# Fieser Kuhn Rule for Calculating 位_{max} in Polyenes

## Fieser-Kuhn Rules to Calculate Wavelength of Maximum Absorption (位_{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 位

_{max}and 蔚

_{max}are related to the number of conjugated double bonds as well as other structural units by the following equation-

位

_{max}= 114 + 5M + n (48.0 x 1.7 n) − 16.5 R

_{endo}− 10 R

_{exo}

蔚

_{max}= (1.74 x 10

^{4})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

位

_{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 位

_{max}value = 453.30 nm

位

_{max}observed value = 452nm

蔚

_{max}= (1.74 x 10

^{4})n

= (1.74 x 10

^{4}) x 11 nm

Calculated 蔚

_{max}value = 19.14 x 10

^{4}

Observed 蔚

_{max}value = 15.2 x 10

^{4}

Similarly you can also calculate for-

**Retinol**

位

_{max}observed: 325 nm

蔚

_{max}= (1.74 x 10

^{4})n

**Lycophene**

位

_{max}observed: 474 nm

蔚

_{max}= (18.6 x 10

^{4})n