Tunnelling Effects in Chemical Reactions

Theoretical analysis of kinetics of a chemical reactions, whether it is done with the aid of the theory of transition states or by chemical dynamics methods, rests on the classical notion of the necessity to overcome an activation barrier, i.e. the saddle point on the PES of a molecular system. Meanwhile, a sizeable contribution to the total rate of some reactions is made by underbarrier trajectories—this is a purely quantum mechanical effect of the system oozing through the energy barrier so that there exists a certain probability of a transition from the reactants to the products even when the internal energy of the system is 

It is evident from Eq. (1.35) that the relative probability of tunnelling strongly depends on the form of the barrier, rising when it is narrow it also rises for the particles of small mass and with falling temperature T. The magnitude of T at which the tunnelling effects prevail over the classical overbarrier transitions is defined by 

At 1 eV (23kcal/mol) and d 3 A, 7J a 50K for protons and 1600X for electrons. In electron transfer reactions, the tunnelling effect may show up even for the distances of several tens of Angstrom units (for d 30 A and S 1 eV, T 160K). 

In typical organic reactions developing at ambient temperature, the role of the tunnelling effects is usually insignificant. When, however, the reaction coordinate is determined predominantly by the shifts of light nuclei, particularly protons, the contributions from tunnelling may become appreciable and, in some cases, even decisive, as will be shown below. 

An overall scheme for quantitative assessment of the influence of tunnelling effects upon the reaction rate has been developed by Miller [113, 114]. The simplest method for calculating the tunnelling rate constant is based on the theory of transition state with correction for tunnelling. This correction consists in formal replacement of the classical motion along the reaction coordinate with the quantum motion. This approach was first formulated in the works by Bell [115]. 

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Bourgin [51] and Roginsky and Rosenkewitsch [52] were the first to pay attention to the possibility of the tunnel mechanism of chemical reactions. They did so quite soon after the creation of quantum mechanics. At that time, the main features of this phenomenon were also understood on the qualitative level. Later on, a large number of theoretical and experimental works were dedicated to more detailed studies on tunnel effects in chemical reactions. This field has attracted the interest of scientists up to the present time. A comprehensive review of the history and the present state of investigations of nuclear tunneling in chemical reactions can be found in the recently published monographs by Bell [53] and Goldanskii et al. [54],... 

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 SCP-IOS approximation has also been used to describe the effects of the curvature coupling elements on tunneling probabilities in chemical reactions. For example, the probability of tunneling through a simple barrier is given within the SCP-IOS model by... 

Ionic dissociation of carbon-carbon a-bonds in hydrocarbons and the formation of authentic hydrocarbon salts, 30, 173 Ionization potentials, 4, 31 Ion-pairing effects in carbanion reactions, 15, 153 Ions, organic, charge density-NMR chemical shift correlations, 11, 125 Isomerization, permutational, of pentavalent phosphorus compounds, 9, 25 Isotope effects and quantum tunneling in enzyme-catalyzed hydrogen transfer. 

Quantum-mechanical tunnelling has been recognized as a possible contributor to the rate of a chemical reaction for many years. For instance, the theory of tunnelling for proton transfer reactions was developed by Bell (1959) in his famous book The Proton in Chemistry. Later, Bell (1980a) published a more thorough treatment of tunnelling in his book The Tunnel Effect in Chemistry. 

The present chapter comprises a review of tunneling phenomena in nuclear, atomic, and solid-state physics, tunneling effects during the transfer of atoms in chemical reactions in gases, liquids, and solids, as well as of tunneling phenomena in electron transfer reactions in gases. 

There is a possibility, indicated by wave-mechanical theories, that microscopic systems may pass from one state to another separated from the first by an energy barrier without actually acquiring the high energy corresponding to the intermediate region. This so-called tunnel-effect appears to operate in the escape of a-particles from nuclei, but for systems with the masses, energies, and distances usually involved in chemical reactions it appears unimportant. 

The two chief experimental criteria for tunneling in chemical reactions are an abnormal isotope effect (the tunnel effect is much more pronounced for hydrogen than for deuterium), which does not concern us here, and a curved Arrhenius plot. The reason for this is that the effect becomes most marked at low temperatures, when the fraction of systems which are able to cross the barrier becomes considerably higher than that calculated from classical considerations. As a result, the rate decreases with decreasing temperature less than expected, and the Arrhenius plot becomes concave upward. We cannot go into the quantum-mechanical details, and refer the reader to the literature on the subject. (See, e.g., Refs. 2b, 23, 77, 99, 105.)... 

Cross-linking can be effected by chemical reactions of reactive groups in the elastomer among one another or with reactive additives. The reaction must not start until after the coating process. This is effected by high temperature, which may be achieved in the last sections of the drying tunnel or in a separate high-temperature tunnel. 

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