Conical intersections handling

The Landau-Zener model illustrates the important variables influencing the probability of non-adiabatic transitions, but as a ID model it is only applicable to bimolecular reaction of two atoms. For most reactions of interest it is too simple to provide accurate results. For reactions involving more than two atoms the PESs are multidimensional, as we have seen above, and the avoided crossing region on a multidimensional surface is described as a conical intersection [61]. The best method for handling this complex multidimensional reactive scattering problem is trajectory calculations. Fernandez-Ramos et al. [52] has discussed approaches to this problem as part of a recent review of bimolecular reaction rate theory. It is fortunate that the vast majority of chemical reactions occur adiabatically. It will only be necessary to delve into the theory of non-adiabatic reactions when a non-adiabatic reaction is present in a reaction model, experimental data are not available, and the reaction rate influences the overall rate appreciably. 

To handle the complex reactive process, we first focus on the dynamics on the Si surface to study how the system evolves towards the conical intersections. Therefore we introduce a reduced set of reactive coordinates, develop the corresponding Hamiltonian and study the time evolution of the system by means of wavepacket propagations on the calculated ah initio potential reaction surface. In the following steps, we include the nonadiabatic coupling elements as well as the laser-molecule interaction to describe the complete relaxation process. The final aim is to drive the reaction systematically through either one or the other of the two conical intersections and thus to influence the resulting product distribution. 

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