On the description of conical intersections-A continuous representation of the local topography of seams of conical intersection of three or more electronic states: A generalization of the two state result

For conical intersections of two states (I,J = I + 1) the vectors defining the branching or g-h plane, the energy difference gradient vector g(I,J), and the interstate coupling vector h(I,J), can be made orthogonal by a one parameter rotation of the degenerate electronic eigenstates. The representation obtained from this rotation is used to construct the parameters that describe the vicinity of the conical intersection seam, the conical parameters, s(x)(I,J)(R), s(y)(I,J)(R), g(I,J)(R), and h(I,J)(R). As a result of the orthogonalization these parameters can be made continuous functions of R, the internuclear coordinates. In this work we generalize this notion to construct continuous parametrizations of conical intersection seams of three or more states. The generalization derives from a recently introduced procedure for using non-degenerate electronic states to construct coupled diabatic states that represent adiabatic states coupled by conical intersections. The procedure is illustrated using the seam of conical intersections of three states in parazolyl as an example. (C) 2014 AIP Publishing LLC.