Transition state theory chemical reaction dynamics

The dynamics of molecular motion must be treated quantum mechanically if one is to have a quantitative description of chemical reactions. Since transition state theory is such a good approximation in classical mechanics—particularly at the lower energies that are most important for determining the thermally averaged rate k(T)—one would like to quantize it. Unfortunately there does not seem to be a way to quantize the basic transition state idea without also introducing other approximations. The heuristic argument goes as follows. 

The dynamics of molecular motion must be treated quantum mechanically if one is to have a quantitative description of chemical reactions. Since transition state theory is such a... 

For most combustion reactions at the temperatures characteristic of flames classical methods for treating the reaction dynamics — transition state theory (TST), statistical theory (ST), and classical trajectory (CT) methods — should be adequate. The TST method requires information about the potential energy surface only in the reactants and transition state regions and, so, can be readily applied to chemical reactions involving many nuclei. Semiempirical applications of TST have been surprisingly successful. We shall... 

The above discussion represents a necessarily brief simnnary of the aspects of chemical reaction dynamics. The theoretical focus of tliis field is concerned with the development of accurate potential energy surfaces and the calculation of scattering dynamics on these surfaces. Experimentally, much effort has been devoted to developing complementary asymptotic techniques for product characterization and frequency- and time-resolved teclmiques to study transition-state spectroscopy and dynamics. It is instructive to see what can be accomplished with all of these capabilities. Of all the benclunark reactions mentioned in section A3.7.2. the reaction F + H2 —> HE + H represents the best example of how theory and experiment can converge to yield a fairly complete picture of the dynamics of a chemical reaction. Thus, the remainder of this chapter focuses on this reaction as a case study in reaction dynamics. 

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. 

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. 

Trahlar DG, Isaacson AD, Garrett BC (1985) Generalised transition state theory. In Baer M (ed) Theory of Chemical Reaction Dynamics, Vol 4. CRC, Boca Raton, p 65... 

The transition state theory provides a useful framework for correlating kinetic data and for codifying useful generalizations about the dynamic behavior of chemical systems. This theory is also known as the activated complex theory, the theory of absolute reaction rates, and Eyring s theory. This section introduces chemical engineers to the terminology, the basic aspects, and the limitations of the theory. 

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. 

The simplest generalization of free-energy-of-solvation concepts to dynamics in solution is provided by transition state theory. In conventional transition state theory, the rate constant of a chemical reaction at temperature T is given by... 

Beyond Transition State Theory (and, therefore, beyond Monte Carlo simulations) dynamical effects coming from recrossings should be introduced. Furthermore, additional quantum mechanical aspects, like tunneling, should be taken into account in some chemical reactions. 

Transition state theory can be used to test reaction dynamics on a molecular scale. Thus one can hypothesize a spatial configuration of the atoms in the transition state and from this calculate A S° the predicted rate constant can then be compared to that observed. If the agreement is not acceptable, the molecular configuration of the transition state can be adjusted until such agreement is obtained. Assuming this molecular configuration approximates the actual form of the intermediate in the reaction, one can learn something about the chemical dynamics of the reaction. 

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