Fieser Kuhn Rule for Calculating λmax in Polyenes
Fieser-Kuhn Rules to Calculate Wavelength of Maximum Absorption (λmax) 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 λmax and εmax are related to the number of conjugated double bonds as well as other structural units by the following equation-
λmax = 114 + 5M + n (48.0 x 1.7 n) − 16.5 Rendo − 10 Rexo
εmax = (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
Rendo is the number of rings with endocyclic double bonds in the conjugated system
Rexo 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
Rendo (number of endocyclic double bonds): 2
Rexo (number of exocyclic double bonds): 0
λmax = 114 + 5M + n (48.0 – 1.7 n) – 16.5 Rendo – 10 Rexo
= 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 λmax value = 453.30 nm
λmax observed value = 452nm
εmax = (1.74 x 104)n
= (1.74 x 104) x 11 nm
Calculated εmax value = 19.14 x 104
Observed εmax value = 15.2 x 104
Similarly you can also calculate for-
Retinol
λmax observed: 325 nm
εmax = (1.74 x 104)n
Lycophene
λmax observed: 474 nm
εmax = (18.6 x 104)n