General Surface Crossings

When two (or more) potential energy surfaces corresponding to different electronic states of a chemical system are close to one another in energy, the electronic wave function should really be written as a linear combination of the different adiabatic wave functions. For simplicity, let us consider the case of only two states, in which case we would write 

Unfortunately, Eq. (15.45) does not admit to simple analytic solutions under realistic sets of chemical conditions. Moreover, if we now try to extend Eq. (15.43) to its time-dependent 

Various models to compute the probability of hopping exist. One of the simplest is the Landau-Zener model for avoided crossings in a single coordinate. The probability of the hop is determined as 

More sophisticated hopping schemes have been proposed for multi-dimensional surfaces and for more general situations than avoided crossings (see, for example, TuUy 1976 Hack et al. 2001 Heller, Segev, and Sergeev 2002). However, further discussion on this topic is not undertaken here. 

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It is definitely necessary to extend this kind of theory to a general case in which the ordinary transition state and the potential surface crossing position are separated from each other. 

The effect of the FC term on ICT and MLCT-based chemosensors appears when the electron transfer rate constant is generalized within the context of nonradiative decay theory [191-193], MLCT excited states are produced directly upon excitation whereas ICT states are produced by a surface crossing from an initially prepared localized excited state (see Fig. 9). Return of the system from the charge transfer excited state to ground state has the overall form of an electron transfer recombination problem that is described by the inverted Marcus curve of Fig. 13. As described by the FC term of Eq. (5), the rate constant for... 

Generally, the occurrence of unimolecular radiationless transitions such as internal conversion and intersystem crossing may be inferred from quantum yield measurements. The common experimental observation in such cases is the lack of a net reaction after absorption of a photon. The Franck-Condon principle that implies radiative transitions with quantum yields of less than unity also applies to radiationless processes, as it prohibits vertical transitions between surfaces separated by large energy gaps and favors those at Zero Order surface crossings. 

There are several ways in which a femtosecond laser pulse can nigger chemical transformations at a surface. Direct optical excitation of the adsorbates is a process of very low probability, owing to the generally small cross section for such processes. The laser pulse can, however, efficiently create excited elecnons in the metal near the surface (the optical penettation depth is typically -10 nm), which rapidly thermalize to a hot Fermi-Dirac distribution by electton-elecnon scattering... 

Photochemical surface reactions of polymer systems are an important field not only from the point of view of micro-electronic materials processing, but also from a more general scientific and materials application perspective. We have reviewed our studies in this field, which include investigations of excimer laser ablation, studies of the photo-oxidation of polymer surfaces, and the use of surface cross-linking and surface polymer depositions for microlithographic applications. With the increasing miniaturization of microelectronic devices, the fundamental and the applied aspects of surface photochemistry of polymers becomes increasingly important. 

In the previous section we gave an overview of some general reaction profiles for photochemistry and highlighted the role of surface crossings. We will now give a description of surface crossings as conical intersections in simple theoretical... 

Photochemical Reactions.—The use of correlation diagrams in chemical dynamics has been discussed in a review article,510 and the problem of potential-surface crossing in diatomic511 and polyatomic molecules has been widely considered in several papers.512 A paper has appeared concerned with the quantum-mechanical expression to describe the relaxation processes in a chemically reacting gas under monochromatic (laser) excitation.513 Other quantum theories of molecular photodissociation have also been published.514 These are too extensive for detailed consideration here, but in general provide solvable models for small-molecule reactions. 

Figure 2 is a microscopic rejjresentation of a near-surface cross section of energetic material. The stippled rectangles represent the general nonhomogenous (made up of more than one type of stufl) and nonisotropic (stuff... 

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