Stereochemistry: Chirality, R/S and E/Z, Conformations and Projections

10.1Chirality and symmetry elements

A molecule is chiral if it cannot be superimposed on its mirror image, like a left and a right hand. A chiral molecule and its mirror image are enantiomers. A molecule that can be superimposed on its mirror image is achiral.

• The sure test is symmetry. A molecule is achiral if it has any improper symmetry element: a plane of symmetry (σ), a centre of symmetry (i) or an alternating axis (S_n). A simple rotation axis (C_n) does not make a molecule achiral.
• A stereocentre (stereogenic centre) is an atom where swapping two groups gives a stereoisomer. A carbon with four different groups is the commonest one. One stereocentre always makes a molecule chiral; two or more may not (meso compounds, 10.2).
• Chirality without a stereocentre: allenes, biphenyls, spiranes, helicenes and cyclophanes (10.5).

Rings: quick rules for disubstituted rings (two identical groups X)

• In 1,3-cyclobutanes and 1,4-cyclohexanes a mirror plane passes through both substituted carbons, so cis and trans are diastereomers but neither is chiral; C1 and C4 are not stereocentres in the chiral sense.
• With two different groups (Br and CH₃), the 1,2-cis isomer loses its mirror plane and becomes chiral; 1,3-cyclobutane and 1,4-cyclohexane isomers stay achiral.
• 1,1-Disubstituted rings have no stereocentre at all.
• Bridged bicyclic compounds (norcamphor, camphor) have bridgehead stereocentres; a ketone next to one bridgehead or the other gives the two enantiomers.

10.2Optical isomerism: enantiomers, diastereomers and meso compounds

Optical activity

Enantiomers have identical physical properties (m.p., b.p., solubility, NMR) except the direction in which they rotate plane-polarised light: (+) dextrorotatory, (−) laevorotatory, by equal amounts. They react differently only with other chiral substances (enzymes, chiral reagents).

• Units: tube length in decimetres (10 cm = 1 dm); concentration in g mL⁻¹. A molar concentration must be converted: 1 M 2-butanol (M = 74) is 0.074 g mL⁻¹.
• From ee: % major = (100 + ee)/2; % minor = (100 − ee)/2. 14 % ee gives 57 : 43.
• A racemic mixture (±) is 50 : 50; it is optically inactive by external compensation and can be resolved (for example through diastereomeric salts with a chiral acid or base).
• The sign of rotation (+/−) has no fixed link to R/S; it is measured, not deduced.

Relationships between two structures

1. Same molecular formula, different connectivity → constitutional isomers (1,2,4- vs 1,3,5-trimethylcyclohexane, whatever the wedges).
2. Same connectivity, superimposable → identical.
3. Same connectivity, mirror images, not superimposable → enantiomers: every stereocentre inverted (2R,3R ↔ 2S,3S).
4. Same connectivity, not mirror images → diastereomers: some but not all centres inverted (2R,3R ↔ 2R,3S), and also cis/trans isomers. Diastereomers have different physical properties.

The quickest method: assign R/S to every centre of both structures and compare the labels.

Meso compounds

• A meso compound has two or more stereocentres but is achiral, because of an internal mirror plane (or centre of symmetry). It needs like stereocentres (same four groups) with opposite labels: (2R,3S)-2,3-dibromobutane, (2R,3S)-butane-2,3-diol, meso-tartaric acid, (3R,4S)-hexane-3,4-diol, (2R,5S)-2,5-dibromohexane.
• (R,R) and (S,S) forms of the same compounds are chiral.
• Meso is optically inactive by internal compensation and cannot be resolved.
• Unlike centres (2,3-dibromopentane: CH₃ and C₂H₅ at the ends) can never give a meso form.

Counting stereoisomers

• n unlike stereocentres: 2ⁿ stereoisomers, all chiral, in 2ⁿ⁻¹ pairs.
• Two like centres (tartaric-acid type): 3 (one pair + meso). Three centres with like ends (pentane-2,3,4-triol type): 4 (two meso + one pair).
• Add each stereogenic C=C as another “centre” (10.4).

10.3R/S nomenclature (Cahn–Ingold–Prelog)

Priority rules

1. Rank the four atoms attached to the stereocentre by atomic number: I > Br > Cl > S > F > O > N > C > H. For isotopes, higher mass first (D > H).
2. If two attached atoms tie, list the three atoms on each (in decreasing order) and compare them at the first point of difference. –CH₂Cl (Cl, H, H) beats –C(OH)₃ (O, O, O) and –COOH, because Cl > O on the first comparison; the number of atoms does not matter until a tie is found.
3. If still tied, move one bond further out along the highest branch and repeat.
4. Multiple bonds are counted as duplicated atoms: –CHO is (O, O, H); –COOH is (O, O, O); –C≡N is (N, N, N); –CH=CH₂ is (C, C, H). A path that reaches an sp² carbon outranks a saturated one at the same point.

Assigning R or S

1. Point the lowest-priority group (usually H) away from you.
2. Trace 1 → 2 → 3. Clockwise = R, anticlockwise = S.
3. If the lowest group is on a wedge (towards you), read the sense and reverse it.
4. In a Fischer projection, if the lowest group is on a horizontal line, read and reverse; if on a vertical line, read directly.
5. Swapping any two groups inverts the label; two swaps restore it.

When the label changes without the molecule changing

• R/S depends on priorities, not on the movement of atoms. A reaction that does not touch any bond to the stereocentre can still flip the label if it changes the priority order. Example: replacing a primary –OH by –Br next to a stereocentre makes –CH₂Br outrank the other branch, so R becomes S although nothing moved.
• Conversely, SN2 inversion at the centre usually flips the label (the new group takes the old group’s priority), but not always: check the priorities again.

10.4Geometrical isomerism and E/Z

• Arises when rotation is blocked (C=C, C=N, rings) and each end of the double bond carries two different groups. Isoprene, CH₂=CH–CH=C(CH₃)₂ and (CH₃)₂C=C(CH₃)C₂H₅ show none, because one carbon carries two identical groups.
• cis/trans works only when the two carbons share a common group. E/Z always works: rank the two groups on each carbon by CIP; higher-ranked groups on the same side = Z (zusammen), opposite sides = E (entgegen). E/Z does not always match trans/cis.
• Cycloalkenes: trans is impossible in small rings; trans-cyclooctene is the smallest stable trans-cycloalkene (it is also chiral).
• Cumulenes: with an odd number of cumulated C=C (butatrienes) the end groups lie in one plane, so they show cis–trans isomerism. With an even number (allenes) the ends are perpendicular: axial chirality instead.
• Oximes and imines (C=N) show E/Z isomerism (the lone pair is the lowest group).

Number of geometrical isomers of a polyene with n stereogenic C=C

• Ends different: 2ⁿ.
• Ends identical (R–CH=CH–…–CH=CH–R): n even, 2ⁿ⁻¹ + 2^{n/2 − 1}; n odd, 2ⁿ⁻¹ + 2^(n−1)/2. For 1,6-diphenylhexa-1,3,5-triene (n = 3): 4 + 2 = 6.