Landau-Zener theory dynamics

The loss of the B state population depends on both the dynamics of the vibrational relaxation and the strength of the coupling of the B state to the repulsive a/a states. In the simulations, the predissociation of the B state molecules is described with the help of the Landau-Zener theory. There, the coupling strength is given by the perturbation energy. Furthermore, the probability for predissociation also depends on the (classical) velocity v t) which relates this process to the vibrational relaxation dynamics of the B state. The theoretical model uses a friction coefficient a to describe the latter process. 

As a model for a rate process, the surface crossing picture described above can be treated within the Landau-Zener theory (Section 2.4) that yields the probability that a transition between the two electronic states occurs during one dynamical crossing event. Here Atr stands for R of Section 2.4. Using this theory to evaluate the rate of such electron transfer processes involves several assumptions ... 

The basic assumptions of the Landau-Zener theory need to be satisfied. These involve the applicability of classical mechanics (e.g. the neglect of tunneling) for the nuclear dynamics and the locality of the curve crossing event. 

Thus this book describes the recent theories of chemical dynamics beyond the Born-Oppenheimer framework from a fundamental perspective of quantum wavepacket dynamics. To formulate these issues on a clear theoretical basis and to develop the novel theories beyond the Born-Oppenheimer approximation, however, we should first learn a basic classical and quantum nuclear dynamics on an adiabatic (the Born-Oppenheimer) potential energy surface. So we learn much from the classic theories of nonadiabatic transition such as the Landau-Zener theory and its variants. 

For example, the ZN theory, which overcomes all the defects of the Landau-Zener-Stueckelberg theory, can be incorporated into various simulation methods in order to clarify the mechanisms of dynamics in realistic molecular systems. Since the nonadiabatic coupling is a vector and thus we can always determine the relevant one-dimensional (ID) direction of the transition in multidimensional space, the 1D ZN theory can be usefully utilized. Furthermore, the comprehension of reaction mechanisms can be deepened, since the formulas are given in simple analytical expressions. Since it is not feasible to treat realistic large systems fully quantum mechanically, it would be appropriate to incorporate the ZN theory into some kind of semiclassical methods. The promising semiclassical methods are (1) the initial value... 

Nonadiabatic transitions play crucial roles in various fields of physics and chemistry [1. 2. 3. 4. 5, 7, 8 9. 10], and it is quite important to develop basic analytical theories so that we can understand fundamental mechanisms of various dynamics. The most fundamental models among them are the Landau-Zener type curve crossing and the Rosen-Zener-Demkov type non-curve-crossing. Furthermore, there is an interesting intermediate case in which two diabatie exponential potentials arc... 

The dynamical behavior of strongly non-adiabatic multimode systems exhibits complex features that can perhaps be better understood by trying first to underline the aspects that they share with simple one-dimensional models basically derived from scattering theory. To this purpose we introduce a minimal model for the Cl and then discuss the limit of validity of an interpretation scheme grounded on the Landau-Zener formula as well as of a simple one-dimensional time-dependent model obtained by treating quantum-mechanically only the coupling mode. 

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