Escape from the double cone: optimized descriptions of the seam space using gateway modes

The conceptual description of nuclear dynamics near a conical intersection generally focuses on the branching plane, the two-dimensional subspace in which the conical topography is evinced, to the exclusion of the seam coordinates, the remaining internal nuclear coordinates. Establishing the limits of the utility of this assumption is an important issue in nonadiabatic dynamics. To accomplish this a careful treatment of the nuclear dynamics near conical intersections is required. The coordinate systems generally available for describing conical intersections are not optimal for such studies. In this work we extend a perturbative description of a conical intersection to describe more general seam spaces. We develop a coordinate system that segregates the interactions coupling the branching plane to the seam space into a set of gateway modes. The size of this set does not increase with the size of the molecule. The gateway modes are illustrated for the 1,2 1A conical intersections in NH3. The connection between the gateway modes and the optimum coordinate system for locating and characterizing seam confluences, intersections of two branches of the same seam, is discussed.