Curve crossing avoided

Also shown in Figures 9 and 10 are the H12 values (in cm-1) obtained by analyzing the avoided curve crossings. In Figure 11 we show plots of the natural... 

An interesting approach to SN2 reactions has been recently advanced by Shaik which leads to verifiable predictions (Shaik, 1981 Pross and Shaik, 1981 Shaik, 1982 Shaik and Pross, 1982). The basic contention of this theory is that the origin for the barrier of SN2 reactions arises from an avoided curve-crossing between two curves containing the reactant and product Heitler-London VB forms. In this treatment, the reacting pair is analysed in terms of a nucleophile being the electron donor (D) and the substrate the electron acceptor (A). For the simple reactions of type (47), the... 

The culprit is the phenomenon of retrograde condensation, which wa6 previously discussed In connection with hydrocarbon dewpoints. This can best be understood by looking at a graph of equilibrium ratios, commonly called K-values, as shown in Figure 2. We have cross-plotted a limited number of curves, to avoid confusion while Illustrating our point. 

In the projection operator formalism, which leads to a rigorous basis for the optical potential, the absorptive imaginary part is associated with transitions out of the elastic channel from which no return occurs. Whereas Pgl transitions are in this category, excitation transfer (ET) transitions are not, since return ( virtual excitation ) can occur during the ET collision. In the event that a localized avoided curve crossing with one other state dominates the inelastic process (expected for many endoergic transfers), the total absorption probability (opacity) can still be defined ... 

Fig. 2. Schematic potential curves showing avoided crossing in higher approximation. The full curves A and B are electronic eigenvalues (with r as parameter) for the complete Hamiltonian, neglecting coupling with nuclear motion. The zero order curves A and B0, including dashed parts through the crossing point, intersect because they are derived from an incomplete Hamiltonian. The arrow represents the possibility of spontaneous radiation from the A state to the...

Conditions 1-4 optimize the position of the zero-order curve crossing, and conditions 5-7 optimize the degree to which crossing is avoided. ... 

It is still surprising that so many of the reactions in water show the correlation between AG°5 and AG+. No theory of which we are aware anticipates such a correlation. The theory of curve crossings (9-11 S. Shaik, personal communication, 1985) ascribes the activation barriers for these reactions to an avoided crossing of surfaces, one for a diradical state and the other for an ionic state. The two surfaces, however, are related by vertical transitions, and solvation energies, particularly, make these far different from the adiabatic differences such as AG°5 (S. Shaik, personal communication, 1985). Unfortunately, the fundamental data necessary to even begin to apply this theory to the present reactions are not available. 

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