Avoided crossing of states

Figure 14.9. (a) Orbital correlation diagram for the direct insertion of carbene into an olefin to form cyclopropane. Symmetry classification is with respect to the vertical bisecting mirror plane. (b) State correlation diagram showing the intended correlations and the avoided crossing of states So and S2. 

Pulsed field ionization of an alkali atom differs from the description just given for H because of the finite sized ionic core, or equivalently, the nonzero quantum defects. There are three important effects. First, the zero field levels can only be spherical nim levels, not parabolic levels. Second, in the E > l/3n5 regime there are avoided crossings of states of different n. Third, ionization can occur at lower fields than in H. Specifically, in H blue states have higher ionization fields than red states, but in an alkali atom this is not the case due to nx changing ionization. 

An (avoided) crossing of So and Si need not even always correspond to a minimum in the excited state surface 64a>. Fig. 1 shows that this will depend on the slopes of the surfaces. Even such crossings which do not actually lead to a minimum in the excited state surface will be called funnels since they can provide efficient return to So- Further, if S2 lies very close to Si, vibronic coupling may make it impossible to describe the nuclear motion as specifically due to only one or the other hypersurface and both will have to be considered. Then, whether Si or S2 undergoes an avoided crossing with So may be immaterial — a funnel is still present and return of the molecule to So probable. 

The EF is the lowest excited state of the same symmetry as the ground state. Its potential energy curve has two deep and well-separated minima (at R = 1.91 and 4.40 bohr), resulting from the avoided crossing of two... 

In conclusion, selective HT quenching of Sf and CB by AN and MA yielded Xc=120, X = 240, and tdpcb = 380 psec, which is attributed to the isomerization via the twisting only in c-Sf. It is also suggested that diabatic isomerization from c-St to l-St proceeds via an avoidable crossing of the D2, Di, and Dq states. To determine the x of M with = can be essentially applied to any M , although it is necessary to find an appropriate molecule as a selective hole quencher. Moreover, the x of M must be longer than 50 psec, because [AN] is 2 M at the maximum to keep the solvent property. 

Fig. 7 Energy diagram showing the avoided crossing of Na" -Cl and Na+Cl configuration curves. State curves resulting from configuration mixing are indicated by dotted lines...

The application of correlation diagrams to photochemical processes goes back to the early work of Laidler and Shuler (1951). More recently, Longuet-Higgins and Abrahamson (1965) showed how orbital-symmetry correlations may be converted into state-symmetry correlations. Here the fundamental consideration is that states of the same symmetry do not cross, i.e. the result is an avoided crossing, while states of different symmetry do cross. The principles involved are illustrated in Fig. 19 for the dimerization of... 

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...

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