Geometric Isomerism: Cis-Trans and E/Z Notation

Geometric isomerism arises when rotation about a bond is restricted, as in a C=C double bond or a ring, so that two groups can be on the same side (cis or Z) or on opposite sides (trans or E) of the bond; E/Z notation, based on the Cahn–Ingold–Prelog priorities, describes these isomers unambiguously. In brief: maleic acid (Z, cis) melts at 135 °C and fumaric acid (E, trans) at about 287 °C, although they have the same formula and connectivity.

The geometric isomers have different physical properties and often different biological effects: vision depends on the change of a cis double bond to trans in retinal, and trans fats differ in their health effects from the cis fats found in natural oils. This article explains the conditions for cis–trans isomerism, how to assign E and Z, compares the properties of some pairs in a table, gives worked examples and describes the stability and interconversion of the isomers.

Why does geometric isomerism exist?

The C=C double bond consists of a σ bond and a π bond, formed by sideways overlap of p orbitals. To rotate one end of the bond relative to the other by 90°, the p orbitals would have to be moved out of alignment, and the π bond would break. This needs about 260–270 kJ/mol, far more than the thermal energy at room temperature (2.5 kJ/mol), so the two arrangements do not interconvert at room temperature, and can be separated. For single bonds, in contrast, the barrier is only a few kJ/mol.

What are the conditions?

Geometric isomers can exist if:

1. there is restricted rotation (a double bond or a ring), and
2. each carbon of the double bond carries two different groups.

Propene, CH₃CH=CH₂, has no geometric isomers, because one carbon has two identical hydrogens. But-2-ene, CH₃CH=CHCH₃, has two: each carbon has a H and a CH₃.

What do cis and trans mean?

In the cis–trans system, cis means that two similar (or the main) groups are on the same side of the double bond or ring, and trans that they are on opposite sides. This works well when each carbon has one H and one other group, as in but-2-ene. For more complex alkenes with three or four different groups, cis–trans is ambiguous, and the E/Z system is used.

How do you assign E and Z?

1. At each carbon of the double bond, rank the two attached groups using the Cahn–Ingold–Prelog (CIP) priority rules: the atom with the higher atomic number has higher priority. If the atoms are the same, move to the next atoms outward and compare the sets of atoms (the first point of difference).
2. Decide whether the two higher-priority groups are on the same side or on opposite sides of the double bond.
3. Z (German zusammen, together): the higher-priority groups are on the same side.
4. E (German entgegen, opposite): the higher-priority groups are on opposite sides.

In the name, the letter is written in parentheses at the start: (E)-but-2-ene, (Z)-3-methylpent-2-ene. Z does not always equal cis: they are the same only when the higher-priority groups are the “obvious” ones.

Properties of geometric isomers

The cis isomers of 1,2-dichloroethene are polar, since the bond dipoles add up, whereas the trans isomer is nonpolar since they cancel; the stronger dipole–dipole forces give cis the higher boiling point. In the trans isomers the molecule is more symmetric, packs better in the crystal and has the higher melting point. In the case of butenedioic acid, the cis acid forms an intramolecular hydrogen bond (and an anhydride on heating), while the trans acid forms strong intermolecular hydrogen bonds and an extended crystal. For the acid strength, maleic acid (pK_a1 = 1.9) is stronger than fumaric (3.0), because the monoanion is stabilized by an intramolecular hydrogen bond.

What about rings?

The substituents on a ring can be on the same face (cis) or on opposite faces (trans), since the ring prevents rotation. 1,2-Dimethylcyclohexane exists as cis and trans isomers. The trans isomer is more stable (about 7 kJ/mol more), because both methyl groups can be equatorial. Cyclopropane and cyclobutane rings give similar pairs.

Worked examples

Example 1: do the geometric isomers exist?

• Pent-2-ene (CH₃CH=CHCH₂CH₃): yes.
• 2-Methylbut-2-ene ((CH₃)₂C=CHCH₃): no, the first carbon has two identical methyl groups.
• 1,2-Dibromoethene: yes. Tribromoethene: no (one carbon has two Br).
• Cyclohexene: not as a simple descriptor, since the ring is too small to have a trans double bond (it would be extremely strained).

Example 2: assigning Z or E to 1-bromo-2-chloroethene

On C1: Br (35) > H (1). On C2: Cl (17) > H. If Br and Cl are on the same side, the compound is (Z)-1-bromo-2-chloroethene. If they are on opposite sides, it is (E).

Example 3: 3-methylpent-2-ene

CH₃–CH=C(CH₃)–CH₂CH₃. On C2: CH₃ > H. On C3: the ethyl group (C with C,H,H) has higher priority than the methyl group (C with H,H,H). If the C1 methyl and the ethyl are on the same side, the isomer is (Z), and if opposite, (E). Note that the methyl on C3 is lower in priority, so this case shows that E/Z cannot be read from the cis/trans relationship of the methyl groups.

Example 4: counting isomers

Hexa-2,4-diene (CH₃CH=CH–CH=CHCH₃) has two double bonds, each of which can be E or Z: (E,E), (Z,Z) and (E,Z), so there are three stereoisomers (the (E,Z) and (Z,E) forms are identical, since the molecule is symmetric).

Example 5: the energy difference between cis- and trans-but-2-ene

With ΔG ≈ 2.8 kJ/mol at 298 K, K = e^2.8/2.479 = 3.1, so at equilibrium (over a catalyst) the mixture contains about 76 % trans and 24 % cis. The cis isomer is destabilized by the steric repulsion between the methyl groups on the same side.

Why does it matter in biology?

• Vision: the chromophore of rhodopsin is 11-cis-retinal. Absorption of a photon converts it to the all-trans form, which changes the shape of the protein and starts the nerve signal.
• Fats: natural unsaturated fatty acids have cis double bonds, which bend the chain and keep the fats liquid (oleic acid, cis, melts at 13 °C). Partial hydrogenation of oils creates trans fatty acids that have straight chains (elaidic acid, trans, melts at 45 °C) and are linked with a higher risk of heart disease.
• Pheromones and drugs: the biological activity of insect sex pheromones depends on the exact Z/E ratio; the anticancer drug cisplatin, cis-[PtCl₂(NH₃)₂], is active but the trans isomer is not.

Who discovered geometric isomerism?

The existence of two different acids with the formula C₄H₄O₄, maleic and fumaric, was known from the 1830s and puzzled chemists. In 1874 van ‘t Hoff suggested that the double bond restricts rotation, and in 1887 Johannes Wislicenus explained the isomers as the arrangement of groups in space on the two sides of the double bond. The E/Z system was introduced in 1968 as part of the extension of the Cahn–Ingold–Prelog rules to double bonds, in a paper by J. E. Blackwood and co-workers.

Which mistakes are common?

• Equating Z with cis in all cases: E/Z uses priorities, not the similarity of groups.
• Looking for geometric isomerism when a carbon has two identical groups: none exists.
• Forgetting the CIP priorities: compare atomic numbers, not the size of the group.
• Thinking that the isomers interconvert easily at room temperature: they need light, heat or a catalyst.
• Assuming cis is always more stable: in most acyclic alkenes, trans is.