — a meso compound. A meso compound has stereocenters but is not chiral overall.

Spotting meso compounds

To identify a meso compound: look for an internal mirror plane of symmetry in a molecule with stereocenters. If one exists, the molecule is meso.

Examples of meso compounds: - Tartaric acid (2R,3S): mirror plane between C2 and C3. - 2,3-dichloroethanol: meso isomer has Cl's on opposite faces. - cis-1,2-dimethylcyclohexane: meso (mirror plane perpendicular to ring).

A meso compound is achiral despite having stereocenters. It does not rotate plane-polarized light.

How many stereoisomers?

For a molecule with $n$ independent stereocenters, the maximum number of stereoisomers is $2^n$. The actual number can be less if: - Some configurations give meso forms. - Some configurations are identical due to molecular symmetry.

Tartaric acid has $n = 2$, so max is $2^2 = 4$. Actual: 3 (because (2R,3S) and (2S,3R) are the same meso compound).

Diastereomers have different physical properties

Diastereomers are different compounds with different physical properties. They have different melting points, different solubilities, different IR spectra (though usually subtly), different chromatographic behavior. They can be separated by ordinary means (distillation, chromatography, crystallization).

Enantiomers, in contrast, have identical physical properties in achiral environments. They cannot be separated by ordinary means. You need a chiral environment — a chiral column, a chiral solvent, an enzyme — to distinguish them.

Epimers (carbohydrate-specific term)

In carbohydrate chemistry, epimers are diastereomers that differ at exactly one stereocenter. Glucose and galactose are epimers (differ at C4); glucose and mannose are epimers (differ at C2). All three are different molecules with different properties; they are diastereomers, not enantiomers.

We'll see more of this in Chapter 32 (carbohydrates).

7.4 Optical activity

Enantiomers interact with plane-polarized light differently. A solution of one enantiomer rotates the plane of polarized light clockwise (when viewed from the light source toward the observer) by a characteristic amount; the other enantiomer rotates it counterclockwise by the same amount.

• Dextrorotatory (+): rotates light clockwise.
• Levorotatory (−): rotates light counterclockwise.

The rotation depends on concentration, path length, wavelength, and temperature, so it is normalized into specific rotation:

$$[\alpha]_T^\lambda = \frac{\alpha_{observed}}{c \cdot l}$$

where $c$ = concentration (g/mL), $l$ = path length (dm), $T$ = temperature, $\lambda$ = wavelength (usually the sodium D line at 589 nm).

Some examples: - $(+)$-glucose: $[\alpha]_D^{20}$ = +52.7° - $(-)$-fructose: $[\alpha]_D^{20}$ = -92.4° - $(+)$-sucrose: +66.5° (glucose + fructose — a diastereomer pair but the net rotation is +) - $(-)$-menthol: -50° - $(S)$-(+)-alanine: +1.8° (nearly undetectable)

A racemic mixture (a 50:50 mix of the two enantiomers) has zero optical rotation — the two enantiomers' rotations cancel exactly.

Optical purity vs. enantiomeric excess

A sample is 95% (S) and 5% (R). Its enantiomeric excess (ee) is 95% − 5% = 90%. Its optical rotation is 90% of the rotation of pure (S). The two measures (ee and optical purity) coincide for a simple two-enantiomer system.

In modern pharmaceutical chemistry, ee is usually measured by chiral HPLC (high-performance liquid chromatography on a chiral stationary phase) — separates the two enantiomers and gives their ratio directly. More accurate than optical rotation for measuring ee.

Polarimetry: how the measurement is done

A polarimeter is a tube with polarizers at each end. Light passes through: 1. A first polarizer, which produces plane-polarized light. 2. A sample cell of length $l$ containing the analyte at concentration $c$. 3. A second polarizer (analyzer), which is rotated to find the angle of greatest extinction.

The angle of rotation of the second polarizer relative to the first is the observed optical rotation $\alpha$.

Used for: - Confirming the identity and purity of optically active compounds. - Measuring sugar content in beverages (saccharimetry). - Checking enantiomeric purity of drugs.

7.5 Fischer projections

Emil Fischer (Nobel Prize 1902) developed a convention for drawing chiral molecules — particularly sugars — as flat planar structures with specific conventions for what wedges mean. Fischer projections are still used today for carbohydrates and amino acids.

Convention: - Horizontal bonds point toward the viewer. - Vertical bonds point away from the viewer. - The main chain is written vertically. - The most-oxidized carbon (aldehyde, carboxylic acid) is at the top.

Example: $(R)$-glyceraldehyde (the simplest chiral carbohydrate).

In Fischer projection:

      CHO
       |
  H — C — OH
       |
      CH₂OH

The central carbon has $CHO$ on top, $CH_2OH$ on bottom (the main chain), $OH$ on right (horizontal = out), $H$ on left (horizontal = out).

This is $(R)$-glyceraldehyde, also called $D$-glyceraldehyde. (The D/L system, which predates the R/S system, assigns D or L by the position of a reference group in the Fischer projection.)

D/L convention for sugars and amino acids

The D/L system is older than R/S and is still standard for biological molecules: - D- means the reference -OH (in sugars) or -NH₂ (in amino acids) is on the right in Fischer projection. - L- means it's on the left.

For amino acids: nature uses L-amino acids (L = (S) for most amino acids, but cysteine is L = (R) due to CIP priority oddity). All proteins are built from L-amino acids.

For sugars: nature uses D-sugars. D-glucose is the universal energy source.

The D/L system tells you nothing about optical rotation. (D)-glucose is dextrorotatory but (D)-fructose is levorotatory.

7.6 Alkene geometry — cis/trans and E/Z

Beyond stereocenters, another common stereoisomerism is the cis/trans (or $E/Z$) isomerism of double bonds. A $C=C$ double bond has restricted rotation (breaking the $\pi$ bond requires ~60 kcal/mol of energy), so the substituents on the two sp² carbons are locked in place.

If the two higher-priority groups are on the same side of the double bond, it's cis (or $Z$, for zusammen, German for "together"). On opposite sides: trans ($E$, for entgegen, "opposite").

The cis/trans language works only for simple cases (both sp² carbons have a hydrogen + a non-hydrogen). For more general cases, use $E/Z$ with Cahn-Ingold-Prelog priority.

Figure 7.3 — (E) and (Z) isomers of 2-butene. In (Z)-2-butene, the two methyls are on the same side of the C=C; in (E)-2-butene, they are on opposite sides. The two are diastereomers: different compounds with different boiling points, melting points, dipole moments, and reactivity.

Assigning E/Z

For a C=C with three or four different substituents: 1. Identify the two groups on each sp² carbon. 2. Assign CIP priority on each carbon (compare the two groups). 3. If the two higher-priority groups are on the same side: Z. 4. If the two higher-priority groups are on opposite sides: E.

E/Z in cyclic systems

Cycloalkenes: the smaller rings (3-7 carbons) typically only have the cis (Z) isomer because the trans is too strained. Larger rings (8+) can have both.

trans-Cyclooctene is famously the smallest stable trans-cycloalkene; it has substantial strain (~10 kcal/mol) but is isolable.

cis/trans in ring substituent positions

Two substituents on a ring are cis (same face) or trans (opposite faces). cis-1,2-dimethylcyclohexane has both methyls on the same face; trans has them on opposite. This is also stereoisomerism.

For 6-membered rings, cis/trans interconverts with chair flipping, but the two configurations are distinct stereoisomers.

7.7 Enantiomer separation: resolution

Once a chiral synthesis gives a racemic mixture, how do you obtain a pure enantiomer? Three main strategies:

1. Resolution by diastereomer formation

The classical method (Pasteur, 1848). Add a pure enantiomer of another chiral compound (a resolving agent); the racemic substrate forms two diastereomers (one with each enantiomer); the diastereomers have different physical properties and can be separated by ordinary crystallization. Then remove the resolving agent.

Example: racemic mandelic acid + (R)-1-phenylethylamine → two diastereomeric salts, separable by crystallization.

2. Chiral chromatography

Use a chiral stationary phase (HPLC or GC column with chiral selector). The two enantiomers elute at different times; collect each separately. Modern chiral HPLC columns are highly developed; many enantiomer pairs can be separated routinely.

3. Asymmetric synthesis

Avoid the racemate altogether: design a synthesis that gives only one enantiomer using chiral catalysts. This is the gold standard in modern pharmaceutical synthesis.

Examples (covered in later chapters): - Sharpless asymmetric epoxidation (Ch 36): chiral titanium catalyst gives one enantiomer of an epoxide. - Asymmetric hydrogenation (Ch 37): chiral Pd or Rh catalysts give chiral alkanes from prochiral alkenes. - Enzyme catalysis: nature's chiral catalysts; lipases and other hydrolases are widely used.

The 2001 Nobel Prize was awarded to Sharpless, Knowles, and Noyori for asymmetric catalysis. These methods have transformed pharmaceutical synthesis.

4. Kinetic resolution

A chiral catalyst (often an enzyme) reacts faster with one enantiomer of a racemate than the other. Stop the reaction halfway: the unreacted material is enriched in one enantiomer; the product is enriched in the other.

7.8 Why stereochemistry matters — the thalidomide theme

Chapter 1 introduced thalidomide as the textbook example of why stereochemistry matters. Chapter 7 gives you the language to describe it precisely.

Thalidomide has one chiral center. It exists as two enantiomers — $(R)$ and $(S)$. They have identical NMR spectra in achiral solvents, identical mass spectra, identical IR spectra, identical melting point, identical molecular weight. Everything a traditional chemist would measure in 1957 gave the same result for both.

But they have different biological activities. The $(R)$ enantiomer is the sedative; the $(S)$ enantiomer is the teratogen. One binds its target protein productively; the other binds a different target productively (and disastrously).

The reason: biological receptors are themselves chiral. Every protein in your body is built from $L$-amino acids — the $(S)$ enantiomer of 19 of the 20 standard amino acids (glycine is achiral). A receptor protein is an asymmetric, chiral environment. When a drug molecule approaches a receptor, the drug's stereochemistry decides whether it fits.

Other drug examples

• Ibuprofen: (S)-(+)-ibuprofen is the active analgesic. (R)-(-)-ibuprofen is converted to (S) in vivo. Sold as racemate.
• Naproxen: (S)-(+)-naproxen is the active form (active as COX inhibitor). (R) is hepatotoxic. Sold as pure (S).
• Levothyroxine (thyroid hormone): the L (S) form is the natural hormone. The D form has different activity.
• Albuterol/salbutamol (asthma drug): only the (R)-(-) form is bronchodilator; the (S)-(+) is inactive or potentially harmful. Some products sold as pure (R).
• Esomeprazole (Nexium): (S)-omeprazole is the active form. Sold as pure (S) — replaced racemic omeprazole.
• Dextromethorphan vs levomethorphan: (R) is cough suppressant; (S) is opioid analgesic and controlled substance.

This is why, as noted in Chapter 1:

• Modern drugs are developed as single enantiomers where possible.
• Racemic drug development requires separate testing of both enantiomers.
• Process chemistry invests heavily in enantioselective synthesis.
• The FDA recommends developing enantiomerically pure drugs for new molecular entities.

Chapter 8 will show how stereochemistry appears in reaction mechanisms — predicting whether a reaction inverts, retains, or racemizes the stereocenter.

Biological Connection 7.1 — Why life is homochiral

All amino acids in proteins are L (with the exception of glycine, which is achiral). All sugars in DNA, RNA, and most metabolism are D. Why?

The leading theory: random selection in early life on Earth got a small homochiral excess that was amplified. Other planets might have life built on D-amino acids and L-sugars. Once life "chose" a handedness, all biology coevolved to it. Biological receptors are chiral; biological products are chiral; biological metabolism is chiral.

A small molecule racemate experiences the chirality of biology when it tries to bind a receptor. One enantiomer fits; the other doesn't (or fits differently). This is the universal source of pharmacological enantiomeric specificity.

7.9 Summary

1. Stereoisomers have the same connectivity but different 3D arrangements. Two types: enantiomers (mirror images) and diastereomers (not mirror images).

2. Chirality arises most commonly from a stereocenter — an sp³ carbon with four different substituents. A molecule with $n$ independent stereocenters can have up to $2^n$ stereoisomers.

3. R/S configuration is assigned via CIP priority: orient with lowest-priority group back, trace 1 → 2 → 3; clockwise = R, counterclockwise = S. R/S is unrelated to (+)/(−).

4. Meso compounds have stereocenters but an internal mirror plane making the molecule identical to its mirror image. They are achiral despite having stereocenters.

5. Optical activity: enantiomers rotate plane-polarized light equally and oppositely. Racemic mixtures show zero rotation. Specific rotation $[\alpha]$ is the standardized measure.

6. Enantiomeric excess (ee): the difference in % between the two enantiomers. Modern measurement: chiral HPLC.

7. E/Z designations for alkenes describe the geometric arrangement across the double bond, using CIP priority.

8. Resolution (separating enantiomers): diastereomer formation, chiral chromatography, asymmetric synthesis, or kinetic resolution.

9. Beyond classical stereocenters: atropisomerism (rotational chirality), axial chirality (allenes), planar chirality (cyclophanes), helical chirality (helicenes, DNA, proteins).

10. Biological consequences: receptors are chiral; enantiomers of a drug usually have different activities. Every pre-clinical drug is tested as both enantiomers; many drugs are sold as pure single enantiomers to avoid the inactive (or harmful) one.

Chapter 8 covers stereochemistry in reactions: what happens to a stereocenter when a bond breaks and forms. Chapter 9 introduces NMR — and the geometry of chapter 7 shows up directly in NMR coupling constants.

Part II (Chs 7-9) sets up the 3D thinking that becomes essential in Part III (mechanism chapters), where the geometry of the transition state determines whether SN2 inverts, whether E2 prefers anti-periplanar, and whether elimination happens at all.