Quantum mechanical tunneling reactions

The presence of nonlinearity in an Arrhenius plot may indicate the presence of quantum mechanical tunnelling at low temperatures, a compound reaction mechanism (i.e., the reaction is not actually elementary) or the unfreezing of vibrational degrees of freedom at high temperatures, to mention some possible sources. 

We have seen that 10" M s is about the fastest second-order rate constant that we might expect to measure this corresponds to a lifetime of about 10 " s at unit reactant concentration. Yet there is evidence, discussed by Grunwald, that certain proton transfers have lifetimes of the order 10 s. These ultrafast reactions are believed to take place via quantum mechanical tunneling through the energy barrier. This phenomenon will only be significant for very small particles, such as protons and electrons. 

Concept of quantum-mechanical tunnelling in proton-uansfer reactions introduced (without experimental evidence) by several authors. 

The second of our principal concerns is the contribution of quantum mechanical tunneling (QMT) to singlet carbene 1,2-H shifts and related reactions. There is strong evidence that QMT is important in the low temperature matrix reactions of (e.g.) t-buty 1 chlorocarbene (18)58 and benzylchlorocarbene (10a).59... 

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. 

Complications that arise with this simple reaction are twofold. First, because of the low mass of the hydrogen atom its movement frequently exhibits non-classical behavior, in particular quantum-mechanical tunneling, which contributes significantly to the observed kinetic isotope effect, and in fact dominates at low temperature (Section 6.3). Secondly, in reaction 10.2 protium rather than deuterium transfer may occur ... 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

This simplified approach is analogous to the more rigorous absolute rate treatment. The important conclusion is that the bimolecular rate constant is related to the magnitude of the barrier that must be surmounted to reach the transition state. Note that there is no activation barrier (/.e., that AG = 0) in cases where no chemical bond is broken prior to chemical reaction. One example is the combination of free radicals. (In other cases where electrons and hydrogen ions can undergo quantum mechanical tunneling, the width of the reaction barrier becomes more important than the height.)... 

Quantum mechanical tunneling. Tunneling is the phenomenon by which a particle transfers through a reaction barrier due to its wave-like property.Figure 1 graphically illustrates this for a carbon-hydrogen-carbon double-well system Hydrogen... 

R. A. Marcus Prof. Miller, has your insightful quantum mechanical flux-flux correlation expression for the rate been used to test some of the simplified quantum mechanical tunneling calculations for reactions I recall that Coltrin and I found a simple path that agreed to a factor of 2, over six or so orders of magnitude of tunneling, with the quantum mechanical results for the collinear symmetric reaction H + H2 — H2 + H [1]. Truhlar has proposed an extension for asymmetric reactions. 

The enzyme-product complexes of the yeast enzyme dissociate rapidly so that the chemical steps are rate-determining.31 This permits the measurement of kinetic isotope effects on the chemical steps of this reaction from the steady state kinetics. It is found that the oxidation of deuterated alcohols RCD2OH and the reduction of benzaldehydes by deuterated NADH (i.e., NADD) are significantly slower than the reactions with the normal isotope (kn/kD = 3 to 5).21,31 This shows that hydride (or deuteride) transfer occurs in the rate-determining step of the reaction. The rate constants of the hydride transfer steps for the horse liver enzyme have been measured from pre-steady state kinetics and found to give the same isotope effects.32,33 Kinetic and kinetic isotope effect data are reviewed in reference 34 and the effects of quantum mechanical tunneling in reference 35. 

This relationship was found to break down for some reactions of yeast alcohol dehydrogenase56 such that (kH/kT)obs > (kD/kT)326. This is unambiguous evidence for quantum mechanical tunneling of the hydrogen. The small mass of the H isotope makes it proportionately more susceptible to tunneling than D or T, and so the classical equation 2.80 underestimates the substitution. The behavior of hydrogen is poised between classical and quantum mechanics.57 58... 

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