Tunneling prefactor

Before presenting the KIE variation with reaction asymmetry for nonadiabatic PT, it will prove useful to first discuss the individual isotope PT rate constant Eq. (10.36) s variation with reaction asymmetry, which must include tunneling prefactor terms as well as the activation free energy. This behavior was analyzed up through quadratic terms in [5] to find... 

Note in passing that the common model in the theory of diffusion of impurities in 3D Debye crystals is the so-called deformational potential approximation with C a>)ccco,p co)ccco and J o ) oc co, which, for a strictly symmetric potential, displays weakly damped oscillations and does not have a well defined rate constant. If the system permits definition of the rate constant at T = 0, the latter is proportional to the square of the tunneling matrix element times the Franck-Condon factor, whereas accurate determination of the prefactor requires specifying the particular spectrum of the bath. 

This formula, aside from the prefactor, is simply a one-dimensional Gamov factor for tunneling in the barrier shown in fig. 12. The temperature dependence of k, being Arrhenius at high temperatures, levels off to near the cross-over temperature which, for A = 0, is equal to ... 

When Va varied within the interval 1-8 cm the tunneling splitting was found to depend nearly linearly on Fj, in agreement with the semiclassical model of section 3.5 [see eq. (3.92)], and the prefactor AjA ranged from 0.1 to 0.3, indicating nonadiabatic tunneling. Since this model is one-dimensional, it fails to explain the difference between splittings in the states with the [Pg.127]

In this case the adjustable parameters of the PES (4.41) are V0 = 18.52 kcal/mol, V = 5.62 kcal/mol, C = 1.07, 11 = 0.91, and w0 = 1.50x 1014s 1 [Bosch et al., 1990], As in the case of malonaldehyde, the PES parameters place this system between the sudden and adiabatic regimes. The PES contour map and the instanton trajectory for this case are shown in Figure 6.11. Benderskii et al. [1993] have utilized the instanton analysis to obtain the prefactor Bt = 54 and the tunneling splitting 1.4 cm-1, which is in excellent agreement with the value 1.30 cm-1 obtained by Bosch et al. [1990] from a quantum mechanical calculation. 

The discussion of Section 2.3, which is concerned with the destruction of coherence by interaction with the environment, applies to this case. As in the case of tunneling in a double well, A(f) 2 can be represented as a product of the attempt frequency of hitting the turning point and the barrier transparency (see Section 3.4). The tunneling splitting is determined by the same parameters and contains only an additional prefactor 3/2 because of the symmetry. 

The rate constants for 14NO and l5NO at 13 K are 8xl0 4s 1 and 5.2x10 4s 1, respectively. The isotope effect, low-activation energy (0.1 versus 0.65 kcal/mol for the gas-phase reaction) and anomalously low prefactor ( 10 2s 1) all point to a tunneling mechanism for this reaction. 

Chidsey [30], Weber and Creager [31] and Murray and co-workers [32] have modeled non-adiabatic heterogeneous electron transfer for long-chain alkane thiol monolayers by using an expression similar to Equation (5.3), except that the energy-dependent prefactor in the tunneling probability expression is excluded. 

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