Diabatic reaction, definition

Closely related to the above merit of VB methods, the unique definition of diabatic states also allows us to derive the energy profiles for diabatic states. Since for many reactions the whole process can be described with very few resonance structures, the comparison between the diabatic and adiabatic state energy profiles can yield insight into the nature governing the reactions [22-24]. In fact, even for complicated enzymatic reactions, simple VB ideas have shown unparalleled value [25, 26]. However, the further utilization of the VB ideas at the empirical and semi-empirical levels should be carefully verified by benchmark ab initio VB... 

The use of the energy-gap reaction coordinate allows us to calculate solvent reorganization energies in a way analogous to that in the Marcus theory for electron transfer reactions.19 The major difference here is that the diabatic states for electron transfer reactions are well-defined, whereas for chemical reactions, the definition of the effective diabatic states is not straightforward. The Marcus theory predicts that... 

There are several fundamental reasons why the GMH and adiabatic formulations are to be preferred over the traditionally employed diabatic formulation. The definition of the diabatic basis set is straightforward for intermolecular ET reactions when the donor and acceptor units are separated before the reaction and form a donor-acceptor complex in the course of diffusion in a liquid solvent. The diabatic states are then defined as those of separate donor and acceptor units. The current trend in experimental design of donor-acceptor systems, however, has focused more attention on intramolecular reactions where the donor and acceptor units are coupled in one molecule by a bridge.The direct donor-acceptor overlap and the mixing to bridge states both lead to electronic delocalization, with the result that the centers of electronic localization and localized diabatic states are ill-defined. It is then more appropriate to use either the GMH or adiabatic formulation. 

A second obvious problem with the ordinary definition of adiabatic reactions is the vagueness of the term product. If the product is what is actually isolated from a reaction flask at the end, few reactions are adiabatic. (Cf. Example 6.7.) If the product Is the first thermally equilibrated species that could in principle be isolated at sufficiently low temperature, many more can be considered adiabatic. A triplet Norrish II reaction is diabatic if an enol and an olefin are considered as products. It would have to be considered adiabatic, however, if the triplet 1,4-biradical, which might easily be observed, were considered the primary photochemical product. (See Section 7.3.2.)... 

The introduction of VB structures (the empirical nature of EVB does not matter here) makes easier the description of the process in terms of diabatic potential surfaces. The latter have been used to describe reactions in vacuo since long time, more than 30 years before the formal definition given by Smith (1969), and continue to represent an important tool for an accurate study of many chemical processes in vacuo (see e.g. the reviews given by Sidis (1992) and by Pacher et al. (1993)), and for qualitative and semiquantitative characterizations of organic reactions (see e.g. Shaik and Hiberty, 1991). Their use in solution has been spurred by Marcus model on electron transfer (ET) reactions (Marcus, 1956), and extended by the Russian school in the sixties to other chemical processes (Levich and Dogonadze, 1959 Levich, 1966 Dogonadze, 1971 German et al., 1971, Albery, 1980). 

We have also learned that the use of diabatic descriptions is very instrumental to describe the dynamics of reactions. This theme has been treated more in detail in another Section. The EVB description introduced by Warshel is very effective in describing the essential aspects of the phenomenon. Here, researcher s good physical sense and experience play an essential role in selecting the VB structures to be used, and the level of approximation in the description of Hamiltonian matrix elements. The chemical approach to the problems of reactions (we introduce again a difference between physical and chemical approach to a problem of molecular sciences) requires more details and more precision the definition of VB methods for accurate description inserted in foolproof computational packages to be used by non-specialists, still constitutes a serious challenge. 

States that most resemble the initial and final states of electron transfer have been often referred to as diabatic states [24, 25] and their corresponding wavefunctions diabats . Although it is known that diabatic states have a formal definition [26, 27], it was shown [28] that charge-localized states satisfy the requirements for diabatic states for condensed phase electron transfer reactions. 

When considering reaction paths on the PE surfaces of excited states, as required for the rationalization of photochemistry [4], two major additional complications arise. First, reliable ab initio energy calculations for excited states are typically much more involved than ground-state calculations. Secondly, multi-dimensional surface crossings are the rule rather than the exception for excited electronic states. The concept of an isolated Born-Oppenheimer(BO) surface, which is usually assumed from the outset in reaction-path theory, is thus not appropriate for excited-state dynamics. At surface crossings (so-called conical intersections [5-7]) the adiabatic PE surfaces exhibit non-differentiable cusps, which preclude the application of the established methods of mathematical reaction-path theory [T3]. As an alternative to non-differentiable adiabatic PE surfaces, so-called diabatic surfaces [8] may be introduced, which are smooth functions of the nuclear coordinates. However, the definition of these diabatic surfaces and associated wave functions is not unique and involves some subtleties [9-11]. 

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