Tunnelling corrections in chemical reaction rates

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... 

H.R. Johnston Large Tunneling Corrections in Chemical Reaction Rates. In Adv. Chem. Phys. 3, 131 (1961). 

LARGE TUNNELLING CORRECTIONS IN CHEMICAL REACTION RATES... 

See also H. S. Johnston and D. Rapp, Large tunneling corrections in chemical reaction rates. II, J. Amer. Chem. Soc. 83 1 (1961) and reference 39. 

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

Reaction Rates, Chemical, Large Tunnelling Corrections in (Johnston) 3 131... 

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... 

The accurate prediction of enzyme kinetics from first principles is one of the central goals of theoretical biochemistry. Currently, there is considerable debate about the applicability of TST to compute rate constants of enzyme-catalyzed reactions. Classical TST is known to be insufficient in some cases, but corrections for dynamical recrossing and quantum mechanical tunneling can be included. Many effects go beyond the framework of TST, as those previously discussed, and the overall importance of these effects for the effective reaction rate is difficult (if not impossible) to determine experimentally. Efforts are presently oriented to compute the quasi-thermodynamic free energy of activation with chemical accuracy (i.e., 1 kcal mol-1), as a way to discern the importance of other effects from the comparison with the effective measured free energy of activation. 

The tunnel correction is not now a fundamentally defined number rather it is defined by the equation Q = kobJk, where kobs is the observed rate constant for a chemical reaction and k is that calculated on the basis of some model which is as good as possible except that it does not allow tunnelling. In this chapter the definition used for k is that calculated by absolute reaction rate theory [3], i.e., k = KRT/Nh)K where X is the equilibrium constant for the formation of the transition state. The factor k, the transmission coefficient, is also a quantum correction on the barrier passage process, but it is in the other direction, that is k < 1. We shall here follow the customary view (though it is not solidly based) that k is temperature-independent and not markedly less than unity. The term k is used following Bell [1] the s stands for semi-classical, that is quantum mechanics is applied to vibrations and rotations, but translation along the reaction coordinate is treated classically. 

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