Von Neumann and Wigner

The plot of the energy along 2xi and 2 3 in the second order picture is shown in Fig. 4b. In this case, the seam of intersection is a curved tine. The energy degeneracy is kept by combined displacements along and 2x3, and the first condition of von Neumann and Wigner (Equation 2) becomes ... 

If the expansion of f and /2 is truncated at first order, one obtains the analog of (3), and the energy splitting occurs only along the branching space vectors. If the second-order terms are included, one obtains the analog of (5). In this case, the conditions of von Neumann and Wigner that define the intersection space are ... 

At this point a small digression is warranted. Both the general significance of the noncrossing rule and the opposite behaviour in photochemical reactions with respect to the corresponding thermal processes have the character of an aesthetic canon. There has been considerable resistance in the literature to the new insight that the true nature of von Neumann and Wigner s proof implies that conical intersections are everywhere, and that... 

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