Adiabatic factor

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. 

Fn in Eq. (33) takes into account the fact that the electron transfer can also occur for reactant molecules without fully overcoming the energy barrier. At normal temperatures for electrode reactions F approaches 1 [131]. Therefore Eq. (33) is often used without the F term, in this equation was estimated to have a value of the order of 60 pm [138]. However, the quantitative estimation of depends on the adiabaticity factor k (see Eq. (24)), which varies with the reactant-electrode separation distance. It was suggested [139] that the electrode reactions should be more adiabatic than the corresponding homogeneous redox reactions. But as the reaction site, for outer-sphere systems, is probably separated from the electrode surface by a layer of solvent molecules [129], k may drop below 1 since the reaction may become less adiabatic. These problems were more extensively discussed in [131]. 

The energy diffusion coefficient can be used in (4.13)-(4.15) to evaluate the adiabatic factor C. The integral can be estimated using the maximum of the exponent... 

These adiabaticity factors are reasonable considering the poor overlap expected for the Eu 4f-orbitals and illustrate the utility of Eq. (g) in rationalizing rate patterns observed for very exothermic reactions. More generally, because the fi2 correction depends on not on the slope of the free-energy plot can be... 

Phase gas, liquid. Use if the order of the reaction is positive and >95% conversion is the target, and for consecutive reactions with an intermediate as the target product. Exchange heat generated if the product of the adiabatic factor x heat generation potential >10. 

The adiabatic factor y is the Massey parameter for vibrational relaxation transition... 

The W transition probability includes an exponential adiabatic factor (Nikitin, 1970) ... 

Non-resonant vibrational energy exchange between molecules of a different kind is usually referred to as W exchange. Let us first consider the W exchange for diatomic molecules A and B with slightly different vibrational quanta ftcoA > Similar to W exchange of anharmonic molecules of the same kind, the adiabatic factors here also mainly determine the smallness of the probability. If a molecule A transfers a quantum (wa -f-1 m va) to a molecule B (vb + 1 vb),... 

Adiabatic pulses are described by their frequency sweep and amplitude profile, which, when combined with the peak rf amplitude cc max), defines the total power of the pulse. The total frequency range, AF, over which the pulse sweeps is commonly many tens of kilohertz and pulse durations, T, are typically of the order of 1 ms, corresponding to frequency sweep rates of 10-100 MHz/s. The degree to which the adiabatic condition is satisfied for the pulse is quantified by the adiabaticity factor Q... 

The Schrodinger equation with the included non-adiabatic factor is precise. However, if the is small, we actually work within the perturbation... 

The dependence of eff on Vy/(xeiZei) is presented in Figure 2.4. The ET rate constant can be explicitly written in terms of this electronic non-adiabatic factor... 

When the proton and electron transfer involve different sites of the reactants, we may expect, in addition to the extra reorganization energy, that the electron transfer may be strongly non-adiabatic (Xei 1) and substantially reduce the effective reaction frequency. Georgievskii and Stuchebrukhov addressed the transition between electronically adiabatic and non-adiabatic CPET and showed that the adiabatic factor that reflects the deviation from adiabaticity has the form ... 

The Butler-Vohner model overestimates the effect of overpotential on the rates and has a symmetric behaviour. The more complete calculations with ISM rates with A = 350 kJ mor are in fair agreement with experiment for the cathodic reduction and, with respect to the Butler-Vohner approach, present some asymmetry due to a more favourable non-adiabatic factor for tunnelling of the electrons in reduction. There is no close agreement for data in the anodic region. Incorporating a correction with a lower A into the Butler-Vohner model... 

Chemistry students should note that the above consideration of collision processes cannot be directly extended to the case of atomic-molecular collisions even in classical physics. This is, in particular, because in a real atomic-molecular system a process of interaction significantly depends on the so-called adiabatic factor, i.e., on the correlation of the collision time and the intrinsic molecular frequencies. 

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