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 λ_{max} and also maximum absorptivity ε_{max}:
λ_{max} = 114 + 5M + n (48.0 – 1.7 n) – 16.5 R_{endo} – 10 R_{exo}
where,
λ_{max }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
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.
and
ε_{max} = (1.74 x 10^{4}) 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 (λ_{max}) and the maximum absorptivity (ε_{max})
Sample Problem 1: β-Carotene
β-carotene is a precursor of vitamin A which is a terpenoid derived from several isoprene units. The observed λ_{max} of β-carotene is 452 nm, while the observed ε_{max} is 15.2 x 10^{4}. Let us therefore use Fieser-Kuhn rules to calculate the λ_{max }and the ε_{max }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 |
R_{endo} (number of endocyclic double bonds) | 2 |
R_{exo} (number of exocyclic double bonds) | 0 |
Substituting in equation λ_{max} = 114 + 5M + n (48.0 – 1.7 n) – 16.5 R_{endo} – 10 R_{exo} |
= 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. λ_{max} = 453.30 nm |
λ_{max} observed practically | 452nm |
Calculate ε_{max} using equation: ε_{max} = (1.74 x 10^{4}) n |
= (1.74 x 10^{4}) 11Calc. ε_{max}= 19.14 x 10^{4} |
Practically observed ε_{max} | 15.2 x 10^{4} |
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 |
R_{endo} (number of endocyclic double bonds) | 0 |
R_{exo} (number of exocyclic double bonds) | 0 |
Substituting in equation λ_{max} = 114 + 5M + n (48.0 – 1.7 n) – 16.5 R_{endo} – 10 R_{exo} |
= 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. λ_{max} = 476.30 nm |
λ_{max} observed practically | 474nm |
Calculate ε_{max} using equation: ε_{max} = (1.74 x 10^{4}) n |
= (1.74 x 10^{4}) 11Calc. ε_{max}= 19.14 x 10^{4} |
Practically observed ε_{max} | 18.6 x 10^{4} |
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 |
R_{endo} (number of endocyclic double bonds) | 1 |
R_{exo} (number of exocyclic double bonds) | 0 |
Substituting in equation λ_{max} = 114 + 5M + n (48.0 – 1.7 n) – 16.5 R_{endo} – 10 R_{exo} |
= 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. λ_{max} = 320 nm |
λ_{max} observed practically | 325 nm |
Calculate ε_{max} using equation: ε_{max} = (1.74 x 10^{4}) n |
= (1.74 x 10^{4}) 5Calc. ε_{max}= 8.7 x 10^{4} |
Practically observed ε_{max} | N/A |
Also Checkout These Other Pages:
- Woodward-Fieser Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Conjugated Dienes and Polyenes
- Woodward-Fieser Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Conjugated Carbonyl Compounds
- Sample Problems Using Woodward-Fieser Rules
Books on Analytical Chemistry and Spectroscopy
Check out these good books for analytical chemistry and spectroscopy
I calculated Beta- Carotene value as 434 nm. I am happy after seeing above article to know about lambda max value…good job..
Very nice working
nice work…
should have posted video instead…
Thank you! It Helps a lot 😀
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?
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.
Great stuff! Can you combine the two equations for retinoic acids?
Thanks Denis. Not sure if we can combine equations for retinoic acids.
Hi ur informations very much helpful to me thanks a lot can u plzzz calculate lembda max of retinol (vitamimA1)
Hi Aaisha,
we have added retinol as sample no. 3 as per your request.
Thank u for sending that rule plz send more ones
Thank you Akul for this nice presentation…