Zener theory

It is instructive to examine further the approximate semi-classical form for R7 shown above because, when viewed as a rate of transition between two intersecting energy sur ces, one anticipates that connection can be made with the well known Landau-Zener theory (10). For a non-linear molecule with N atoms, the potentials (Q) depend on 3N-6 internal degrees of fi eedom (for a linear molecule, Vj f depend on 3N-5 internal coordinates). The subspace S... 

DR. MARSHALL NEWTON (Brookhaven National Laboratory) The Landau-Zener theory in the weak-coupling regime may be derived by perturbation theory, as Dr. Sutin mentioned earlier. The complete derivation is much more general than the perturbation theory, and allows one to include an arbitrary degree of coupling. Thus, one can go continuously from nonadiabatic to the adiabatic limits. 

The Landau-Zener theory is comparatively successful in explaining the overall behavior of the reactions of oriented molecules at thermal energies where neutral... 

Keywords electron-capture dissociation electron-transfer dissociation electron transfer Rydberg orbital Landau-Zener theory... 

We have examined the proton transfer reaction AH-B A -H+B in liquid methyl chloride, where the AH-B complex corresponds to phenol-amine. The intermolecular and the complex-solvent potentials have a Lennard-Jones and a Coulomb component as described in detail in the original papers. There have been other quantum studies of this system. Azzouz and Borgis performed two calculations one based on centroid theory and another on the Landau-Zener theory. The two methods gave similar results. Hammes-Schiffer and Tully used a mixed quantum-classical method and predicted a rate that is one order of magnitude larger and a kinetic isotope effect that is one order of magnitude smaller than the Azzouz-Borgis results. 

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]. 

C. Zener. Theory of growth of spherical precipitates from solid solution. J. Appl. Phys., 20 950-953, 1949. 

The eigenvectors are positive and negative combinations of 4 and Ta, respectively. f d ( Fa) is a wave function where the mobile electron is at the donor (acceptor). In a time dependent theory, the wave function is set equal to at t=0. The electronic wave packet moves across the barrier to the acceptor. Landau-Zener theory [23,24] provides the probability for crossing to the upper surface at the avoided crossing ... 

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 theory of non-adiabatic electron transfer was developed by Levich, Dogonadze and Kuznetsov (Levich and Dogonadze, 1959 Levich et al. 1970). These authors, utilizing the Landau-Zener theory for the intersection area crossing suggesting harmonic onedimensional potential surface, proposed a formula for non-adiabatic ET... 

E.E.Nikitin, The Landau-Zener theory in atomic collision theory, in Proceedings of the Third USSR summer school on physics of elecronic and atomic collisions, Leningrad, Physical-Technical Institute, 1976, p. 131... 

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. 

Equation (16.51) was derived from the Landau-Zener theory for transitions between electronic states at the crossing of the corresponding potential surfaces, however... 

Although the Landau-Zener theory predicts all the experimental trends observed for E- V transfer, and, although more sophisticated techniques for handling the nonadiabatic transition are available, ° no calculations have been performed as yet for deactivation of I or Br by this mechanism. The major difficulty is that the theory is very sensitive to the details of the potential curves in the region of interaction. In general, these curves will be multidimensional surfaces. On the other hand, if our object is to learn about the potential from comparison of theory and experiment, it is just this sensitivity that we should demand from theory. It seems likely, therefore, that future theoretical work in this area will be very beneficial to our understanding of E- V transfer. 

Breakdown of the Landau-Zener Theory in the Presence of Relaxation... 

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