Conical intersections phase-change rule

We can now proceed to discuss the phase-change rule and its use to locate conical intersections. 

In this section, the systematic search for conical intersections based on the Longuet-Higgins phase-change rule is described. For conciseness sake, we limit the present discussion to Hiickel-type systems only, unless specifically noted otherwise. The first step in the antilysis is the determination of the LH loops containing a conical intersection for the reaction of interest. 

Localized molecular orbital/generalized valence bond (LMO/GVB) method, direct molecular dynamics, ab initio multiple spawning (AIMS), 413-414 Longuet-Higgins phase-change rule conical intersections ... 

The phase-change rule, also known as the Berry phase [101], the geometric phase effect [102,103] or the molecular Aharonov-Bohm effect [104—106], was used by several authors to verify that two near-by surfaces actually cross, and are not repelled apart. This point is of particular relevance for states of the same symmetry. The total electronic wave function and the total nuclear wave function of both the upper and the lower states change their phases upon being transported in a closed loop around a point of conical intersection. Any one of them may be used in the search for degeneracies. 

S. Zilberg, Y. Haas, Chem. Eur. J. 5, 1755 (1999). Molecular Photochemistry A General Method for Localizing Conical Intersections Using the Phase-Change Rule. 

To apply the phase-change rule discussed in the previous section, we choose the reactant A with wave function A> and the two chemically equivalent products B and C with wave functions B> and C>, which differ by a rotation of the methylene group through 180, as anchors as indicated in Figure 6.7. The transition from B to C involves a HOMO-LUMO crossing and hence is phase-inverting, whereas the transitions from A to B or C are equivalent the total number of phase changes on the closed-loop A-B-C-A is thus odd, and a conical intersection must be contained within the loop. The... 

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