Hyperline, -dimensional

The same classification into winding numbers can be used in a system with N nuclear degrees of freedom, in which the Cl seam is an N — 2)-dimensional hyperline as in Fig. 1. For example, if we take N = 3, then the seam is a line the... 

Different topological situations are possible for unavoided crossings between surfaces. One can have intersections between states of different spin multiplicity [an (n - l)-dimensional intersection space in this case, since the interstate coupling vector vanishes by symmetry], or between two singlet surfaces or two triplets [and one has an n - 2)-dimensional conical intersection hyperline in this case]. We have encountered situations in which both types of... 

Figure 6.5. Conical intersection of two potential energy surfaces S, and Sg the coordinates x, and Xj define the branching space, while the touching point corresponds to an (F - 2)-dimensional hyperline. Excitation of reactant R yields R, and passage through the funnel yields products P, and P, (by permission from Klessinger, 1995).

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