Multiple electronic states paths

Because the concept of minimum energy path is not well-defined when multiple electronic states are involved, the initial data set is simply taken as the union of points which one considers important on each of the electronic states—for example, local minima on each electronic state. The weights of each data point, Wi in Eq. (2.34), were taken to be the same on all electronic states because they only depend on the location of the data points. Hence, the difference between electronic states (V he[)ard(R)) is manifested only in the parameters of each of the Taylor expansions ... 

Higher-order processes contribute in both the excitation of the core electron and relaxation of the core hole. These multi-electron processes are significant because of the strong perturbation caused by the creation or the annihilation of a core hole. In these processes, additional electrons are excited (shake-up) or ionized (shake-off). Two electron processes, double autoionization and double Auger decay, were mentioned above. The final states reached in core hole decay may be excited states and also may autoionize. It is clear that excitation of a core electron and the relaxation of the core hole provide many paths leading to multiple-electron excited states. These states have a unique chemistry relative to the single-electron excited states produced by arc lamp, laser, or vacuum ultraviolet (VUV) excitation. 

In the previous sections it has been implicitly assumed that the unimolecular reaction is electronically adiabatic and, thus, occurs on a single potential energy surface. Electronically excited states (i.e., multiple potential energy surfaces) for unimolecular reactions was discussed in chapter 3 and it is assumed that the reader has read and is familiar with this material (Nikitin, 1974 Hirst, 1985 Steinfeld et al., 1989). Transitions between electronic states are particularly important for the unimolecular decomposition of ions. For example, the following two dissociation paths ... 

A further important property of a MQC description is the ability to correctly describe the time evolution of the electronic coefficients. A proper description of the electronic phase coherence is expected to be particularly important in the case of multiple curve-crossings that are frequently encountered in bound-state relaxation dynamics [163]. Within the limits of the classical-path approximation, the MPT method naturally accounts for the coherent time evolution of the electronic coefficients (see Fig. 5). This conclusion is also supported by the numerical results for the transient oscillations of the electronic population, which were reproduced quite well by the MFT method. Similarly, it has been shown that the MFT method in general does a good job in reproducing coherent nuclear motion on coupled potential-energy surfaces. 

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