## Introduction

Woodward-Fieser rules work well for conjugated dienes and polyenes with upto 4-double bonds or less. Certain plant pigments such as carotenoids have even more than 4 conjugated double bonds. For conjugated polyenes having more than 4 double bonds, the Fieser-Kuhn rules must be applied in order to obtain the wavelength of maximum absorption.

## Fieser-Kuhn Rule for Conjugated Polyenes

According to the Fieser-Kuhn rule the following equation can be used to solve for the wavelength of maximum absorption λmax and also maximum absorptivity εmax:

λmax = 114 + 5M + n (48.0 – 1.7 n) – 16.5 Rendo – 10 Rexo

where,
λmax is the wavelength of maximum absorption
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.

and

εmax = (1.74 x 104) n

where,
εmax
is the maximum absorptivity
n is the number of conjugated double bonds.

Thus using the above equations, one can get the wavelength of maximum absorbance (λmax) and the maximum absorptivity (εmax)

## Sample Problem 1: β-Carotene

β-carotene is a precursor of vitamin A which is a terpenoid derived from several isoprene units. The observed λmax of β-carotene is 452 nm, while the observed εmax is 15.2 x 104. Let us therefore use Fieser-Kuhn rules to calculate the λmax and the εmax for β-carotene.

 Name of Compound β-Carotene 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 Substituting in equation λmax = 114 + 5M + n (48.0 – 1.7 n) – 16.5 Rendo – 10 Rexo = 114 + 5(10) + 11 (48.0-1.7(11)) – 16.5 (2) – 10 (0)= 114 + 50 + 11 (29.3) – 33 – 0= 114 + 50 + 322.3 – 33 Calc. λmax = 453.30 nm λmax observed practically 452nm Calculate εmax using equation: εmax = (1.74 x 104) n = (1.74 x 104) 11Calc. εmax= 19.14 x 104 Practically observed εmax 15.2 x 104

## Sample Problem 2: all-trans-Lycophene

Lycophene (all-trans-lycophene) is a bright red carotenoid pigment found in tomatoes and other red fruits and vegetables. However, lycophene has no vitamin A like activity.

 Name of Compound all-trans-lycophene Base Value 114 nm M (number of alkyl substituents) 8 n (number of conjugated double bonds) 11 Rendo (number of endocyclic double bonds) 0 Rexo (number of exocyclic double bonds) 0 Substituting in equation λmax = 114 + 5M + n (48.0 – 1.7 n) – 16.5 Rendo – 10 Rexo = 114 + 5(8) + 11 (48.0-1.7(11)) – 16.5 (0) – 10 (0)= 114 + 40 + 11 (29.3) – 0 – 0= 114 + 40 + 322.3 – 0 Calc. λmax = 476.30 nm λmax observed practically 474nm Calculate εmax using equation: εmax = (1.74 x 104) n = (1.74 x 104) 11Calc. εmax= 19.14 x 104 Practically observed εmax 18.6 x 104

## Sample Problem 3: Retinol

Retinol is an animal form of vitamin A and is essential for vision.

 Name of Compound Retinol Base Value 114 nm M (number of alkyl substituents) 5 n (number of conjugated double bonds) 5 Rendo (number of endocyclic double bonds) 1 Rexo (number of exocyclic double bonds) 0 Substituting in equation λmax = 114 + 5M + n (48.0 – 1.7 n) – 16.5 Rendo – 10 Rexo = 114 + 5(5) + 5 (48.0-1.7(5)) – 16.5 (1) – 10 (0) = 114 + 25 + 5 (39.5) – 16.5 – 0 = 114 + 25 + 197.5 – 16.5 – 0 Calc. λmax = 320 nm λmax observed practically 325 nm Calculate εmax using equation: εmax = (1.74 x 104) n = (1.74 x 104) 5Calc. εmax= 8.7 x 104 Practically observed εmax N/A

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### This Post Has 18 Comments

1. steven kessy

thanks a lot for providing more detail concerning fieser-kuhn rule

2. nembrice kitumi

Thank you very much for your work

3. Yakobo Rijuwa

Be blessed…helps a lot

4. Joy

Good job well done… Please can u add the lambda Max of myrcene and Alfa -tepinene To the examples above.. An my email ID possible… Thanks

5. islam yasser

thanks,
but i have a question
in retinol,aren’t the alkyl substituent supposed to be four ?

6. Toru

I can’t understand how i consider the ring residue for the cyclic alkene system by using woodward fieser rule.

7. sruthy

I calculated Beta- Carotene value as 434 nm. I am happy after seeing above article to know about lambda max value…good job..

8. govind koranga

Very nice working

9. anant

nice work…

10. Mira

Thank you! It Helps a lot 😀

11. William Popplewell

Great presentation, and very useful thank you. I was trying to calculate the lamba max for astaxanthin (an analogue of beta carotene). I calculated it to 447.7 nm but i was wondering if the endocyclic carbonyls at the terminal ends of the conjugation would have any alternative effects?

1. Akul Mehta

Hi William,
Firstly, the Fieser-Kuhn rules were not developed for carbonyls. Furthermore, in astaxanthin, the carbonyls are actually counted as exocyclic double bonds as they are outside of the ring. Your calculation does come close though to the observed lambda max of 478 nm. However, the rules do not specify anything for carbonyls. If you do find something, please do share it on this page. Thanks.

1. D M

Great stuff! Can you combine the two equations for retinoic acids?

1. Akul Mehta

Thanks Denis. Not sure if we can combine equations for retinoic acids.

12. Aaisha salma

Hi ur informations very much helpful to me thanks a lot can u plzzz calculate lembda max of retinol (vitamimA1)

1. Akul Mehta

Hi Aaisha,
we have added retinol as sample no. 3 as per your request.

1. govind koranga

Thank u for sending that rule plz send more ones

13. Dr Cyril

Thank you Akul for this nice presentation…

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