Landau-Zener relation

Relation to Landau-Zener Surface Hopping Rates... 

The probability P in equations (61) and (62) may be related to the electronic coupling matrix element through equation (63) by application of the Landau-Zener model ... 

In the framework of the Landau-Zener model, P is related to H by means of equation (75). These equations are also valid when both the stretching and solvent reorganization coordinates are taken into account as in the case of dissociative electron transfer. 

The probability may be related to H by application38 39 of the Landau-Zener model40 42 ... 

The probability of a diabatic hop, P, is given to good approximation by the Landau-Zener (LZ) relation, ... 

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. 

Thus a wavepacket initiated in well A passes to well B by a curve crossing. Prof. Fleming showed an interesting case of persistent coherence in such a situation, despite the erratic pattern of the eigenvalue separations. An alternative, possibly more revealing approach, is to employ Stuckelberg-Landau-Zener theory, which relates the interference (i.e., coherence) in the two different wells via the area shown in Fig. 2. A variety of applications to time-independent problems may be found in the literature [1]. 

The transmission factor is related to the transition probability (P0) at the intersection of two potential energy surfaces, as given by the Landau-Zener theory.24... 

The transition coefficient k is related to the probability of the transition in the crossing area (P) and is described by the Landau-Zener equation (Landau, 1932, Zener, 1933)... 

The well-known Landau-Zener [155-158] formula relating to the probability of an electronic jump near the crossing point of two potential-energy curves or surfaces has been seriously critiqued [4, 154], New treatments of greater validity have been formulated [154, 159, 160]. 

Relation (12) describes a thermally activated transition with activation energy = ( j — A) /4 j equal to the potential at the point of intersection. The preexponential factor in Eqn. (12) is equal to the vibration frequency co/2n multiplied by the transmission coefficient P representing the Landau-Zener factor [16] for the transition between the terms in the region of their... 

Electron-jump in reactions of alkali atoms is another example of non-adiabatic transitions. Several aspects of this mechanism have been explored in connection with experimental measurements (Herschbach, 1966 Kinsey, 1971). The role of vibrational motion in the electron-jump model has been investigated (Kendall and Grice, 1972) for alkali-dihalide reactions. It was assumed that the transition is sudden, and that reaction probabilities are proportional to the overlap (Franck-Condon) integral between vibrational wavefunctions of the dihalide X2 and vibrational or continuum wave-functions of the negative ion X2. Related calculations have been carried out by Grice and Herschbach (1973). Further developments on the electron-jump mechanism may be expected from analytical extensions of the Landau-Zener-Stueckelberg formula (Nikitin and Ovchinnikova, 1972 Delos and Thorson, 1972), and from computational studies with realistic atom-atom potentials (Evans and Lane, 1973 Redmon and Micha, 1974). 

The nuclear frequency is related to the solvent and inner-shell reorganization energies as well as the corresponsing vibration frequencies. The electronic factor can be described on the basis of the Landau-Zener framework and is related to the electronic coupling matrix element... 

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