Reaction mechanisms transition-state theory

Garret, B. C. and Truhlar, D. G. Generalized transition state theory. Classical mechanical theory and applications to collinear reactions of hydrogen molecules, J.Phys.Chem., 83 (1979), 1052-1079... 

Generalized Transition State Theory. Classical Mechanical Theory and Applications to Collinear Reactions of Hydrogen Molecules. 

Miller W H 1974 Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants J. Chem. Phys. 61 1823-34... 

There is another useiiil way of depicting the ideas embodied in the variable transition state theory of elimination reactions. This is to construct a three-dimensional potential energy diagram. Suppose that we consider the case of an ethyl halide. The two stepwise reaction paths both require the formation of high-energy intermediates. The El mechanism requires formation of a carbocation whereas the Elcb mechanism proceeds via a caibanion intermediate. 

Benzofuroxan 79 can be generated from 2-nitrophenyl azide 80 (Scheme 49). Neighboring-group assistance within the pyrolysis leads to a one-step mechanism with an activation barrier of 24.6 kcal/mol at the CCSD(T)/6-31 lG(2d,p) level [99JPC(A)9086]. This value closely resembles the experimental one of 25.5 kcal/mol. Based on the ab initio results for this reaction, rate constants were computed using variational transition state theory. 

Quantum mechanical effects—tunneling and interference, resonances, and electronic nonadiabaticity— play important roles in many chemical reactions. Rigorous quantum dynamics studies, that is, numerically accurate solutions of either the time-independent or time-dependent Schrodinger equations, provide the most correct and detailed description of a chemical reaction. While hmited to relatively small numbers of atoms by the standards of ordinary chemistry, numerically accurate quantum dynamics provides not only detailed insight into the nature of specific reactions, but benchmark results on which to base more approximate approaches, such as transition state theory and quasiclassical trajectories, which can be applied to larger systems. 

Transition state theory has been useful in providing a rationale for the so-called kinetic isotope effect. The kinetic isotope effect is used by enzy-mologists to probe various aspects of mechanism. Importantly, measured kinetic isotope effects have also been used to monitor if non-classical behaviour is a feature of enzyme-catalysed hydrogen transfer reactions. The kinetic isotope effect arises because of the differential reactivity of, for example, a C-H (protium), a C-D (deuterium) and a C-T (tritium) bond. 

Figure 22 shows an application of the present method to the H3 reaction system and the thermal rate constant is calculated. The final result with tunneling effects included agree well with the quantum mechanical transition state theory calculations, although the latter is not shown here. 

Kinetics on the level of individual molecules is often referred to as reaction dynamics. Subtle details are taken into account, such as the effect of the orientation of molecules in a collision that may result in a reaction, and the distribution of energy over a molecule s various degrees of freedom. This is the fundamental level of study needed if we want to link reactivity to quantum mechanics, which is really what rules the game at this fundamental level. This is the domain of molecular beam experiments, laser spectroscopy, ah initio theoretical chemistry and transition state theory. It is at this level that we can learn what determines whether a chemical reaction is feasible. 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

Various statistical treatments of reaction kinetics provide a physical picture for the underlying molecular basis for Arrhenius temperature dependence. One of the most common approaches is Eyring transition state theory, which postulates a thermal equilibrium between reactants and the transition state. Applying statistical mechanical methods to this equilibrium and to the inherent rate of activated molecules transiting the barrier leads to the Eyring equation (Eq. 10.3), where k is the Boltzmann constant, h is the Planck s constant, and AG is the relative free energy of the transition state [note Eq. (10.3) ignores a transmission factor, which is normally 1, in the preexponential term]. 

Transition state theory, as embodied in Eq. 10.3, or implicitly in Arrhenius theory, is inherently semiclassical. Quantum mechanics plays a role only in consideration of the quantized nature of molecular vibrations, etc., in a statistical fashion. But, a critical assumption is that only those molecules with energies exceeding that of the transition state barrier may undergo reaction. In reality, however, the quantum nature of the nuclei themselves permits reaction by some fraction of molecules possessing less than the energy required to surmount the barrier. This phenomenon forms the basis for QMT. ... 

This chapter treats the descriptions of the molecular events that lead to the kinetic phenomena that one observes in the laboratory. These events are referred to as the mechanism of the reaction. The chapter begins with definitions of the various terms that are basic to the concept of reaction mechanisms, indicates how elementary events may be combined to yield a description that is consistent with observed macroscopic phenomena, and discusses some of the techniques that may be used to elucidate the mechanism of a reaction. Finally, two basic molecular theories of chemical kinetics are discussed—the kinetic theory of gases and the transition state theory. The determination of a reaction mechanism is a much more complex problem than that of obtaining an accurate rate expression, and the well-educated chemical engineer should have a knowledge of and an appreciation for some of the techniques used in such studies. 

Although the collision and transition state theories represent two important methods of attacking the theoretical calculation of reaction rates, they are not the only approaches available. Alternative methods include theories based on nonequilibrium statistical mechanics, stochastic theories, and Monte Carlo simulations of chemical dynamics. Consult the texts by Johnson (62), Laidler (60), and Benson (59) and the review by Wayne (63) for a further introduction to the theoretical aspects of reaction kinetics. 

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