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The figure shows a search for the conical intersection along a single coordinate, although two coordinates are generally required see ref 15, If a symmetry element is conserved along a phase inverting reaction path between two critical points and the two crossing states belong to different irreducible representations, a one-dimensional search is sufficient The reason is that the derivative of the electronic Born-Oppenheimer Hamihonian with respect to any symmetry-preserving coordinate is a totally symmetric operator. All matrix elements of mis operator between states of different irreducible representations and hence the coupling V vanish. This is the case: both transition states belong to C2v symmetry, the biradical TS transforms as a2 and the zwitterion TS as a1. The coordinate connecting the two transition states is a phase inverting one and the conserved symmetry element is the C2 rotation
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We are indebted to one of the reviewers for a discussion of this point
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