Linear Conjugated Molecules The Polyenes

The wavefunctions of delocalized 7T orbitals of linear conjugated molecules can be drawn following the number of nodes (open circles) 

Orbital is the highest occupied molecular orbital (HOMO) in the ground state. It corresponds to the structural formula of the molecule, with double bonds between and C2, and between C3 and C4. Orbital is likewise the lowest unoccupied molecular orbital (LUMO) in the ground state and corresponds to a biradical structure of the molecule with unpaired electrons on Gj and C4. Such a biradical structure can be a very simple but sometimes useful representation of the excited molecule (in states Si or T.  

The orbitals q)2 and q)3 have one nodal line each, passing either through two atoms or through two bonds but since these orbitals have the same number of nodes, it follows that they must have the same energy (they are degenerate). The same remark applies to the first antibonding orbitals cpA and (p5, which have two nodal lines each. 

The fact that these HOMOs and LUMOs have a two-fold degeneracy implies that there are four isoenergetic one-electron transitions to yield the first excited states this complication is however resolved by the interaction of these one-electron excitations, and this is known as configuration interaction. The concept of configuration interaction (Cl) is somewhat similar to that of the interaction of atomic orbitals to form molecular orbitals. An electron configuration defines the distribution of electrons in the available orbitals, and an actual state is a combination of any number of such electron configurations, the state wavefunction being 

In benzene and its derivatives the transition Sq-1 is symmetry forbidden, while the So-1 is allowed this is readily seen from the absorption 

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