Chemical reactions quantum-mechanical tunneling

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. 

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.)... 

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 section gives an introduction to the effects of symmetry and quantum mechanical tunneling on chemical reactions in general and hydrogen transfer in particular. 

This chapter presents some effects symmetry has on the rates and mechanisms of chemical reactions. The reaction kinetics of low mass groups like dihydrogen or dideuterium, in particular at low temperatures, is strongly influenced by quantum mechanical tunneling processes and the Fermi postulate of the symmetry of the... 

In 1933 Bell [1] predicted that, due to quantum mechanical effects, the rate of transfer of a hydrogen atom (H-atom) or proton would become temperature independent at low temperatures. Since that time, kineticists have embraced the concept of quantum mechanical tunneling (QMT) so enthusiastically that it is frequently invoked on the flimsiest of experimental evidence, often using data obtained at, or above, room temperature. At such elevated temperatures, conclusive evidence that the rate of an H-atom or proton transfer is enhanced above that due to over the top of the barrier thermal activation, and can only be explained by there being a significant contribution from QMT, is rare. Significant has been italicized in the foregoing sentence because QMT will always make some contribution to the rate of such transfers. The QMT contribution to the transfer rate becomes more obvious at low temperatures. For this reason, the unequivocal identification of QMT in simple chemical systems requires that their rates of reaction be measured at low temperatures. 

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. 

Breakdown of the Swain-Schaad relationship leads to different exponentials in Eq. (17.10) and represents a sign that the rate of the chemical reaction is partially influenced by the quantum mechanical tunneling (Bell, 1980 Devault, 1984 Khnman, 1991 Bahnson Klinman, 1995 Bruice Benkovic, 2000 Knapp Klinman, 2(X)2). 

Sometimes chemical reactions occur to some extent by quantum-mechanical tunneling. Usually systems must surmount the col in the potential energy surface (Fig. 3), but quantum-mechanical theory allows the possibility of going from the initial state A-fBC to the final state AB -I- C without passage over the col. This arises when very light species, such as electrons and hydrogen atoms, are involved in the reaction. For example, in a reaction such as. 

It is well known that at very low temperatures quantum mechanical tunneling effect plays a part in the chemical reaction of hydrogen. Miyazaki and coworkers (Fujitani et al. 1991 ... 

One of the central issues in studying reaction dynamics isf how you describe the flux over the reaction barrier, whether from simple collision theory, or transition state theory, to modified generalized Langevin theory, Kramer s theory...or even to quantum mechanical tunnelling - This is a selective not exhaustive list of possibilities (7,8). When the timescale of the photo chemical event (be it photodissociation, isomerization, charge transfer)... 

CONTEXT Problems in quantum mechanics can often be approached from different perspectives, and it becomes important to see when two processes, although described differently, are actually the same. For example, quantum mechanical tunneling has a dramatic impact on many chemical reactions that involve hydrogen transfer, because hydrogens are relatively light (which increases their tunneling probability). When there are several equivalent... 

Reality suggests that a quantum dynamics rather than classical dynamics computation on the surface would be desirable, but much of chemistry is expected to be explainable with classical mechanics only, having derived a potential energy surface with quantum mechanics. This is because we are now only interested in the motion of atoms rather than electrons. Since atoms are much heavier than electrons it is possible to treat their motion classically. Quantum scattering approaches for small systems are available now, but most chemical phenomena is still treated by a classical approach. A chemical reaction or interaction is a classical trajectory on a potential surface. Such treatments leave out phenomena such as tunneling but are still the state of the art in much of computational chemistry. 

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