Conjugation and Absorption Wavelength

Introduction

Ethene absorbs only in the far ultraviolet, near 171 nm. β-Carotene, the pigment in carrots, contains eleven C=C bonds in an alternating chain and absorbs blue light near 450 nm, which is why carrots look orange. The difference is conjugation . When π bonds alternate with single bonds, their electrons spread over the whole chain, the gap between orbitals shrinks, and absorption moves steadily towards longer wavelengths. This single idea explains the colour of most organic dyes and pigments.

Core explanation

What conjugation means. A conjugated system has alternating single and double (or triple) bonds, so that each carbon in the chain has a p orbital lying parallel to its neighbours. These p orbitals overlap sideways along the whole chain, creating π molecular orbitals that extend over many atoms. Lone pairs on atoms next to a double bond, and aromatic rings, can also be part of a conjugated system. Two double bonds separated by two or more single bonds (as in penta-1,4-diene) are isolated , not conjugated.

More p orbitals, more molecular orbitals. When n p orbitals combine, they form n π molecular orbitals: half bonding, half antibonding. Ethene (2 p orbitals) has one π and one π . Buta-1,3-diene (4 p orbitals) has two bonding and two antibonding orbitals. As the chain grows, the orbitals crowd closer together in energy.

The shrinking gap. Because more orbitals are packed into a similar overall energy range, the HOMO rises and the LUMO falls as conjugation extends. The HOMO–LUMO gap becomes smaller, so the π → π transition needs less energy and λmax moves to longer wavelength. Intensity usually rises as well, because the transition involves electrons spread over a longer region.

Typical data for polyenes (π → π bands):

Compound Conjugated C=C λmax / nm --- --- --- Ethene 1 171 Buta-1,3-diene 2 217 Hexa-1,3,5-triene 3 258 Octatetraene 4 about 290 β-Carotene 11 about 450

Each added C=C increases λmax by roughly 30–40 nm in the short polyenes, with the increase becoming smaller for very long chains.

From colourless to coloured. Once λmax passes about 400 nm, the compound absorbs visible light and appears coloured. Roughly seven or eight conjugated double bonds are needed for a simple polyene to absorb in the visible region. Aromatic rings joined through azo groups (–N=N–) or carbonyl groups achieve the same effect with fewer atoms, which is why azo dyes are so widely used.

Extending conjugation by chemistry. Adding a lone-pair donor (such as –OH or –NH₂) or deprotonating a phenol extends delocalisation and shifts λmax to longer wavelength. This is the basis of acid–base indicators: protonation or deprotonation changes the extent of conjugation and therefore the colour.

Step-by-step reasoning

To compare the λmax of two compounds:

1. Draw each structure and highlight alternating single and multiple bonds. 2. Count the atoms in the longest continuous conjugated system, including attached aromatic rings and lone-pair groups. 3. Check that no sp³ carbon breaks the chain. 4. The compound with more extensive conjugation has the smaller gap and the longer λmax.

Visual explanation

Draw energy levels for ethene, butadiene and hexatriene side by side. Ethene has two widely spaced levels; butadiene has four more closely spaced levels; hexatriene has six, closer still. Draw the HOMO → LUMO arrow in each: the arrow gets shorter from left to right, matching the rising λmax.

Real-world analogy

A guitar string produces lower-pitched notes as it gets longer. A longer conjugated chain behaves similarly: electrons delocalised over a longer "string" have more closely spaced energy levels, so the molecule "resonates" with lower-energy, longer-wavelength light.

Real-world example

Lycopene, which colours tomatoes red, has eleven conjugated C=C bonds and absorbs strongly around 470–500 nm. Retinal, the light-sensing molecule in the eye, is a conjugated polyene attached to a protein; absorption of a visible photon changes its shape and triggers a nerve signal.

Why?

Why does an sp³ carbon break conjugation? An sp³ carbon has no spare p orbital, so the sideways overlap cannot pass through it. The π systems on either side behave independently, each with its own large HOMO–LUMO gap.

Common misconception

"More double bonds anywhere in the molecule always means longer λmax." Only double bonds that are conjugated with one another count. Penta-1,4-diene, with isolated C=C bonds, absorbs near 178 nm, close to ethene, whereas conjugated penta-1,3-diene absorbs near 223 nm.

Worked example

Question: Place in order of increasing λmax: benzene, hexa-1,3,5-triene, ethene.

Reasoning: Ethene has one isolated C=C (171 nm). Hexa-1,3,5-triene has three conjugated C=C bonds in a chain (258 nm). Benzene has a cyclic six-electron system whose strongest bands lie near 180–204 nm, with only a weak band at 254 nm; comparing the intense π → π bands, benzene's are below the triene's.

Answer: Ethene < benzene < hexa-1,3,5-triene.

Quick check

1. Explain briefly why buta-1,3-diene absorbs at a longer wavelength than ethene. Answer: Its four p orbitals form a conjugated system with a smaller HOMO–LUMO gap, so lower-energy, longer-wavelength light is absorbed.

Exam focus

A full-mark explanation links four steps: more conjugation → more delocalised electrons → smaller energy gap between orbitals → absorption of longer-wavelength (lower-energy) light. If a compound becomes coloured, add that λmax has moved into the visible region.

Advanced insight

A simple "particle in a box" model treats the π electrons as free to move along a chain of length L. The energy levels scale as 1/L², so the gap shrinks as the chain lengthens. Real polyenes show bond-length alternation, which keeps a finite gap even for very long chains; this is why λmax levels off rather than rising indefinitely.

Summary

Conjugation occurs when π bonds alternate with single bonds, allowing p orbitals to overlap and electrons to delocalise over many atoms. Extending conjugation raises the HOMO and lowers the LUMO, narrowing the gap and shifting λmax to longer wavelength with greater intensity. When λmax exceeds about 400 nm the compound is coloured. sp³ centres break conjugation; lone-pair donors extend it.

Practice questions

1. Define a conjugated system. Answer: A system of alternating single and multiple bonds, or lone pairs next to π bonds, in which parallel p orbitals overlap to delocalise electrons. 2. Explain why β-carotene is coloured but buta-1,3-diene is not. Answer: β-Carotene has eleven conjugated C=C bonds, giving a small gap and λmax in the visible region; butadiene's two conjugated bonds give λmax at 217 nm, in the ultraviolet. 3. Which absorbs at longer wavelength, penta-1,3-diene or penta-1,4-diene? Explain. Answer: Penta-1,3-diene, because its double bonds are conjugated; in penta-1,4-diene an sp³ carbon separates them. 4. How can adding a base change the colour of a phenol-based indicator? Answer: Deprotonation forms a phenoxide ion whose lone pairs extend the conjugated system, reducing the energy gap and shifting absorption to longer wavelength.