Previously I discussed the importance concept of twin states in chemical bonding and photophysics. In certain situations this needs to be extended to three states, particularly in molecules with close to triangular symmetry.
A nice paper, Towards experimental determination of conical intersection properties: a twin state based comparison with bound excited states by Shmuel Zilberg and Yehuda Haas just appeared in PhysChemChemPhys.
The paper discusses how the lowest lying triplet state can be close in geometry and energy a conical intersection between the two lowest lying singlet states (S0/S1).
The paper focuses on the specific case of the organic molecule acepentalene shown below. Unfortunately, it has not be synthesized yet in its neutral form. The molecule has three possible degenerate valence bond structures, all related by C3v symmetry.
All of the discussion is in the framework of the Born-Oppenheimer approximation. I note that the relevant vibrational frequencies (~2000 cm-1) mean that the zero point energies are comparable to the energy barriers (~ 6 kcal/mol ~ 2000 cm-1) between the three degenerate ground states.
The resonance energy which mixes the valence bond structures can been estimated to be about 3000 cm-1, from about one third of the gap between the S0/S1 intersection and the S2 state.
The fact that all these energy scales are comparable suggests vibronic effects may be important requiring a full quantum treatment of the combined electronic and vibrational degrees of freedom.