Geometric phase effect , molecular systems

Potential fluid dynamics, molecular systems, modulus-phase formalism, quantum mechanics and, 265—266 Pragmatic models, Renner-Teller effect, triatomic molecules, 618-621 Probability densities, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 705-711 Projection operators, geometric phase theory, eigenvector evolution, 16-17 Projective Hilbert space, Berry s phase, 209-210... 

The discussion so far has focused on two-state conical intersections, which are the most common conical intersections, and which have been studied extensively. Three-state degeneracies imposed by symmetry have been studied in the context of the Jahn-Teller problem for many decades,but only minor attention had been given to accidental three-state degeneracies in molecules until recently. As most molecular systems in nature have low or no symmetry, these accidental intersections may have a great impact on the photophysics and photochemistry of those molecular systems, as has been found in accidental two-state intersections.Three-state degeneracies may provide a more efficient relaxation pathway when more than one interstate transition is needed. Moreover, they introduce more complicated geometric phase effects,and they can affect the system s dynamics and pathways available for radiationless transitions. 

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

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