conical intersection 

https://doi.org/10.1351/goldbook.CT07347
Point of crossing between two electronic states of the same spin multiplicity (most commonly singlets or triplets).
Notes:
  1. In a polyatomic molecule two potential energy surfaces are allowed to cross along a (3N − 8)-dimensional subspace of the (3N − 6)-dimensional nuclear coordinate space (the intersection space) even if they have the same spatial/spin symmetry (N is the number of nuclei). Each point of the intersection space corresponds to a conical intersection. If the energy is plotted against two special internal geometrical coordinates, x1 and x2, which define the so-called branching plane, the potential energy surface would have the form of a double cone in the region surrounding the degeneracy. In the remaining (3N − 8) directions, the energies of the ground and excited state remain degenerate; movement in the branching plane lifts the degeneracy.
  2. From a mechanistic point of view, conical intersections often provide the channel mediating radiationless deactivation and photochemical reaction.
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 317 [Terms] [Paper]