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. 

Figure 13. A scheme for energy transfer from excited Cr to Nd. Despite the varying transition synunetries, the energy of the two transitions shown by slanted arrows are similar enongh so that there can be a coupled resonance (wiggly arrow 4) between them. This is sometimes called a resonance radiationless transition. In this kind of diagram the curved states of the configurational coordinate plot (Fig. 1) are collapsed to show the band width in energy. Wiggly lines indicate non-radiative transitions due to the crossing of state levels and vibrational heat loss. Modified after Marfimin (1979).

The state correlation diagram for the [2+2] cycloaddition of Eq. 15.1. The intended crossing of states witli like symmetry is shown with dotted lines, while the avoided crossing is shown as a solid colored line. 

Transition state geometries for reactions of open-shell molecules, particularly radical ions, pose special problems for DFT methods. In contrast to closed-shell systems whose ground state wavefunction is always totally symmetric, rearrangements of radicals and radical ions frequently involve crossings of states of different symmetry. In this situation, the molecule must lose symmetry to effect an adiabatic passage from reactants to products. In radical ions this loss often involves a localization of spin and charge, and it seems that DFT methods tend to oppose this localization. 

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