7.4 Cis–Trans Isomerism in Alkenes

Structure and Isomerism of Alkenes

Carbon-carbon double bonds define alkenes. These bonds consist of a sigma bond and a pi bond, creating a planar structure with restricted rotation. This restricted rotation is what makes cis-trans isomerism possible: substituents locked on the same side or opposite sides of the double bond produce distinct molecules with different physical and chemical properties.

Structure of Carbon-Carbon Double Bonds

A carbon-carbon double bond is made of two components: one sigma ($\sigma$) bond and one pi ($\pi$) bond.

• The $\sigma$ bond forms from head-on overlap of $sp^2$ hybrid orbitals along the internuclear axis.
• The $\pi$ bond forms from sideways overlap of unhybridized p orbitals, placing electron density above and below the molecular plane.

Because the $\pi$ bond requires continuous p-orbital overlap, rotation around the double bond is restricted. Rotating one carbon relative to the other would break the $\pi$ bond, which costs roughly 264 kJ/mol of energy. That's far too much to happen at room temperature, so the two ends of the double bond stay locked in place.

Each doubly bonded carbon has trigonal planar geometry with bond angles of approximately 120°. The remaining $sp^2$ orbitals form $\sigma$ bonds to other atoms or groups (hydrogen, methyl, halogen, etc.). The overall result is a flat, rigid framework around the double bond.

Conditions for Cis-Trans Isomerism

Not every alkene shows cis-trans isomerism. The requirement is straightforward: each carbon of the double bond must bear two different substituents.

Consider 2-butene ($CH_3CH=CHCH_3$). Each doubly bonded carbon carries one $H$ and one $CH_3$, so two arrangements exist:

• Cis-2-butene: both $CH_3$ groups on the same side of the double bond
• Trans-2-butene: $CH_3$ groups on opposite sides

These are configurational isomers (also called geometric isomers). They have the same connectivity but different spatial arrangements, and they cannot interconvert without breaking the $\pi$ bond. This distinguishes them from conformational isomers like the gauche and anti forms of butane, which interconvert freely through single-bond rotation.

If either carbon of the double bond has two identical substituents, cis-trans isomerism is impossible. For example, propene ($CH_3CH=CH_2$) has two hydrogens on the terminal carbon, so there's only one possible arrangement.

Drawing and Naming Alkene Isomers

Follow these steps to correctly draw and name cis-trans isomers:

1. Identify substituents on each doubly bonded carbon. List the two groups attached to each carbon of the double bond.

2. Determine higher priority on each carbon using Cahn-Ingold-Prelog (CIP) priority rules:

   • Compare atomic number of the atoms directly attached to the doubly bonded carbon. Higher atomic number = higher priority (e.g., $Br > Cl > C > H$).
   • If the first atoms are the same, move outward and compare the next set of atoms until you find a difference (e.g., $CH_2CH_3 > CH_3$ because at the first point of difference, carbon beats hydrogen).

3. Draw the two isomers. Place the higher-priority groups on the same side for cis, or on opposite sides for trans.

4. Name using IUPAC rules:

   • Choose the longest continuous carbon chain containing the double bond as the parent chain.
   • Number the chain so the double bond gets the lowest possible locant. The position is indicated by the lower-numbered carbon (e.g., 2-butene, not 3-butene).
   • Add cis- or trans- as a prefix based on the arrangement of higher-priority substituents.
   • Include other substituents as prefixes with their position numbers (e.g., trans-4-chloro-2-pentene).

Stereochemistry and the E/Z System

The cis-trans labels work well for simple disubstituted alkenes, but they become ambiguous when three or four different groups are attached to the double bond. The E/Z system handles all cases unambiguously.

The E/Z system uses the same CIP priority rules described above, applied to both carbons of the double bond:

• Z (zusammen, German for "together"): higher-priority groups on the same side. This often corresponds to cis, but not always.
• E (entgegen, German for "opposite"): higher-priority groups on opposite sides. This often corresponds to trans, but not always.

For example, consider 1-bromo-2-chloroethene ($BrCH=CHCl$). On one carbon, $Br > H$; on the other, $Cl > H$. If $Br$ and $Cl$ are on the same side, the molecule is (Z). If they're on opposite sides, it's (E). Calling this "cis" or "trans" would be unclear because there's no obvious reference group, which is exactly why the E/Z system exists.