Landau-Zener formula nonadiabatic transition

This result is due to Dykhne [48] and Davis and Pechukas [49] and has been extended to A-level systems [50]. The conditions of validity of the so-called Dykhne-Davis-Pechukas (DDP) formula has been established in [51,52], This formula allows us to calculate in the adiabatic asymptotic limit the probability of the nonadiabatic transitions. This formula captures, for example, the result of the Landau-Zener formula, which we study below. 

Another practical method is TSH (18), in which ordinary classical trajectories are run until they come close to the surface crossing region where the trajectories are jumped to the other surface with probability given by the Landau-Zener formula. This method is simple and convenient, but suffers from the following drawbacks all phases are completely neglected and only the probabilities (not the probability amplitudes) are handled the detailed balance is not necessarily satisfied and nonadiabatic transitions at energies... 

The details of the nonadiabatic transition can be handled in a variety of The simplest approach is to use the Landau-Zener formula for the probability of crossing. " For a single crossing the probability of a transition from the zero-order curve corresponding to X -FHY(0) to that corresponding to X-FHY(n) is given by... 

The situation is radically different in the inverted region, as well as in certain cases of nonequihbrium back transfer (see below), which are always nonadiabatic whatever the coupling strength is. For large V, the ET rate is no longer controlled by transport to the transition region but rather by nonadiabatic transitions between adiabatic states (see Fig. 9.1). Therefore, one should expect a decrease of the ET rate with increasing V to follow the solvent-controlled plateau. Usually, the Landau-Zener formula is used for the description of nonadiabatic transitions in the classical limit [162,163]. 

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... 

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