Avoided crossing definition

Fig. 28. Schematic of potential energy surfaces of the vinoxy radical system. All energies are in eV, include zero-point energy, and are relative to CH2CHO (X2A//). Calculated energies are compared with experimentally-determined values in parentheses. Transition states 1—5 are labelled, along with the rate constant definitions from RRKM calculations. The solid potential curves to the left of vinoxy retain Cs symmetry. The avoided crossing (dotted lines) which forms TS5 arises when Cs symmetry is broken by out-of-plane motion. (From Osborn et al.67)...

Figure 15.7 Near approach (or avoided crossing) of two electronic states as a function of nuclear coordinate Q. The inset expands the region of the avoided crossing to facilitate the definition of quantities appearing in the Landau-Zener surface-hopping-probability model...

Wolfsberg-Helmholtz, 43 zero-overlap, 38, 40 Aromaticity, 150 Aromatic compounds, 150-160 Arsenium ions, 119 Asymmetric synthesis definition, 9 Avoided crossing, 206... 

The frequency exaltation of the Kekule-type b2u modes of the electronically excited l B state is not limited to benzene and its derivatives. A similar observation was made by Michl and co-workers238 for [ 14]-annulene, who explained the phenomenon in terms of the avoided crossing of the Kekule structures similar to the above. Other hydrocarbons such as naphthalene, anthracene, etc. have been reported to exhibit the same phenomenon. Thus, in naphthalene,239240 the Kekule-type mode undergoes a frequency exaltation of 189 cm 1 in the 11 B2u state relative to the ground state. In anthracene, two Kekule-type modes exist. One was assigned and undergoes an upshift of 231 cm-1.241-243 The second anthracene mode has not been definitely assigned yet. It is calculated to be exalted by 96 cm-1.243... 

We now discuss the A = +1 CD in more detail. Three features will be stressed which describe the saddle behaviour of the MO. The first has already been discussed in connection with the definition of dia-batic MO cmves [6a,b] asymptotic to the R— oo three-body breakup threshold. Each stiff MO, with positive energy gradient at il = 0, has fixed quantum numbers (nA,0,m) and is the precursor of a complete in-saddle sequence of MO whose other members are all promoted MO with quantum numbers (ha, = even, m). The promoted MO show avoided crossings with other members of the sequence [6c]. The dia-batic connection of all avoided crossings connects the stiff precmsor MO near il = 0 with the R oo three-body break-up threshold. Note that the precursor MO are those e with positive gradient near J2 = 0 in Fig. la and are therefore easily recognised. 

While photocycloadditions are typically not concerted, pericyclic processes, our analysis of the thermal [2+2] reaction from Chapter 15 is instructive. Recall that suprafacial-suprafacial [2+2] cycloaddition reactions are thermally forbidden. Such reactions typically lead to an avoided crossing in the state correlation diagram, and that presents a perfect situation for funnel formation. This can be seen in Figure 16.17, where a portion of Figure 15.4 is reproduced using the symmetry and state definitions explained in detail in Section 15.2.2. The barrier to the thermal process is substantial, but the first excited state has a surface that comes close to the thermal barrier. At this point a funnel will form allowing the photochemical process to proceed. It is for this reason that reactions that are thermally forbidden are often efficient photochemical processes. It is debatable, however, whether to consider the [2+2] photochemical reactions orbital symmetry "allowed". Rather, the thermal forbiddenness tends to produce energy surface features that are conducive to efficient photochemical processes. As we will see below, even systems that could react via a photochemically "allowed" concerted pathway, often choose a stepwise mechanism instead. 

For the s Tnmetry allowed conical intersection and the symmetry required conical intersection as well (the definition due to Yarkony, see Ref. [117]), the mechanism of converting conical intersection to avoided crossing and the role of the laser have been thus evident. Yet, even for other types of conical intersection, the conversion of conical intersection by an appropriate choice of VE(i2, t) may be possible depending on the electronic-state origin [316] of the appearance of the degeneracy. Therefore the idea of laser conversion of conical intersection is worth further investigation both experimentally and theoretically. 

In the remaining cases, the Cl crosses between zones and the result is ambiguous. We are limited as to what conclusions can be drawn and judgement has to be exercised. The only definite thing we can say in (d) is that it is not doing any good, since none of the 95 per cent Cl extends into the zone of practical benefit. Most of the Cl is in the zone of practical detriment, so we would almost certainly want to avoid whatever caused this effect, even if it is not yet proven to be doing practical harm, (e) definitely does no practical harm, and may be beneficial. The Cl is quite wide and a... 

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