Conical intersections (CXs) play a central role in photophysics and photochemistry, 1,2 serving as the "funnels" for nonadiabatic dynamics between coupled potential energy surfaces representing different electronic states. For the special case of two coupled electronic states, the CX is really a "conical seam" of dimension N int -2 where N int is the number of internal (vibrational) degrees of freedom. Within this (N int -2)dimensional subspace the two states in question are degenerate, and when plotted in two dimensions this seam collapses to a point and the topology is that of a double cone, hence "CX". For points within the seam space, even an infinitesimal displacement outside of this space will lift the degeneracy, and this twodimensional "branching space" is spanned by a pair of nonorthogonal vectors that are usually labeled g and h. For a two-state intersection between Born-Oppenheimer electronic potential energy surfaces E J (R) and E K (R), these branching-plane vectors consist of the gradient-difference vector,