Tunneling factor, nuclear

The quantity / is just a further combination of constants already in Eq. (10-70). The value of Z is taken to be the collision frequency between reaction partners and is often set at the gas-phase collision frequency, 1011 L mol-1 s-1. This choice is not particularly critical, however, since / is nearly unity unless is very large. Other authors29-30 give expressions for Z in terms of the nuclear tunneling factors and the molecular dimensions. 

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. 

Classically, the rate of electron transfer is determined by the rate of passage of the system over the barrier defined by the surfaces. In the semiclassical model (13) a nuclear tunneling factor that measures the increase in rate arising from... 

According to a recent model (13) nuclear tunneling factors for the inner-sphere modes can be defined by... 

The value of log rn for the Fe(H20) 2+ - Fe(H20)6 + exchange (which features a relatively large inner-sphere barrier) is plotted as a function of 1/T in Figure 5. The nuclear tunneling factors are close to unity at room temperature but become very large at low temperatures. As a consequence of nuclear tunneling, the electron transfer rates at low temperatures will be much faster than those calculated from the classical model. 

Figure 5. Plot of the logarithm of the nuclear tunneling factor vs. 1/T for the Fe(H20)62 -Fe(H20)63 exchange reaction. The slope of the linear portion below 150 K is equal to Ein/4R (13).

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. 

The nuclear tunnelling factor can be accurately estimated from a 1-mode model based on the high frequency inner-sphere breathing mode (10, Tl)... 

Electronic non-adiabaticity can give rise to a factor K which is less than unity the nuclear tunnelling factor, T, on the other hand, is always greater than or equal to unity. 

Non-resonant Golden Rule Nuclear Tunnelling Factor 1 (298) for Self-exchange. 

Non-resonant Nuclear Tunnelling Factor T(298) for Self-exchange in Aqueous Solution... 

Because typical metal-ligand stretching frequencies are ca. 2 kT at room temperature (T), the possibility that the inner-shell nuclei will tunnel through the potential barrier needs to be considered. This is allowed for through the nuclear-tunneling factor, T j, which is defined by ... 

The high-T limit of Eq. (f) is Eq. (m) of 12.2.3.3.1. At lower T, F 1, and it is necessary to include the nuclear-tunneling factor in this latter equation. When this is done ", results that agree with those given by Eq. (f) are obtained to 20 K. 

The above treatment neglects nuclear-tunneling effects. The nuclear-tunneling factors calculated for a (hypothetical) electron transfer having the inner-sphere parameters of and [Fe(HjO)jp ions (see Table 1 in 12.2.3.3.4) and no solvent re-... 

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