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🟪Woodward–Fieser Rules Calculator - UV λmax of Dienes and Enones

The Woodward–Fieser rules estimate the wavelength of maximum π→π* absorption (λmax) of a conjugated system as a base value plus increments. For conjugated dienes the base is 214 nm (acyclic or heteroannular) or 253 nm (homoannular). Increments are +30 for each extending double bond, +5 per alkyl group or ring residue, +5 per exocyclic double bond, +6 for –OR, +30 for –SR, +5 for –Cl/–Br and +60 for –NR₂. So 1,3-butadiene, with no substituents, is calculated at 214 nm (observed 217 nm). 2,3-Dimethylbutadiene gives 214 + 2×5 = 224 nm (observed 226 nm), and cholesta-3,5-diene, with three ring residues and one exocyclic double bond, gives 214 + 15 + 5 = 234 nm (observed 235 nm). α,β-Unsaturated carbonyl compounds start from 215 nm (acyclic or six-ring ketone), 202 (five-ring ketone), 210 (aldehyde) or 195 (acid/ester). Substituent increments depend on position: alkyl α +10, β +12, γ and beyond +18, and tabulated values apply to –OH, –OR, –Cl, –Br, –NR₂ and others. Extended conjugation adds +30, an exocyclic double bond +5 and a homoannular diene component +39, followed by a solvent correction. Mesityl oxide, (CH₃)₂C=CH–CO–CH₃, gives 215 + 2×12 = 239 nm (observed ≈ 237 nm) and cholest-4-en-3-one 215 + 24 + 5 = 244 nm (observed 241 nm). Every term here is a counter, and the breakdown and total update live. Fifteen textbook examples are built in. For polyenes with more than four conjugated double bonds the Fieser–Kuhn equation gives λmax and εmax (β-carotene: 453 nm calculated, 452 nm observed). A reference tab covers σ→σ*, n→σ*, π→π* and n→π* transitions with typical λ and ε, key terms such as chromophore and auxochrome, wavelength–energy conversion and a complementary-colour table.

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How to use UV–Vis λmax (Woodward–Fieser)

  1. 1Choose the system: conjugated diene/polyene, α,β-unsaturated carbonyl, or long polyene (Fieser–Kuhn)
  2. 2Pick the parent type and count extending double bonds, alkyl groups or ring residues, exocyclic double bonds and substituents by position, or start from a textbook example
  3. 3Read the estimated λmax with its term-by-term breakdown and solvent correction, copy the working and compare with the observed value

FAQ

How do you apply the Woodward–Fieser rules?
Choose the parent value (dienes: 214 nm acyclic/heteroannular, 253 nm homoannular; enones: 215 nm acyclic or six-ring, 202 nm five-ring, and so on), then add increments: +30 for each double bond extending conjugation, +5 for each alkyl group or ring residue and each exocyclic double bond on a diene, plus the tabulated values for polar groups. For 2,3-dimethyl-1,3-butadiene, 214 + 2×5 = 224 nm against 226 nm observed. Agreement is usually within about ±5 nm.
What are ring residues and exocyclic double bonds?
A ring residue is a ring carbon attached to a carbon of the conjugated system; it counts like an alkyl group (+5 on dienes, +10/+12/+18 by position on enones). A double bond is exocyclic to a ring when one of its carbons belongs to that ring but the bond lies outside it; each adds +5, and a bond exocyclic to two rings counts twice. In cholesta-3,5-diene the C5=C6 bond lies in ring B but C5 is also in ring A, so it is exocyclic to ring A.
How does the solvent correction work for enones?
The rules predict values in ethanol. Tables list corrections (water −8, chloroform +1, dioxane +5, ether +7, hexane/cyclohexane +11) that are added to a value measured in that solvent to convert it to ethanol. To predict λmax in that solvent you subtract them: mesityl oxide in hexane is about 239 − 11 = 228 nm. This matches the red shift of π→π* bands in polar solvents.
When should I use the Fieser–Kuhn rule instead?
Woodward–Fieser rules cover up to four conjugated double bonds; beyond that each extra double bond shifts λmax less. Fieser–Kuhn uses λmax = 114 + 5M + n(48.0 − 1.7n) − 16.5 R_endo − 10 R_exo and εmax = 1.74×10⁴ n, where M is the number of alkyl groups and n the number of conjugated double bonds. β-Carotene (n = 11, M = 10, R_endo = 2) gives 453 nm against 452 nm observed; lycopene gives 476 nm against 474 nm.

Features

  • Diene Woodward–Fieser rules: heteroannular/homoannular base, extended conjugation, alkyl, exocyclic and polar groups
  • Enones, enals, unsaturated acids and esters (Woodward–Fieser–Scott) with α/β/γ/δ position increments
  • Eight solvent corrections (water, methanol, ethanol, chloroform, dioxane, ether, hexane, cyclohexane) with the sign explained
  • 15 textbook examples (butadiene, cholestadienes, mesityl oxide, carvone, cholestenone…) with calculated and observed values
  • Fieser–Kuhn λmax and εmax for long polyenes, with the predicted colour
  • Electronic transition types with typical λ and ε, plus chromophore, auxochrome and shift terminology
  • Wavelength to eV, kJ/mol, wavenumber and frequency, and a visible-colour complement table
  • Diagrams of homoannular/heteroannular dienes and α, β, γ, δ positions; one-click copy of the working