Rate theory tunneling correction

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] ... 

Reaction Rates, Chemical, Collision Theory of (Widom). Reaction Rates, Chemical, Large Tunnelling Corrections 5 353... 

Quantum Theory of the DNA Molecule (Lowdin) Tunnelling Corrections, Large, in Chemical Reaction Rates 8 177... 

Results of a PEPICO study of the dissociation dynamics of 2-bromobutane ions have been analysed with tunnelling-corrected RRKM statistical theory using vibrational frequencies obtained from ab initio MO calculations. It has been concluded that the slow rate of loss of HBr, to form the but-2-ene ion, occurs via a concerted mechanism in which tunnelling is a feature of the proton transfer. 

Langevin Theory of Polymer Dynamics in Dilute Solution (Zwanzig) Large Tunnelling Corrections in Chemical Reaction Rates (Johnston) Lattices, Linear, Reversible Kinetics on, with Neighbor Effects... 

The simplest way to combine electronic stnicture calculations with nuclear dynamics is to use harmonic analysis to estimate both vibrational averaging effects on physico-chemical observables and reaction rates in terms of conventional transition state theory, possibly extended to incorporate tunneling corrections. This requires, at least, the knowledge of the structures, energetics, and harmonic force fields of the relevant stationary points (i.e. energy minima and first order saddle points connecting pairs of minima). Small anq)litude vibrations around stationary points are expressed in terms of normal modes Q, which are linearly related to cartesian coordinates x... 

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.

The need to include quantum mechanical effects in reaction rate constants was realized early in the development of rate theories. Wigner [8] considered the lowest order terms in an -expansion of the phase-space probability distribution function around the saddle point, resulting in a separable approximation, in which bound modes are quantized and a correction is included for quantum motion along the reaction coordinate - the so-called Wigner tunneling correction. This separable approximation was adopted in the standard ad hoc procedure for quan-... 

Similar definitions of the "tunneling correction" are obtained by using the adiabatic formulations of the exact and semiclassical rate theory considered in Sec.5.III. 

III). In conditions of vibration-rotational adiabaticity, will represent an apparent tunneling correction which is necessary only to obtain the correct values of the rate constant when using the collision theory expression (51.Ill), instead of Eyring s equation (67.Ill) (corrected by the real tunneling factor ). 

Our analysis rests on accurate formulations of reaction rate theory including relevant well-defined dynamic factors which can be considered as "tunneling corrections only under certain conditions. 

All above conclusions are involved as special cases in the general consequences of the collision theory rate equation (51j III) derived in Sec.7.III. The corresponding consequences from the statistical formulation (67.Ill) of the reaction rate theory were also discussed there. The current interpretations of kinetic isotope effects are based on transition state theory. The correction for proton tunneling is first taken into consideration by BELL et al./155/. More extensive work in this direction has been carried out by CALDIN et al. /I53/. In this treatment estimations of the tunneling correction are made using one-dimensional (parabolic) barrier by neglecting the coupling of the proton motion with other motions of reactants or solvent. 

In this Section we discuss and compare the results obtained using the various theories of Section 3, and a variational transition state theory with a tunnelling correction [9]. The reaction we concentrate on is H+BrH - HBr+H. We emphasize the rate constants, but also discuss reaction cross sections. The potential energy surface we used in the H+BrH computations is of a semiempirical diatomics in molecules type, the form of which (called DIM-3C) is due to Last and Baer [ll]. The surface contains a three-centre integral term that has been parameter-ised [33] by comparing ESA-CSA calculations with an experimental [3] room temperature rate constant for the D+BrH -) DBr+H reaction. The minimum potential energy path is collinear, and there is a strong... 

Rate expressions are recommended to be used as relative quantities only. PPL, phenethyl phenyl ether a-PPE", a-radical of PPL )8-PPE, )8-radical of PPL TST, transition state theory including anharmonic corrections TST, transition state theory including anharmonic corrections and Wigner tunneling correction SS, steady-state approximation for intermediate. 

Where k is the rate constant, k is the transmission coefficient from the collision theory, Piunn is the tunneling correction, and the Qs are the standard partition functions (see Felipe et al. in this volume). By substituting appropriate carbon atoms with different isotopes on the molecule, one can calculate the ratio of the rate constants (kinetics isotopic effect). 

A study of the reaction between Me-OBr and Cl has been carried out at the QClSD(T)/6-311-l-l-G(3df,2p)//MP2/6-311-l-G(d,p) level of theory using canonical variational TST with a small curvature tunneling correction. The calculations predict an anti-E2 elimination accompanied by a small amount of a syn-El elimination reaction that increases in importance as the temperamre is increased and an even smaller amount of S 2 0 reaction giving CH3-OCI. The energy barriers, transition structures, rate constants, and temperature dependences of the rate constants between 200 and 3000 K are given for the three reactions. 

In Fig. 5.1, thermal rate constants obtained from accurate full-dimensional calculations are compared to transition state theory results [40] (left panel) and reduced dimensionality quantum calculations (right panel). Experimental results [41] are also displayed. Classical transition state theory (TST) and variational transition state theory (VTST) drastically underestimate the thermal rate constant. This shows that tunneling effects are very prominent in the H2 + OH reaction. Including different types of tunneling corrections [40], increased values of the thermal rate constant can be obtained. However, it should be noted that different tunneling corrections result in considerably different results. This reflects the ambiguity of quantum transition state... 

The Tunneling Correction to the Rate Constant in the Transition-State Theory... 

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