Curve crossing model

The forbidden retro-[ls -I- 2s]-cycloaddition can now be treated using a simple curve-crossing model analagous to the Marcus-Hush theory of electron-transfer [11]. The ground state at the quadricyclane-like geometry is the... 

Within a local complex potential curve crossing model, the cross section for the simple DEA reaction e + AB AB A + B, where AB is a diatomic molecule, may be expressed as [18]... 

Carrean-Yasnda Model (full curve) Cross Model (full curve) For portions of the Cross equation that predict portions of the complete flow curve h-ih, 1 ho-1 . [1 + (k1y)2P 2 110-11 =(KiT Tl-11 1 oo... 

Phulkar S, Rao BSM, Schuchmann H-P, von Sonntag C (1990) Radiolysis of tertiary butyl hydroperoxide in agueous solution. Reductive cleavage by the solvated electron, the hydrogen atom, and, in particular, the superoxide radical anion. Z Naturforsch 45b 1425-1432 Pross A, Yamataka H, Nagase S (1991) Reactivity in radical abstraction reactions - application of the curve crossing model. J Phys Org Chem 4 135-140 Rao PS, Flayon E (1975) Reaction of hydroxyl radicals with oligopeptides in aqueous solutions. A pulse radiolysis study. J Phys Chem 79 109-115... 

A. Pross, H. Yamataka, S. Nagase, J. Phys. Org. Chem. 4, 135 (1991). Reactivity in Radical Abstraction Reactions Application of the Curve Crossing Model. 

A last method to be mentioned here of simplifying the description of polyatomic interactions is a simple modification of the two-particle curve crossing model. The two-particle LZ cross section (13) is based upon the assumption that both crossings to be passed are completely equivalent, i.e. they are... 

The very basic mathematics, i.e., Stokes phenomenon, which underlies semiclassical theory, is briefly explained in this section by taking the Airy function as an example. The Stokes constant and connection matrix in the case of the Weber function are provided, since the Weber function is useful in many applications. Finally, the Stokes phenomenon of the linear curve-crossing model discussed in Sec. IV is explained briefly. 

We thank the Israel Commission for Basic Research for financial support. We are grateful to Professor R. D. Levine for suggesting the curve-crossing model and for his enlightening discussions. 

The third situation, figure 3.13(c), is an example of electronic predissociation. That is, the molecule passes from one electronic state, which is bound, to a dissociative state. The reaction rate is then dependent on the strength of the coupling between the two surfaces, a problem that can be understood by curve crossing models... 

The latter is, except for a couple of terms related to solvent reorganization, the Marcus equation. It should be noted that such curve-crossing models have been used in connection with VB methods to rationalize chemical reactivity and selectivity in a more general sense. ... 

To define a curve-crossing model one needs to define an effective force constant and bond length. The bond order of the cyclic state through which one can admit the reaction to proceed has n=7/6=1.17. From typical bond length data for a C-C and C=C bonds [33]... 

Our purpose has been to review the MC-SCF method with particular reference to transforming to a VB model in order to interpret the results. While theoretical computation can now yield accurate and detailed information about chemical reactivity, with present computing technology, we will always be limited to the study of prototype reactions. Thus we must also try to understand why the potential surfaces have the topology they have in terms of simple models. The examination of models that reproduce the computed surface topology is very important because it allows one apply the results obtained obtained for prototype systems in a qualitative way to real systems. In particular it can be seen that the empirical models such as the Evans [25J curve crossing model that has been extensively applied recently by Shaik[26] and co-workers can now be implemented rigorously. 

In agreement with the foregoing predictions, SH3 has been shown, by recent post-SCF computations, to display a tiny barrier for decomposition to SH2 + H [65 b]. As for SiH 5, the prediction of the curve crossing model is at variance with the interpretation of experimental observations by Nakamura et al. [64]. Some confirmation of our theoretical prediction is provided by a high-level ab-initio study [65 a] which has shown that SiH 5 is a true transition state, above SiH4 -h H. Further experimental confirmation appears to be underway [68]. 

We are just beginning to explore the fascinating area of hypercoordination, but a global picture with three classes of hypercoordination already emerges from the curve crossing model. The species of the different classes share one common feature, they all possess delocalized electrons and multi-center bonding . The three classes differ though in the manners by which this electronic delocalization is stabilized or not with respect to the normal-coordinated constituents. STATEMENT 6 summarizes the main features of these classes. 

The Landau-Zener theory of curve crossing model... 

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