Ultraviolet-Visible (UV-Vis) Spectroscopy – Fieser-Kuhn Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Polyenes (with Sample Problems)

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.

beta-carotene solved using fieser-kuhn rules

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.

Wavelength of maximum absorption for all-trans-lycophene

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.

Retinol

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

Also Checkout These Other Pages:

  1. Woodward-Fieser Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Conjugated Dienes and Polyenes
  2. Woodward-Fieser Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Conjugated Carbonyl Compounds
  3. Sample Problems Using Woodward-Fieser Rules

Books on Analytical Chemistry and Spectroscopy

Check out these good books for analytical chemistry and spectroscopy

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…
    should have posted video instead…

  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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