Origin of the conical intersection between the singlet ionic excited surfaces of twisted ethylene

The potential surfaces of the two valence ionic singlet excited states of twisted ethylene are known to exhibit a conical intersection for a twist angle of the double bond near 82°, and no pyramidalization of the CH₂ groups. The factors responsible for the stabilization of the symmetric excited state near 90° are shown to be ( )² and ( ^*)² double excitations. The analysis is performed in the Quasi Degenerate Perturbation Theory formalism. The analogy with the ¹A_g³B_u ordering problem of the diradical ground and lower triplet states through a double spin polarization of the system is established.