Fieser Kuhn Rule for Calculating λ_max in Polyenes

Fieser-Kuhn Rules to Calculate Wavelength of Maximum Absorption (λ_max) of Polyenes

Woodward-Fieser rule work well for conjugated dienes and polyenes with upto four-double bonds or less but not hold good for more than four double bonds. If a conjugated polyene contains more than four double bonds, then Fieser-Kuhn rules are used.
According to this approach, both λ_max and ε_max are related to the number of conjugated double bonds as well as other structural units by the following equation-
λ_max = 114 + 5M + n (48.0 x 1.7 n) − 16.5 R_endo − 10 R_exo
ε_max = (1.74 x 10⁴)n
Where, M is the number of alkyl substituents / ring residues in the conjugated system
n is the number of conjugated double bonds
R_endo is the number of rings with endocyclic double bonds in the conjugated system
R_exo is the number of rings with exocyclic double bonds in the conjugated system.

Base Value: 114 nm
M (number of alkyl substituents): 10
n (number of conjugated double bonds): 11
R_endo (number of endocyclic double bonds): 2
R_exo (number of exocyclic double bonds): 0
λ_max = 114 + 5M + n (48.0 – 1.7 n) – 16.5 R_endo – 10 R_exo
= 114 + (5 x 10) + 11 [48.0 - (1.7 x 11)] – (16.5 x 2) – (10 x 0)
= 114 + 50 + (11 x 29.3) – 33 – 0
= 114 + 50 + 322.3 – 33
Calculated λ_max value = 453.30 nm
λ_max observed value = 452nm
ε_max = (1.74 x 10⁴)n
= (1.74 x 10⁴) x 11 nm
Calculated ε_max value = 19.14 x 10⁴
Observed ε_max value = 15.2 x 10⁴

Similarly you can also calculate for-
Retinol
λ_max observed: 325 nm
ε_max = (1.74 x 10⁴)n

Lycophene
λ_max observed: 474 nm
ε_max = (18.6 x 10⁴)n

Woodward Fieser Rule for Calculating λmax in Dienes

Woodward Fieser Rule for Calculating λmax in α, β Unsaturated Carbonyl Compounds