Jahn-Teller molecule, geometrical phase

Floppy molecules, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 701-711 Floquet theory, geometric phase theory principles of, 33-36... 

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... 

II electronic states, 638-640 vibronic coupling, 628-631 triatomic molecules, 594-598 Hamiltonian equations, 612-615 pragmatic models, 620-621 Kramers doublets, geometric phase theory linear Jahn-Teller effect, 20-22 spin-orbit coupling, 20-22 Kramers-Kronig reciprocity, wave function analycity, 201 -205 Kramers theorem ... 

The model Hamiltonian of Section II captures some of the essential features of the electronic and vibrational structure of polyatomic molecules, like benzene and 5ym-triazine, that have both nondegenerate and degenerate, Jahn-Teller active, electronic levels. In this section interference experiments are described which will be sensitive to the geometric phase development accompanying adiabatic nuclear motion on either of the electronic potential energy surfaces in the Jahn-Teller pair. 

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. 

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