Rate constant tunneling correction

Miller W H 1979 Tunneling corrections to unimolecular rate constants, with applications to formaldehyde J. Am. Chem. See. 101 6810-14... 

Theoretical calculations published concurrently appeared to support these suggestions. Inclusion of tunneling corrections for the calculated rate constants was found to lower the apparent and A values, consistent with the experimentally... 

The rate of hydrogen transfer can be calculated using the direct dynamics approach of Truhlar and co-workers which combines canonical variational transition state theory (CVT) [82, 83] with semi-classical multidimensional tunnelling corrections [84], The rate constant is calculated using [83] ... 

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. 

In both TST and VTST, quantum mechanical tunneling is introduced into the rate constant expression as a correction factor usually referred to as k. A short discussion of k which is used largely with TST is presented in Section 6.3.1. Tunneling has been explored much more thoroughly in connection with VTST and this work will be discussed later. 

In the discussion of TST in Chapter 4 tunneling was introduced as a multiplicative correction factor to the TST rate constant. TST tunneling is usually discussed in one of three approximations. In first order (for small tunneling), Wigner has shown the correction is given by the u2/24 law... 

In the theoretical model used the overall rate constant k is represented as the product of the no-tunnelling rate constant k° by the tunnelling correction P, ... 

Such a method has recently been developed by Miller. et. al. (28). It uses short lengths of classical trajectory, calculated on an upside-down potential energy surface, to obtain a nonlocal correction to the classical (canonical) equilibrium probability density Peq(p, ) at each point then uses this corrected density to evaluate the rate constant via eq. 4. The method appears to handle the anharmonic tunneling in the reactions H+HH and D+HH fairly well (28), and can... 

One can conclude from equation (4.2.33) that the correction SR to the effective radius due to tunnelling (the second term) decreases with both the decrease of parameters ao, tq characterizing tunnelling strength, and the increase of temperature (diffusion coefficient). Since this correction makes the contribution to the rate constant, SK = AitDSR, independent on D, the... 

Corrections to transition-state theory due to quantum tunneling along the reaction coordinate give a thermal rate constant that is larger than the prediction obtained from classical transition-state theory. 

The rate constant predicted by conventional transition-state theory can turn out to be too small, compared to experimental data, when quantum tunneling plays a role. We would like to correct for this deviation, in a simple fashion. That is, to keep the basic theoretical framework of conventional transition-state theory, and only modify the assumption concerning the motion in the reaction coordinate. A key assumption in conventional transition-state theory is that motion in the reaction coordinate can be described by classical mechanics, and that a point of no return exists along the reaction path. 

H — CH + reaction. The data used for the evaluation of the rate constant (5,16) are collected in Table 5,10, The tunnelling correction... 

Temperature dependence of the rate constant for the process CH4 + H —> CH3 + I-I2- The dashed and full lines, respectively, represent the TST treatments without and with applying Eckart s correction for the quantum mechanical tunnelling, Experimental oata are taken from Ref.452 (A). 453 ( ) and Ref. 454 (O). 

Figure 35 Measured dissociation rate constant k E) for CD2CO. The solid line is a fit based on RRKM theory including tunneling corrections. Redrawn from Ref. 33.

Fig. 2.21. (a) Time-resolved LIF decay profiles for two closely spaced rotational levels of vibrationally excited CH3O (X). The solid line is an exponential fit for the decay convoluted with the dump laser pulse shape function, (b) Measured state specific unimolecular dissociation rate constants for CH3O (X) compared to calculated k E, J) curves without and with tunneling corrections. 

Inclusion of dynamical effects allows calculation of corrections to simple Transition State Theory, often described by a transmission coefficient k to be multiplied with the TST rate constant (Section 12.1), or used in connection with variational TST (Section 12.3). Classical dynamics allow corrections due to recrossing to be calculated, while a quantum treatment is necessary for including tunnelling effects. Owing to the stringent... 

A reaction involving hydrogen atom transfer is usually characterized by a significant tunneling effect, which is represented in the rate constant calculation by the tunneling correction factor kw as... 

The tunneling correction may distinctly improve the values of calculated rate constants for reactions with high energy barriers, especially at low temperatures.1 9 A reasonable correction of the rate constant may be obtained, even in a one-dimensional approximation, using the Eckart type of potential.10 In this approach, the asymmetric potential is characterized by the forward and backward barrier heights and the imaginary frequency of the transition state.1 A number of different kinds of tunneling corrections have been evaluated by... 

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