This morning I read a really interesting paper Biradicaloid and Polyenic Character of Quinoidal Oligothiophenes Revealed by the Presence of a Low-Lying Double-Exciton State by an Italian group. These molecules are of particular interest because of their possible applications in photonics (non-linear optics, photovoltaic cells). A biradical is a molecule which has two spatially separated unpaired (or weakly paired) spins.
One of the main results of the paper is that as one increases the number of thiophene groups in the middle of the molecule the energy gap to the lowest optically active state decreases, the amount of biradical character of the ground state increases and there is a lower lying "dark" state which has "double exciton" character, analogous to the 2A_g state in polyenes.
I found the paper particularly interesting because I believe it should be possible to make a connection with the valence bond description of the excited states in polyenes.
Below are the possible valence bond diagrams for hexatriene. There is a one-to-one mapping of these states to the valence bond states of the quinoidal thiophene molecule shown on the bottom left above [denoted 2P-1T in the paper]. In particular, the "quinoidal" and "biradicaloid" states correspond to stuctures R_1 and R_k below, respectively.
The contribution of these different valence bond states to the low lying excited states is shown below.
The relative energies and coupling matrix elements between the different VB states will determine the character of the ground and first excited state.