Landau-Zener-Stueckelberg theory

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... 

Then fie may be thought of as the phase accumulated by the function C](r) during the period /3. To find B in (C.7) we should compare the phase < (/6 + t,t) to that calculated in the adiabatic approximation 4>sd. According to the standard arguments of Landau-Zener-Stueckelberg theory, this difference arises mostly from passing the point Q(r ) = Qc where the adiabaticity is violated. In the vicinity of this point Eqs. (C.9) simplify to... 

According the standard arguments of the Landau-Zener-Stueckelberg theory, this difference emerges mostly from passing the point Q x ) = Qc where the adiabaticity is violated. In the vicinity of this point eqs. (B.9) simplify to... 

The problem of nonadiabatic tunneling in the Landau-Zener approximation has been solved by Ovchinnikova [1965]. For further refinements of the theory beyond this approximation see Laing et al. [1977], Holstein [1978], Coveney et al. [1985], Nakamura [1987]. The nonadiabatic transition probability for a more general case of dissipative tunneling is derived in appendix B. We quote here only the result for the dissipationless case obtained in the Landau-Zener limit. When < F (Xe), the total transition probability is the product of the adiabatic tunneling rate, calculated in the previous sections, and the Landau-Zener-Stueckelberg-like factor... 

Equation (96) differs from those found earlier by Stueckelberg [15] and Bates [89], Stueckelberg [15] used the perturbation theory to calculate PAB (b) at b > jPc and applied a Landau-Zener type of formula for b < Re. It was then found that the main contribution to distant collisions with b > PC. ... 

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