Tunneling transmission coefficient

Note that both k and AG 0 depend on temperature. The transmission coefficient is sometimes called the tunneling transmission coefficient because tunneling is the main quantum effect on the reaction coordinate. 

Under these conditions the tunneling transmission coefficient is ... 

Tunneling transmission coefficients and related spin dependent current in FIF and FIS nanostructures have been proposed to be calculated on the basis of the transport equation without a use of quasi-classical approximations. It has been shown that in the case of spin conservation in the scattering events the scattering potential shifted from the emitter to collector interface gives rise of the transmission coefficient. The same scattering well shift, on the contrary, leads to the coefficient decrease. Interplay between these two factors can add 3-5 % to TMR of FIF and FIS nanostructures when the insulator has the thickness of 1 nm. 

Some care must be exercised when using the reverse saturation current obtained from the semilogarithmic current voltage plot and equation 12 to determine the metal-semiconductor barrier height c()g. Card and Rhoderick have shown that if the interfacial oxide is sufficiently thick so that the electron tunnelling transmission coefficient is no longer unity then the reverse saturation current is reduced to a value equal to the product of the reverse saturation current when no interfacial layer is present and the transmission coefficient of the interfacial oxide> that is... 

At this point one can include optimized multidimensional tunneling in each (i = 1,2,..., 7) of the VTST calculations. The tunneling transmission coefficient of stage 2 for ensemble member i is called and is evaluated by treating the primary zone in the ground-state approximation (see the section titled Quantum Effects on Reaction Coordinate Motion ) and the secondary zone in the zero-order canonical mean shape approximation explained in the section titled Reactions in Liquids , to give an improved transmission coefficient that includes tunneling ... 

Many computational studies in heterocyclic chemistry deal with proton transfer reactions between different tautomeric structures. Activation energies of these reactions obtained from quantum chemical calculations need further corrections, since tunneling effects may lower the effective barriers considerably. These effects can either be estimated by simple models or computed more precisely via the determination of the transmission coefficients within the framework of variational transition state calculations [92CPC235, 93JA2408]. 

In the case where they represent quantum vibrational modes, this leads to the appearance of a small tunnel factor in the transmission coefficient k. ... 

The term exp[iax] in equations (2.47) indicates travel in the positive x-direction, while exp[—iax] refers to travel in the opposite direction. The coefficient A is, then, the amplitude of the incident wave, B is the amplitude of the reflected wave, and F is the amplitude of the transmitted wave. In region III, the particle moves in the positive x-direction, so that G is zero. The relative probability of tunneling is given by the transmission coefficient T... 

The transmission coefficient T in equation (2.58) is the relative probability that a particle impinging on the potential barrier tunnels through the barrier. The reflection coefficient R in equation (2.59) is the relative probability that the particle bounces off the barrier and moves in the negative v-direction. Since the particle must do one or the other of these two possibilities, the sum of T and R should equal unity... 

Fig. 12 The Fig. 11 intramolecular circuit can be decomposed into four tunneling paths, to apply the parallel superposition rule, and predict the transmission coefficient through Fig. 11 molecule. Molecules 1 and 2 are for the contribution of two short tunnel paths and molecules 3 and 4 for the contribution of the two longer paths through the central perylene wire... 

A recently proposed semiclassical model, in which an electronic transmission coefficient and a nuclear tunneling factor are introduced as corrections to the classical activated-complex expression, is described. The nuclear tunneling corrections are shown to be important only at low temperatures or when the electron transfer is very exothermic. By contrast, corrections for nonadiabaticity may be significant for most outer-sphere reactions of metal complexes. The rate constants for the Fe(H20)6 +-Fe(H20)6 +> Ru(NH3)62+-Ru(NH3)63+ and Ru(bpy)32+-Ru(bpy)33+ electron exchange reactions predicted by the semiclassical model are in very good agreement with the observed values. The implications of the model for optically-induced electron transfer in mixed-valence systems are noted. 

To summarize, in this article we have discussed some aspects of a semiclassical electron-transfer model (13) in which quantum-mechanical effects associated with the inner-sphere are allowed for through a nuclear tunneling factor, and electronic factors are incorporated through an electronic transmission coefficient or adiabaticity factor. We focussed on the various time scales that characterize the electron transfer process and we presented one example to indicate how considerations of the time scales can be used in understanding nonequilibrium phenomena. 

CCVTST/SCT denotes CVTST plus a small curvature tunnel transmission (SCT) coefficient. dAll vibrations treated by classical mechanics, tunneling and nonclassical reflection are neglected. Alhambra, C. et al. (see Figs. 11.10 and 11.11) employ the term classical . 

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