Avoided crossing model

The results of the derivation (which is reproduced in Appendix A) are summarized in Figure 7. This figure applies to both reactive and resonance stabilized (such as benzene) systems. The compounds A and B are the reactant and product in a pericyclic reaction, or the two equivalent Kekule structures in an aromatic system. The parameter t, is the reaction coordinate in a pericyclic reaction or the coordinate interchanging two Kekule structures in aromatic (and antiaromatic) systems. The avoided crossing model [26-28] predicts that the two eigenfunctions of the two-state system may be fomred by in-phase and out-of-phase combinations of the noninteracting basic states A) and B). State A) differs from B) by the spin-pairing scheme. 

Zeno paradox. On the other hand, recovering these interferences from a single path leads to excessive correlation, as evidenced by the highly oscillatory results obtained with TSH for Tully s third, extended coupling with reflection, model. This is remedied effortlessly in FMS, and one may speculate that FMS will tend to the opposite behavior Interferences that are truly present will tend to be damped if insufficient basis functions are available. This is probably preferable to the behavior seen in TSH, where there is a tendency to accentuate phase interferences and it is often unclear whether the interference effects are treated correctly. This last point can be seen in the results of the second, dual avoided crossing, model, where the TSH results exhibit oscillation, but with the wrong structure at low energies. The correct behavior can be reproduced by the FMS calculations with only ten basis functions [38]. 

This avoided crossing model for describing a reaction barrier is striking in its generality. It has been applied in a detailed theoretical analysis to reaction... 

Despite our natural satisfaction with this explanation, we noted that it nevertheless does not provide a clear physical mechanism for the effect. For example, it was not evident why the frequency exaltation is state selective, i.e., it is not observed in any other state, and the frequency of all other modes are reduced upon excitation. It was deemed necessary, therefore, to articulate the avoided crossing model, derive a clear physical origin of the frequency exaltation of the Kekule mode, its state, and mode specificity, and establish the connection of the phenomenon to the jr-distortivity in the ground state. This was achieved in 1996.209... 

Fig. 2. Simple ID scattering avoided crossing model. Energies and distances are in atomic units. Solid and short dashed are the two diagonal diabats, long dashed curve is the off-diagonal diabat, dotted, and dash dot are the adiabatic energy surfaces...

On the basis of these observations, Teller proposed that conical intersections provide a very fast decay channel from the lowest excited states of polyatomics that would explain the lack of fluorescence from the excited state. Despite the fact that the ideas of Teller, Zimmerman, Michl and Salem represented an important refinement of the avoided crossing model, conical intersections were thortght to he extremely rare or inaccessible (i.e. located too high in energy) in organic compoimds and thus were disregarded for many years. 

Tsuji, H. Toshimitsu, A. Tamao, K. Michl, J. UV, MCD, and LD Spectra of a Conformationally Constrained Ortho-Tetrasilane Support for the Avoided Crossing Model of Conformational Effects on Excited State. J. Phys. Chem. A 2001, 105, 10246-10248. 

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