Conical intersection, nonadiabatic coupling

Table 3 shows the nonadiabatic levels of B2 symmetry and their absorption intensities between 16000 and 16300 cm l. The equilibrium symmetric-stretch and bending coordinates of the electronic species are different by about 6 and 24%, respectively [17], whereas the antisymmetric stretch is equal. Therefore, the conical intersection preferably couples a2B2(vi,v2,0) combination states with their X Ai partners, but this interaction is perturbed by the A B2 antisymmetric-stretch species. Above 15000 cm l, the nonadiabatic intensity distribution is thus modulated by the maxima due to n> states with large A B2 symmetric stretch-bending character, whereas A B2 pure overtones are much weaker (e.g. bands 409 and 415 of Table 3). As the energy increases, these vibronic interactions give rise to a more and more irregular spectrum.

By following Section II.B, we shall be more specific about what is meant by strong and weak interactions. It turns out that such a criterion can be assumed, based on whether two consecutive states do, or do not, form a conical intersection or a parabolical intersection (it is important to mention that only consecutive states can form these intersections). The two types of intersections are characterized by the fact that the nonadiabatic coupling terms, at the points of the intersection, become infinite (these points can be considered as the black holes in molecular systems and it is mainly through these black holes that electronic states interact with each other.). Based on what was said so far we suggest breaking up complete Hilbert space of size A into L sub-Hilbert spaces of varying sizes Np,P = 1,..., L where... 

As a last example of a molecular system exhibiting nonadiabatic dynamics caused by a conical intersection, we consider a model that recently has been proposed by Seidner and Domcke to describe ultrafast cis-trans isomerization processes in unsaturated hydrocarbons [172]. Photochemical reactions of this type are known to involve large-amplitode motion on coupled potential-energy surfaces [169], thus representing another stringent test for a mixed quantum-classical description that is complementary to Models 1 and II. A number of theoretical investigations, including quantum wave-packet studies [163, 164, 172], time-resolved pump-probe spectra [164, 181], and various mixed... 

Figure 21.5. A schematic representation of a conical intersection between two electronic states of a molecule. Coordinates qi and q2 are the nonadiabatic coupling vector and the gradient difference vector, along which the degeneracy between the states is lifted (see color insert).

Figure 12 Computed branching space vectors (gradient difference vector xx and nonadiabatic coupling vector x2) for Sj/S0 conical intersection of benzene.

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