Landau-Zener Semiclassical Approximation

To return now to the semiclassical model of nonadiabatic behavior, one can describe reactions on the spin-state (diabatic) PESs as follows The system will move throughout phase space on the reactant PES until it reaches a point where the product PES has the same energy as the reactant one. At that point, it may either remain on the reactant PES or hop over onto the product one. The Landau-Zener formula for curve crossing in one-dimensional systems has often been used in a multidimensional context (10) as a useful approximation for the probability p with which this hop occurs, leaving (1 - p) oi the trajectories to continue on the initial PES (Fig. 1) ... 

To use Eq. [55], one must estimate the nuclear speed R along the reaction coordinate in question. A harmonic approximation for the reaction coordinate (e.g., the S-S stretching coordinate for the example in Figure 2) affords a simple means to do this, " and one that is consistent with the semiclassical nature of Landau-Zener theory. Having computed the (linear) harmonic frequency v for the mode in question, using some flavor of quantum chemistry, one may compute the classical turning points of the harmonic potential ... 

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