Difficulty: Intermediate to Advanced | Prerequisites: Alkyne chemistry (Ch. 13), alkene addition reactions, hybridisation (sp, sp², sp³), basic MO concepts.
This chapter moves from isolated double bonds to systems where two or more double bonds interact through conjugation. Conjugation has real, measurable consequences: conjugated dienes are more stable than you would predict by simply doubling an alkene's energy, their central C–C single bond is unusually short, and they open up new reaction pathways (1,2- vs. 1,4-addition) that isolated alkenes cannot access. Understanding molecular orbital (MO) theory for these systems is essential groundwork for the Diels-Alder reaction and, later, for UV-Vis spectroscopy and pericyclic reactions. You should already be comfortable drawing Lewis structures, identifying hybridisation, and reading energy diagrams.
Conjugated dienes (alternating single and double bonds, all sp² carbons) are thermodynamically more stable than non-conjugated dienes by about 3.5 kcal/mol, owing to electron delocalisation across the pi system. Their MO picture has four molecular orbitals (two bonding, two antibonding) built from four p-orbitals, and the number of nodes increases with energy. Dienes can adopt s-trans or s-cis conformations by rotation about the central single bond; s-trans is lower in energy, but s-cis is the reactive geometry for Diels-Alder reactions.
Conjugated diene
A molecule with two double bonds separated by exactly one single bond, so that all four carbons are sp²-hybridised and their p-orbitals overlap continuously. Think of it as: a chain of double bonds that "talk" to each other through overlapping p-orbitals, with no sp³ carbon breaking the conversation.
Non-conjugated (isolated) diene
A molecule with two double bonds separated by two or more single bonds. An sp³ carbon sits between them and breaks the p-orbital overlap. In simple terms, the double bonds are too far apart to interact electronically.
Cumulated diene (allene)
A molecule in which two double bonds share the same carbon (C=C=C). The central carbon is sp-hybridised and the two pi systems are perpendicular to each other. Think of it as: two double bonds stacked on top of each other at right angles, which is a special and relatively rare arrangement.
s-trans conformation
The conformation of a conjugated diene in which the two double bonds are on opposite sides of the central C–C single bond (anti-periplanar). This is the lower-energy conformer because it minimises steric strain. In simple terms, the molecule is stretched out flat, with the double-bond "arms" pointing in opposite directions.
s-cis conformation
The conformation of a conjugated diene in which the two double bonds are on the same side of the central C–C single bond (syn-periplanar). Higher in energy by about 2.8 kcal/mol for 1,3-butadiene due to steric repulsion between the terminal hydrogens. Think of it as: the molecule is curled up so both double bonds point the same way. This is the shape needed for Diels-Alder reactions.
HOMO (highest occupied molecular orbital)
The molecular orbital of highest energy that contains electrons in the ground state. For a conjugated diene, this is π₂, which has one node. In simple terms, the "top filled shelf" of the molecule's electron bookcase.
LUMO (lowest unoccupied molecular orbital)
The molecular orbital of lowest energy that is empty in the ground state. For a conjugated diene, this is π₃, which has two nodes. Think of it as: the first empty shelf above the filled ones, and the place where incoming electrons would go.
Node (in an MO)
A point or plane where the wavefunction passes through zero and the probability of finding an electron is zero. More nodes means higher energy. In simple terms, a node is a dead spot in the orbital where there is no electron density, like a still point on a vibrating guitar string.
Conjugated: Double bonds separated by one single bond. All carbons sp². Continuous p-orbital overlap. Example: 1,3-butadiene.
Non-conjugated (isolated): Double bonds separated by two or more single bonds. At least one sp³ carbon breaks the pi overlap. Example: 1,4-pentadiene.
Cumulated (allene): Double bonds share a central carbon (C=C=C). Central carbon is sp-hybridised. The two pi bonds are perpendicular. Example: propadiene (allene).
Conjugation is not limited to C=C bonds. A C=O bond adjacent to a C=C bond, or even an aromatic ring adjacent to a C=C or C=O, creates a conjugated system as long as every atom in the chain is sp² (or sp) with an available p-orbital.
The "s" stands for "single bond": these are conformations (interconvertible by rotation), not configurations (which would require bond breaking).
s-trans is the more stable conformer. In 1,3-butadiene, s-trans is lower by ~2.8 kcal/mol with an activation barrier of ~5 kcal/mol for rotation to s-cis.
s-cis has steric repulsion between the terminal hydrogens (or substituents). Substituted dienes (e.g. 2,3-dimethyl-1,3-butadiene) have even larger energy differences (~6.0 kcal/mol) because of methyl-methyl steric clash in the s-cis form.
Locked conformations: Cyclic dienes can be locked into one conformer. Cyclopentadiene is locked s-cis (ring prevents rotation), making it exceptionally reactive in Diels-Alder reactions. Cyclohexadiene is locked s-trans and cannot undergo Diels-Alder.
The experimental evidence comes from heats of hydrogenation:
One isolated alkene: ΔH ≈ −30 kcal/mol
Non-conjugated diene (two isolated double bonds): ΔH ≈ −60 kcal/mol (exactly 2 × 30)
Conjugated diene: ΔH ≈ −56.5 kcal/mol
The conjugated diene releases 3.5 kcal/mol less energy than expected. Since both the conjugated and non-conjugated dienes hydrogenate to the same alkane product, the difference means the conjugated diene started at a lower energy (more stable) position.
This extra stability arises from electron delocalisation: the p-orbitals overlap across all four carbons, spreading electron density over a larger volume and lowering the system's energy.
Comparing n-butane, 1-butene, and 1,3-butadiene:
C–C (n-butane, sp³–sp³): 1.54 Å, bond energy 85 kcal/mol
C=C (1-butene, sp²–sp²): 1.33 Å, bond energy 148 kcal/mol
Central C–C of 1,3-butadiene (sp²–sp²): 1.47 Å
The central single bond in 1,3-butadiene is shorter than a typical C–C single bond because both carbons are sp²-hybridised (shorter bond lengths from greater s-character) and because there is partial pi-bonding character from delocalisation. Resonance structures that place a double bond between C2 and C3 (with charges) capture this, but molecular orbital theory gives a more complete picture.
Before tackling dienes, recall the alkene case:
Two p-orbitals combine to form two molecular orbitals.
π₁ (bonding, HOMO): In-phase overlap, constructive interference, zero nodes between the carbons. Both electrons sit here.
π₂ (antibonding, LUMO):* Out-of-phase overlap, destructive interference, one node between the carbons. Empty in the ground state.
Bond enthalpy of the pi bond: ~65 kcal/mol.
Four p-orbitals (one from each sp² carbon) combine to form four molecular orbitals:
π₁ (lowest energy, bonding): All p-orbitals in phase. Zero nodes. Contributes bonding between all adjacent carbons.
π₂ (bonding, HOMO): One node (between C2 and C3). Bonding between C1–C2 and C3–C4, but antibonding between C2–C3. Net effect is still bonding overall.
π₃ (antibonding, LUMO): Two nodes. Empty in the ground state.
π₄ (highest energy, antibonding): Three nodes. All adjacent p-orbitals are out of phase. Empty.
The four pi electrons fill π₁ and π₂ (two electrons each). The pattern to remember: the number of nodes increases by one as you go up in energy, starting from zero nodes for the lowest MO.
The HOMO-LUMO gap determines reactivity and light absorption. For frontier molecular orbital (FMO) theory, reactions are controlled by the interaction between the HOMO of one reactant and the LUMO of another.
Heat of hydrogenation, isolated alkene: ~−30 kcal/mol
Heat of hydrogenation, non-conjugated diene: ~−60 kcal/mol
Heat of hydrogenation, conjugated diene: ~−56.5 kcal/mol
Conjugation stabilisation energy: ~3.5 kcal/mol
s-trans → s-cis energy difference (1,3-butadiene): ~2.8 kcal/mol
s-trans → s-cis barrier (1,3-butadiene): ~5 kcal/mol
Central C–C bond in 1,3-butadiene: 1.47 Å
Conjugated diene systems are the basis for natural and synthetic rubber. Polymerisation of 1,3-butadiene or isoprene (2-methyl-1,3-butadiene) produces long conjugated and cross-linked polymer chains with the elasticity needed for tyres, seals, and hoses. Beta-carotene, the orange pigment in carrots, is an extended conjugated system of 11 alternating double bonds, and its colour comes from the HOMO-LUMO transition absorbing visible light.
Students often confuse configurations (E/Z, requiring bond breaking to interconvert) with conformations (s-cis/s-trans, interconvertible by rotation). The "s" prefix should be the reminder: it stands for single bond rotation.
Students sometimes think that s-cis is more stable because "cis" sounds simpler. s-trans is the more stable conformer for open-chain dienes. s-cis has steric strain.
A common error is thinking that more nodes in an MO means fewer electrons. Nodes determine energy level, not occupancy. You fill from the bottom up, two electrons per orbital (Aufbau principle), regardless of node count.
Students sometimes assume that the central C–C bond in a conjugated diene is a full double bond because of resonance. It is not. It has partial double-bond character (shorter and stronger than a normal single bond) but remains predominantly a single bond.
⚠️ Be able to classify any diene as conjugated, non-conjugated, or cumulated by looking at the hybridisation of the carbons between the double bonds.
⚠️ Know the energy ordering of diene MOs (π₁ through π₄), how many nodes each has, and which are occupied. Drawing the node diagrams is a very common exam question.
⚠️ Understand why conjugated dienes are more stable than non-conjugated dienes using heats of hydrogenation data. Be ready to calculate or explain the 3.5 kcal/mol stabilisation.
⚠️ Remember that only the s-cis conformer can undergo Diels-Alder reactions. Cyclopentadiene (locked s-cis) is highly reactive; cyclohexadiene (locked s-trans) is unreactive in Diels-Alder.
True or False: A non-conjugated diene has an sp³-hybridised carbon between its two double bonds.
Fill in the blank: The HOMO of 1,3-butadiene is π₂, which has __________ node(s).
True or False: The s-cis conformer of 1,3-butadiene is lower in energy than the s-trans conformer.
Fill in the blank: Four p-orbitals in a conjugated diene produce __________ molecular orbitals.
True or False: Cyclopentadiene is locked in an s-cis conformation and is therefore highly reactive in Diels-Alder reactions.
Q: Using heats of hydrogenation, explain why a conjugated diene is more stable than a non-conjugated diene.
A: A non-conjugated diene releases ~60 kcal/mol on hydrogenation (2 × 30 for each isolated double bond). A conjugated diene releases only ~56.5 kcal/mol. Since both give the same alkane product, the conjugated diene must have started at a lower (more stable) energy, by about 3.5 kcal/mol. This stabilisation comes from p-orbital overlap and electron delocalisation.
Q: How many nodes does each molecular orbital of 1,3-butadiene have?
A: π₁ has 0 nodes, π₂ has 1 node, π₃ has 2 nodes, π₄ has 3 nodes.
Q: Why is the central C–C bond in 1,3-butadiene (1.47 Å) shorter than a typical C–C single bond (1.54 Å)?
A: Two reasons. First, both carbons are sp²-hybridised, which gives shorter bonds due to greater s-character. Second, conjugation provides partial pi-bonding character across the central bond through delocalisation of the four pi electrons.
Q: Why is cyclohexadiene unreactive in the Diels-Alder reaction while cyclopentadiene is highly reactive?
A: Cyclohexadiene is locked in an s-trans conformation by the ring geometry, and only the s-cis conformer can participate in Diels-Alder. Cyclopentadiene is locked s-cis, so it is pre-organised for the [4+2] cycloaddition.
Q: Identify the HOMO and LUMO of 1,3-butadiene and state how many electrons are in each.
A: HOMO = π₂ (contains 2 electrons). LUMO = π₃ (contains 0 electrons).
The MO framework developed here for dienes feeds directly into the Diels-Alder reaction (next set of notes), where the HOMO of the diene interacts with the LUMO of the dienophile. Conjugation and delocalisation also connect to aromaticity (Ch. 15), where a fully conjugated cyclic system with 4n+2 pi electrons achieves special stability. The concept of nodes and orbital symmetry returns in pericyclic reaction theory (Woodward-Hoffmann rules) later in the course.
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