Excited electronic states in molecules

The promotion of electron in a polyatomic molecule to an excited states means that the electronic occupies an orbital of higher energy than occurs in the ground-state configuration. As an example, we consider the molecule ethylene C$_2$H$_4$. In the ground state, the highest energy MOs occupied by electrons are the $\pi$ orbitals formed from the $p_z$ orbitals on each of the $sp^2$ hybridized carbons. The highest-energy occupied orbital plays such a central role in molecular quantum mechanics that it has a special name called the highest occupied molecular orbital or HOMO. Absorption of a photon can excite the $\pi$ electron to a previously unoccupied $\pi^*$ orbital, called a $\pi\rightarrow\pi^*$ transition. The previously unoccupied MO is known as the lowest unoccupied molecular orbital or LUMO. If the occupancy of the $\pi$ orbital is reduced by 1, and the occupancy of an anti-bonding $\pi^*$ orbital is increased by 1, the overall bond order is reduced from 2 to 1 and the CC bond is longer and weaker. This can affect the conformational flexibility of the molecule and change is properties considerably from those of the ground state.

Conjugated systems are particularly important because the HOMO is an extended $\pi$ orbital that is delocalized over the entire molecule. The wave functio of an electron in such an orbital is similar to a particle-in-a-box, in which the box length $L$ is the length of the molecule. Since the longest wavelength is $2L$, the wavelength increases with the length of the molecule, itself. Hence, the frequency at which the $\pi\rightarrow\pi^*$ transition occurs becomes lower. For a long enough molecule, the frequency shifts down into the visible. This means that some component of visible light will be absorbed leaving the remaining components as observable. For example, the molecule beta-carotene absorbs high frequency, short wavelength light (blue, violet), leaving orange and yellow as observable. The presence of carotenoids in many types of trees is the reason their leaves appear bright yellow and orange in the fall.