In a conjugated pi-system, electrons are able to capture certain photons as the electrons resonate along a certain distance of p-orbitals - similar to how a radio antenna detects photons along its length. Typically, the more conjugated (longer) the pi-system is, the longer the wavelength of photon can be captured. Compounds whose molecules contain a sufficient number of conjugated bonds can absorb light in the visible region, and therefore appear colorful to the eye, usually appearing yellow or red.
Many dyes make use of conjugated electron systems to absorb visible light, giving rise to strong colors. For example, the long conjugated hydrocarbon chain in beta-carotene leads to its strong orange color. When an electron in the system absorbs a photon of light of the right wavelength, it can be promoted to a higher energy level. A simple model of the energy levels is provided by the quantum-mechanical problem of a one-dimensional particle in a box of length L, representing the movement of a π electron along a long conjugated chain of carbon atoms. In this model the lowest possible absorption energy corresponds to the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). For a chain of n C=C bonds or 2n carbon atoms in the molecular ground state, there are 2n π electrons occupying n molecular orbitals, so that the energy gap is
Since the box length L increases approximately linearly with the number of C=C bonds n, this means that the energy ΔE of a photon absorbed in the HOMO–LUMO transition is approximately proportional to 1/n. The photon wavelength λ = hc/ΔE is then approximately proportional to n. Although this model is very approximate, λ does in general increase with n (or L) for similar molecules. For example, the HOMO–LUMO absorption wavelengths for conjugated butadiene, hexatriene and octatetraene are 217 nm, 252 nm and 304 nm respectively. However, for good numerical agreement of the particle in a box model with experiment, the single-bond/double-bond bond length alternations of the polyenes must be taken into account. Alternatively, one can use the Hückel method which is also designed to model the electronic structure of conjugated systems.
Many electronic transitions in conjugated π-systems are from a predominantly bonding molecular orbital (MO) to a predominantly antibonding MO (π to π), but electrons from non-bonding lone pairs can also be promoted to a π-system MO (n to π) as often happens in charge-transfer complexes. A HOMO to LUMO transition is made by an electron if it is allowed by the selection rules for electromagnetic transitions. Conjugated systems of fewer than eight conjugated double bonds absorb only in the ultraviolet region and are colorless to the human eye. With every double bond added, the system absorbs photons of longer wavelength (and lower energy), and the compound ranges from yellow to red in color. Compounds that are blue or green typically do not rely on conjugated double bonds alone.
This absorption of light in the ultraviolet to visible spectrum can be quantified using ultraviolet–visible spectroscopy, and forms the basis for the entire field of photochemistry.
Conjugated systems that are widely used for synthetic pigments and dyes are diazo and azo compounds and phthalocyanine compounds.