A Hamiltonian, Hd,(2), “rigorously” diabatic in the vicinity of Rx, a point of conical intersection, is constructed using second-order degenerate perturbation theory. Near an Rx on a C2v seam of conical intersection of two states of different symmetry, Hd,(2) may exhibit a confluence with a Cs seam of conical intersection of two states of the same symmetry. Thus by construction, there exists a “rigorous” diabatic representation of the vicinity of this confluence. A procedure for defining a unique linear combination of the degenerate states at a conical intersection is found to be useful for determining the parameters for Hd,(2) and for identifying approximate symmetries in situations where point group symmetry is rigorously absent.

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