Conical intersections geometric phase effect

The phase-change nale, also known as the Ben 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 bansported in a closed loop around a point of conical intersection. Any one of them may be used in the search for degeneracies. 

Han S, Yarkony DR (2003) Conical intersections of three states. Energies, derivative couplings, and the geometric phase effect in the neighborhood of degeneracy subspaces. Application to the allyl radical. J Chem Phys 119 11562... 

C2H-molecule (1,2) and (2,3) conical intersections, 111-112 H3 molecule, 104-109 Wigner rotation matrix and, 89-92 Yang-Mills field, 203-205 Aharonov-Anandan phase, properties, 209 Aharonov-Bohm effect. See Geometric phase effect... 

Geometric phase effect (GPE) conical intersections, 4-8 adiabatic eigenstates, 8-11 topographical energy, 568-569 curl equations, 11-17 degenerate states chemistry, x-xiii electronic states ... 

Geometric phase effect (GPE) (Continued) adiabatic states, conical intersections invariant operators, 735-737 Jahn-Teller theorem, 733-735 antilinear operator properties, 721-723 degenerate/near-degenerate vibration levels, 728-733... 

Spin multiplicity, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 706-711 Spin-orbit coupling conical intersections ... 

Another subtle consequence of conical intersections is the geometric phase effect [42,51], which occurs even when the dynamics is confined to low energies avoiding the neighbourhood of the CL It is the result of transporting the electronic wave function on a closed loop around the CL This leads to a sign change in the electronic wave function when it returns to its initial position... 

III. NUCLEAR WAVE FUNCTIONS AND THE GEOMETRIC PHASE EFFECT FOR CONICAL INTERSECTIONS... 

In conclusion, the conceptual aspects of the geometric phase effect for conically intersecting systems seem now to be well understood. It is important to include this effect not only for bimolecular reactions but also for photodissociation processes occurring in these systems, unless a careful analysis shows it to be nonsignificant. 

Key words Geometric phase effect - Conical intersection - Molecular Aharonov-Bohm effect -Berry s phase... 

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