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Effect of conjugation on absorption maximum

The Π−Π* transition of ethylene requires of light at 171 nm (164 kcal/mole), slightly into the vacuum ultraviolet region. In conjugated 

Fig.1.1 in 1,3-butadiene, the Π−Π* transition absorbs at a wavelength of 217 nm  (219 kcal (mole) or 540 kj/mole), compared with 171 nm (164 kcal/mole or 686 kj/mole) for ethylene. this.This longer-wavelength(lower energy) absorption result from a smaller energy difference between the HOMO and LUMO and LUMO in butadiene than in ethylene

system, however, there are electronic transtitions with lower energies that correspond to wavelengths longer than 200 nm. Let us compare the energy levels of ethylene and 1,3-butadiene.


In ethylene there is only one occupied MO. The only possible transition is the excitation of an electron from the occupied  MO to the unoccupied MO. In butadiene there are four possible transitions involving excitation of an electron from either of the field orbitals into either of the empty ones. The lowest energy transition, corresponding to absorption of light of the longest wavelength, is excitation of an electron from the HOMO to the LUMO. This is a Π2→Π3* transition.
Notice in fig 1.1 that the HOMO of butadiene is higher in energy than the HOMO Of ethylene.
Also, the LUMO of butadiene is lower in energy than the LUMO of ethylene. Both of these differences reduce the relative energy of the Π−Π* transition in butadiene. The resulting absorption is at 217nm (219 kcal (mole).

Just as conjugated dienes absob at longer wavelength than simple alkenes, the conjugated trienes absorb at even longer wavelengths.

Fig.1.2. 1,3,5 -hexatriene ha a smaller energy difference (108 kcal/mole or 452 kj/mole) between its HOMO and LUMO than dooes 1,3-butadiene (129 kcal/mole or 540 kj/mole). The Π−Π* transition corresponding to this energy difference absorbs at a longer wavelength :228 nm, compared with 217 nm for 1,3-butadiene

In 1,3,5- hexatriene, for example, (Fig.1.4), the HOMO is Π3 and the LUMO is Π4*. The lowest energy transition is the excitation of an electron from Π3 into Π4*. The HOMO in 1,3,5-hexatriene is slightly higher in energy than that for 1,3-butadiene, and the hexatriene LUMO is slightly lower in energy. Once again the narrowing of the energy between the HOMO and the LUMO gives a lower energy, longer wavelength absorption. The principal Π−Π* transition in 1,3,5-hexateiene occurs at 258nm (108kcal/mole).
Similar to the conjugated alkenes, other conjugated compounds such as aldehydes, ketones, etc.also absorb at longer wavelengths as compared to the simple uncojugated compounds.

Another way to point out the narrowing of the HOMO-LUMO energy as the conjugated system grows is to lok at the number of nodes in the molecular orbitals. In general, the HOMO of a conjugated system with N pi electrons has N/2- 1 nodes: none for ethylene, one for butadiene, two for 1,3,5-hexatriene and so on. The LUMO always has one more node. Usually the more nodes an orbital already has, the less additional energy is involved in adding one more node. 
In other words, the longer the conjugated system, lesser is the difference between HOMO and LUMO energy and hence the higher are the values of λmax and εmax.
In general, the longer the conjugated system, the higher are the values of λmax and εmax.

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