Reactions and Transition State Theory

Another theory that also helps us understand how chemical reactions take place is called transition state theory (TST), the development of which is attributed primarily to the American chemist Henry Eyring (1901-81), who spent most of his career at the University of Utah in Salt Lake City. In TST, we picture an energy barrier that the reacting molecules must pass over before they can become products. Consider an analogy. 

Replace the football with molecules. The molecules are all at the same temperature, but they are moving at different speeds and, therefore, with different kinetic energies. 

Two outcomes can result from the transition state. The transition state species can just break apart into the original molecules with no net change, or it can continue on and form the products of the reaction. 

A reasonable question to ask is if it s possible for the products of a reaction, once they have formed, to colUde with each other, go back through the transition state, and reform the reactants with which we started originally The answer is yes. 

The transition state is the moiecuiar intermediate occurring at the highest point on the energy ievei diagram for a chemicai reaction. 

---

UNI MOLECULAR REACTIONS AND TRANSITION STATE THEORY TRANSITION-STATE THEORY (Thermodynamics)... 

Song K and Chesnavich W J 1989 Multiple transition states in chemical reactions variational transition state theory studies of the HO2 and HeH2 systems J. Chem. Rhys. 91 4664-78... 

Show how collision theory and transition state theory account for the temperature dependence of reactions (Sections... 

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. 

It is worthwhile to first review several elementary concepts of reaction rates and transition state theory, since deviations from such classical behavior often signal tunneling in reactions. For a simple unimolecular reaction. A—>B, the rate of decrease of reactant concentration (equal to rate of product formation) can be described by the first-order rate equation (Eq. 10.1). 

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. 

While the collision theory of reactions is intuitive, and the calculation of encounter rates is relatively straightforward, the calculation of the cross-sections, especially the steric requirements, from such a dynamic model is difficult. A very different and less detailed approach was begun in the 1930s that sidesteps some of the difficulties. Variously known as absolute rate theory, activated complex theory, and transition state theory (TST), this class of model ignores the rates at which molecules encounter each other, and instead lets thermodynamic/statistical considerations predict how many combinations of reactants are in the transition-state configuration under reaction conditions. 

For a temperature of 1000 K, calculate the pre-exponential factor in the specific reaction rate constant for (a) any simple bimolecular reaction and (b) any simple unimolecular decomposition reaction following transition state theory. 

In this section, you used collision theory and transition state theory to explain how reaction rates are affected hy various factors. You considered simple reactions, consisting of a single-step collision between reactants. Not all reactions are simple, however. In fact, most chemical reactions take place via several steps, occurring in sequence. In the next section, you will learn about the steps that make up reactions and discover how these steps relate to reaction rates. 

Use collision theory and transition state theory to explain how concentration, temperature, surface area, and the nature of reactants control the rate of a chemical reaction. 

For our purpose elementary steps can be chosen to include any reaction that cannot be further broken down so as to involve reactions in which the specified intermediates are produced or consumed. Ideally, elementary steps should consist of irreducible molecular events, usually with a molecularity no greater than two. Such steps are amenable to treatment by fundamental chemical principles such as collision and transition state theories. Often such a choice is not feasible because of lack of knowledge of the detailed chemistry involved. Each of these elementary reactions, even when carefully chosen, may itself have a definite mechanism, but theory may be unable to elucidate this finer detail [Moore (2)]. 

However, definitive proof for these proposals are difficult to obtain because of the difficulties in temperature measurement alluded to above and that the reaction might be occurring under non-equilibrium conditions, where the conventional rate expressions and transition state theory assumptions may not be valid. 

A direct dynamics simulation of the. S N2 identity reaction of CD3C1 at the MP2/6-31G level of theory110 found that the dynamics of the trajectories from the transition state were inconsistent with both RRKM and transition state theory. 

For many years this reaction was quoted as the classic example of an elementary bimolecular reaction, and used as a test of collision and transition state theories, but it has now been shown to be a complex non-chain reaction. 

Figure 5.39 shows the schematic diagram of the transition state for an exothermic reaction. The transition-state theory assumes that the rate of formation of a transition-state intermediate is very fast and the decomposition of the unstable intermediate is slow and is the rate-determining step. On the other hand, the collision theory states that the rate of the reaction is controlled by collisions among the reactants. The rate of formation of the intermediate is very slow and is followed by the rapid decomposition of the intermediates into products. Based on these two theories, the following expression can be derived to account for the temperature dependence of the rate constant ... 

The evaluation of kinetic barrier heights (21-105 kJ mol-1) from the temperature dependence of rates has been one of the most important contributions of DNMR to conformational processes. However, only a handful of these studies have addressed gas-phase processes, mainly due to the need for instrumentation improvements just recently achieved as described above. It has become customary to discuss exchange processes in terms of the Arrhenius equation and transition state theory (TST) of reaction rates [57] which is summarized by the Eyring equation. The Arrhenius equation in the following form is used to obtain the activation energy ( act) and frequency factor (A) from the slope and intercept,... 

The MIF phenomenon was first observed by Clayton in 1973 for the isotopic oxygen content in the earliest solids in the solar system, the so-called calcium-aluminum-rich inclusions (CAIs) in carbonaceous chondritic meteorites [1]. The slope of versus plot for the CAIs was close to unity, the CAIs being equally deficient in the heavy O isotopes, deficient in the S notation sense, while the ozone is equally enriched in those isotopes in that sense, as in Figure 2.2. Both are examples of an MIF. Interest in this striking phenomenon for the CAIs is motivated by what it may reveal about the formation of the early solar system. Standard reaction rate transition state theory [3], and behavior of oxygen an other isotope fractionation in many other systems, would have led, instead, to the slope... 

Subsequently, Banks and White reported a gas-phase study of the reactions of thiiranes with ammonia and secondary amines <2001JOG5981>. B3LYP/6-31- -G(d) and HF/6-31G(d) computations and transition-state theory were used, and the reactivity of a thiirane with a secondary amine was ascribed to the net effect of steric hindrance and polarizability. 2-Fluorothiirane was calculated to react with ammonia more than 10 times as fast as thiirane. Reaction at C-2 was calculated to be slower by a factor of 2.4 x 10 than reaction at C-1. 2-Methylthiirane reacts more slowly than thiirane and the regioselectivity in favor of C-1 was 12.8. In 2,2-dimethylthiirane, the analogous regioselectivity rose to 124. 

Lasaga, A. C. (1983) Rate Laws of Chemical Reactions, Chap. 1, and Transition State Theory, Chap. 4. In Reviews in Mineralogy 8, Kinetics of Geochemical Processes, Mineralogical Society, Washington, DC. 

The second point is that the new phase-space representation permits the definition of a true dividing surface in phase space which truly separates the reactant and product sides of a reaction. Traditional transition state theory of chemical reactions, based simply on coordinate-space definitions of the degrees of freedom, required an empirical correction factor, the transmission... 

J. B. Anderson (1973) Statistical theories of chemical reactions Distributions in the transition region. J. Chew,. Phys., 58, pp. 4684-4692 C.H. Bennett (1977) Molecular Dynamics and Transition State Theory the Simulation of Infrequent Events. In Algorithms for Chemical Computations, ed. R. E. Christoffersen, pp. 63-97 Washington, D.C. Amer. Chem. Soc. D. Chandler (1978) Statistical mechanics of isomerization dynamics in liquids and the transition state approximation. J. Chem,. Phys., 68, pp. 2959-2970... 

Four factors have marked effects on the rates of chemical reactions. They are (1) nature of the reactants, (2) concentrations of the reactants, (3) temperature, and (4) the presence of a catalyst. Understanding their effects can help us control the rates of reactions in desirable ways. The study of these factors gives important insight into the details of the processes by which a reaction occurs. This kind of study is the basis for developing theories of chemical kinetics. Now we study these factors and the related theories—collision theory and transition state theory. 

As a specific example that illustrates the ideas of collision theory and transition state theory, consider the reaction of iodide ions with methyl chloride. 

Because the value of RT is less than 1 kcal/mol up to about 500 K, this last expression reduces to E = Aff. We now have a tie-in between the empirical Arrhenius equation and transition-state theory and a way to evaluate the enthalpy of activation of a reaction. 

---