Relative likelihood of encountering conical intersections and avoided intersections on the potential energy surfaces of polyatomic molecules

A principle which should prove useful in computations of couled potential energy surfaces was proposed. In particular, a theorem where U₁ and U₂ were adiabtic electronic energy levels, with U₂ the higher level by convention was proved. This paper proves a theorem which says that when one encounters a local minimum of the gap between two potential energy surfaces, almost always it was the shoulder of a conical intersection.