Time-reversal symmetry conical intersections

D. Perturbation Theory, Time-Reversal Symmetry, and Conical Intersections... 

Prom Table 1, it is seen that there is more than one type of conical intersection. For molecules with even (odd) / = 2 (77 = 3 or 5). The origin of the differences is, as explained by Mead, time reversal symmetry. For odd (even) and are (are not) linearly independent. Here T is the time reversal operator. See appendix A. Thus for odd (even) electron systems, the intersection of two potential energy surfaces requires the degeneracy of four (two) electronic states. As discussed below, this leads to the values of 77 reported in Table 1. 

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