First Part

A Practical Guide to Estimating \(\lambda_{max}\) in Conjugated
Polyene Systems using
the Fieser-Kuhn rule.

D.R © UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO 2025

Los derechos patrimoniales pertenecen a la Universidad Nacional Autónoma de México. Ciudad Universitaria, Coyoacán, C.P. 04510, Ciudad de México, México.

Entidad editora: Facultad de Estudios Superiores Cuautitlán.
Este contenido digital se elaboró con el apoyo de la DGAPA- PAPIME PE211025 Integración, validación e implementación de un manual de prácticas digital basado en la técnica de UV-Visible, para el apoyo de la práctica docente en la FES Cuautitlán.

Autores: Benjamín Velasco Bejarano, Anuar Gómez Tagle González, Víctor Manuel Díaz Sánchez, Lourdes Aguilera Arreola y José Félix Olivares Landín.

Excepto donde se indique lo contrario, este contenido digital está bajo una licencia Creative Commons Atribución-No comercial Compartir Igual (CC-BY-NC-SA) 4.0 Internacional https://creativecommons.org/licenses/by-nc-sa/4. 0/deed.es. Fecha de asignación de la licencia 2025-10. Para un uso diferente escribir a: unidadjuridicafesc@cuautitlan.unam.mx
Con la licencia usted es libre de compartir: copiar y redistribuir el material en cualquier medio o formato Adaptar: remezclar, transformar y construir a partir del material. La licenciante no puede revocar estas libertades en tanto usted siga los términos de la licencia.

Forma sugerida de citar: Velasco-Bejarano B., Gómez-Tagle A., Diaz Sánchez V. M., Aguilera Arreola L. y Olivares Landín J. F., Facultad de Estudios Superiores Cuautitlán (2025). Introducción a la aplicación de la regla de Fieser-Kuhn. [Recuperado: fecha de consulta, URL del recurso en el RU-FES Cuautitlán].


First Part

Introduction

This document introduces the theoretical and methodological foundations required to understand the application of the Fieser–Kuhn rule in UV–Vis spectroscopy. It begins by presenting the general characteristics of conjugated polyene systems and their biological relevance, with representative examples such as lycopene and β-carotene. UV–Vis absorption spectroscopy principles are reviewed, including electronic transitions, molecular orbital considerations, and the role of π-electron conjugation in spectroscopic properties.


The document explains how the Fieser–Kuhn rule can be used to estimate maximum absorption in open-chain conjugated polyenes., This methodology is employed through worked examples and practice problems, allowing readers to compare calculated values (λmax, calc) with experimental data (λmax, exp).

Objective

To recognize the structural features of conjugated polyene systems in natural products and to understand how UV–Vis spectroscopy can be used to determine their maximum absorption wavelength, λmax (nm).


1.

Polyenes in Natural products.

¿What polyenes are?

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Definition

In natural products polyenes are biosynthesized by living organisms. They contain two or more conjugated carbon–carbon double bonds. The π electrons are relocated along the molecular framework, which strongly influences the chemical and spectroscopic behavior of the molecule, such as in UV–Vis spectroscopic properties. These properties allow to understand the relationship between molecular structure and the maximum absorption wavelength.5

Importance of polyenes in biological functions.

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Functions

Polyenes exhibit a wide range of biological properties. Many acts as antioxidants capable of scavenging reactive oxygen species (ROS), thereby protecting biological systems from oxidative damage. Some polyenes act as antimicrobicides and function as defensive secondary metabolites. Some of t are pigments and their intense coloration play a crucial role by facilitating pollination and seed dispersal, in plants.

Examples of Polyenes in Natural Products.

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Pigmentos

  • Lycopene (Red/Tomato): Lycopene is a highly conjugated carotenoid responsible for the red coloration of tomatoes. Its extended conjugated polyene system is associated with strong antioxidant activity and characteristic absorption in the visible region.4
  • \β‑Carotene (Orange/Carrot-Provitamin A): β‑Carotene is a carotenoid present in carrots, green vegetables, and marigold flowers. It functions as a provitamin A precursor and acts as an antioxidant in biological systems.4,5
  • Vitamin A (Retinol): Retinol is a metabolite derived from β‑carotene and plays an essential role in vision, immune system function, and reproduction.6,7
2.

UV-Vis Spectroscopy

UV-Vis absorption spectroscopy is a rapid and non‑destructive analytical technique widely used to investigate electronic transitions in organic molecules8. The technique measures the absorption of electromagnetic radiation in the ultraviolet and visible regions of the spectrum and enables the determination of the maximum absorption wavelength, λmax (nm), of conjugated chromophores such as polyenes.
The spectroscopic behavior of polyenes is governed by electronic transitions involving π and n electrons. Upon absorption of energy, electrons are promoted from lower‑energy molecular orbitals to higher‑energy excited states.
Absorption occurs when a photon withinregion190–800 nm is absorbed by an electron. And is promoted from the Highest Ocupated Molecular orbital (HOMO) to the Lowest Unoccupated Molecular Orbital (LUMO). As the number of conjugated double bonds increases, the HOMO–LUMO energy gap decreases, requiring less energy, and thus the absorption occurs at longer wavelengths in the ultraviolet–visible region. The Fieser–Kuhn rule provides an empirical method for estimating λmax, calc, of open-chain conjugated polyenes. Comparison of calculated values with experimental measurements (λmax, exp) allows to hypothesize a structure of highly conjugated systems present in natural products, such as carotenoids.

Energy Level Diagram

HOMO LUMO
3.

Conjugation and Energy Considerations

Conjugation refers to the alternating arrangement of multiple and single bonds allowing delocalization of π electrons across a molecular framework. As the number of conjugated double bonds increases, the HOMO–LUMO energy gap decreases, resulting in absorption at longer wavelengths and a characteristic bathochromic shift.
The value of λmax may be influenced by several structural factors including extension of the conjugated system, the presence of auxochromic substituents, and changes in the surrounding chemical environment. A displacement toward longer wavelengths is referred to as a bathochromic shift, whereas a shift toward shorter wavelengths is known as a hypsochromic shift.
π Electrons: electrons present in a π system, formed overlapping of p orbitals.

σ Electrons: electrons forming σ bonds through frontal overlap of orbitals.

n Electrons: non‑bonding electrons localized on heteroatoms such as oxygen, nitrogen, or sulfur.
4.

The Fieser–Kuhn Rule

The absorption process

The Fieser–Kuhn rule is a set of empirical and semi‑empirical correlations originally proposed by Louis F. Fieser and Mary Fieser and later refined by Werner Kuhn. The rule provides a method for predicting the position of the most intense UV–Vis absorption band in open‑chain conjugated polyene systems. Calculated values of the maximum absorption wavelength (λmax, calc) can be compared with experimentally measured values (λmax, exp) to evaluate the plausibility of proposed molecular structures. The position of λmax is influenced by the geometric configuration of the polyene chain. All-trans carotenoids typically display absorption at longer wavelengths, whereas cis isomers exhibit hypsochromic shifts due to reduced effective conjugation.

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