Interactions Zener electron

In the study of (electronic) curve crossing problems, one distinguishes between a situation where two electronic curves, Ej R), j — 1,2, approach each other at a point R = Rq so that the difference AE[R = Rq) = E iR = Rq) — Fi is relatively small and a situation where the two electronic curves interact so that AE R) Const is relatively large. The first case is usually treated by the Landau-Zener fonnula [87-92] and the second is based on the Demkov approach [93]. It is well known that whereas the Landau-Zener type interactions are... 

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

This mixed classical/quantum expression is valid for classical nuclear behavior and, strictly speaking, for the case of direct two-site interaction rather than superexchange, as the Landau-Zener expression was derived from the time-dependent Schrodinger equation assuming a two-state (reactant/product) electronic system with direct coupling. Nevertheless, it becomes clear on physical grounds that the form of Eqs. 4-5 can serve to define an effective A in the superexchange case in terms of the Rabi precession frequency characteristic of the two trap sites embedded in the complex system wherein 2A/h would be computed from this net effective Rabi precession frequency. 

The c/a ratio is greater than for V02, which implies that the n band (i.e. that with d-orbital lobes in the basal plane) is more occupied than in V02 (Goodenough 1971, p. 352). But we think that if it were not ferromagnetic, the n band, in contradistinction to V02, would be wholly above the Fermi energy. The Hubbard correlation term U, however, produces localized moments for the 3d2 states, as explained in Chapter 3, and these, if oriented ferromagnetically, would just fill the tjj band. The filled band (for spin-up electrons) will now overlap the n band, allowing ferromagnetic interaction of Zener or RKK Y type between the d2 moments, as described in Chapter 3. The T2 term in the resistivity could be explained as in Chapter 2, Section 6. 

The nature of the local field in the ferromagnetic metals is probably that proposed by Zener.4 It can be described as involving the interaction between the unpaired spins of atomic electrons and those of some electrons involved in forming one-electron bonds between the metal atoms. 

In this expression 8 is the Massey parameter, which depends on the mean thermal velocity v, and AF is the difference in slopes of the initial and final terms at the crossing point. Of course, (2.66) is of typical TST form. It can be generalized to arbitrarily large electronic interactions in a straightforward manner by replacing B with the Zener transmission factor... 

These monolayers provide a significant opportunity to compare the extent of electronic communication across the p3p bridge when bound to a metal electrode as opposed to being coupled to a molecular species, e.g. within a dimeric metal complex. Electronic interaction of the redox orbitals and the metallic states causes splitting between the product and reactant hypersurfaces, which is quantified by HabL the matrix coupling element. The Landau-Zener treatment [15] of a non-adiabatic reaction yields the following equation ... 

To understand the factors that are important in controlling the rates of ET reactions, it is best to refer to a specific theoretical model [35]. Choosing a model defines terms and allows us to analyze the results of experiments in precise ways. There are two main types of models classical and quantum mechanical. One way of smoothly moving from the use of a classical to a quantum mechanical model is provided by semiclassical (Landau-Zener) ET theory [36-38]. At high temperature, quantum mechanical models become equivalent in most respects to semiclassical ones. Thus the appropriate choice of model depends on the type of ET reaction that we are interested in studying. Ones in which the electron donor and acceptor have strong electronic interaction with each other prior to the ET event are well described by a classical model. In these systems an ET reaction always proceeds to products if the reactants reach the top of the reaction barrier (strong-... 

Electron transfer in proteins generally involves redox centers separated by long distances. The electronic interaction between redox sites is relatively weak and the transition state for the ET reaction must be formed many times before there is a successhil conversion from reactants to products the process is electronically nonadiabatic. A Eandau-Zener treatment of the reactant-product transition probability produces the familiar semiclassical expression for the rate of nonadiabatic electron transfer between a donor (D) and acceptor (A) held at fixed distance (equation 1). Biological electron flow over long distances with a relatively small release of free energy is possible because the protein fold creates a suitable balance between AG° and k as well as adequate electronic coupling between distant redox centers. 

In Zener breakdown, the field may be so high that it exerts sufficient forces on a covalently bound electron to free it, which creates two carriers, an electron and a hole, to conduct the current. In this breakdown process, shown in Fig. 1.17a, an electron makes the transition, or tunnels, from the valence band to the conduction band without the interaction of any particles. It is essentially a band-to-band tunneling process. In... 

Terminal-CO. In accordance with earlier studies [3], the occurrence of terminal-CO with such an exceptionally high vCO fi equency (2095-2072 cm ) discloses electron-deficient nature for the metal adsorbing sites. The electron-drain may be effected via direct interactions between the metal atoms and the oxide support [5,6], or by means of oxygen-mediated Ni°/Ni electron-exchange interactions. A model pioneered by Zener [34] expounds the physical justification for such interactions. 

II is mainly ionic in character and function IV completely so, representing the interaction of H+ and H-. Of these IV corresponds to a known state, the first electronically excited state of the molecule. As might have been anticipated from the ionic character of the wave function, the state differs in its properties from the other known excited states, having r, = 1.29 A and v, = 1358 cm-1, whereas the others have values of rt and v, close to those for the normal hydrogen molecule-ion, 1.06 A and 2250 cm-1. The calculations of Zener and Guillemin and of Hylleraas have shown that at the equilibrium distance the wave function for this state involves some contribution from wave functions for one normal and one excited atom (with n = 2,1 = 1), and with increase in Tab this contribution increases, the molecule in this state dissociating into a normal and an excited atom. 

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