Mapping the intersection space of the ground and first excited states of fulvene

Constrained optimizations in the space of S-1/S-0 intersection are used to map the seam of degeneracy at which the singlet-excited state of fulvene undergoes radiationless decay to the ground state. The relevant seam of intersection lies along a coordinate composed of methylene torsion and C-C bond inversion, and connects the conical intersection (CI) minima of C-2v and C-2 symmetry. These results are consistent with a previous second derivative analysis of the CI minima, and also with MMVB dynamics, for which decay to the ground state occurs at all twisted angles. The constrained optimizations are carried out using a conical intersection optimization algorithm based on projected gradients. The constraint is applied before projection, in order to avoid optimization errors due to cancellation between the components of the composite optimization gradient.