Transition states unimolecular reaction rates

The QET is not the only theory in the field indeed, several apparently competitive statistical theories to describe the rate constant of a unimolecular reaction have been formulated. [10,14] Unfortunately, none of these theories has been able to quantitatively describe all reactions of a given ion. Nonetheless, QET is well established and even the simplified form allows sufficient insight into the behavior of isolated ions. Thus, we start out the chapter from the basic assumptions of QET. Following this trail will lead us from the neutral molecule to ions, and over transition states and reaction rates to fragmentation products and thus, through the basic concepts and definitions of gas phase ion chemistry. 

The first step, which is rate determining, is an ionization to a carbocation (carbonium ion in earlier terminology) intermediate, which reacts with the nucleophile in the second step. Because the transition state for the rate-determining step includes R-X but not Y , the reaction is unimolecular and is labeled S l. First-order kinetics are involved, with the rate being independent of the nucleophile identity and concentration. 

According to the transition state theory, the rate constant of unimolecular reaction (at high pressure in the gas phase) is the following [5] ... 

Experimental rate constants, kinetic isotope effects and chemical branching ratios for the CF2CFCICH3-do, -d, -d2, and -d2 molecules have been experimentally measured and interpreted using statistical unimolecular reaction rate theory.52 The structural properties of the transition states needed for the theory have been calculated by DFT at the B3PW91 /6-31 G(d,p/) level. 

This type of substitution is called an SN1 reaction, for Substitution, Nucleophilic, unimolecular. The term unimolecular means there is only one molecule involved in the transition state of the rate-limiting step. The mechanism of the SnI reaction of tert-butyl bromide with methanol is shown here. Ionization of the alkyl halide (first step) is the rate-limiting step. 

A process following the rate law shown in Eq. (20.65) is said to be an SN1 (substitution, nucleophilic, unimolecular) process. The term unimolecular refers to the fact that a single species is required to form the transition state. Because the rate of such a reaction depends on the rate of dissociation of the M-X bond, the mechanism is also known as a dissociative pathway. In aqueous solutions, the solvent is also a potential nucleophile, and it solvates the transition state. In fact, the activated complex in such cases would be indistinguishable from the aqua complex [ML H20] in which a molecule of H20 actually completes the coordination sphere of the metal ion after X leaves. This situation is represented by the dotted curve in Figure 20.1 where the aqua complex is an intermediate that has lower energy than [ML,]. The species [ML H20] is called an intermediate because it has a lower energy than that of the activated complex, [MLJ. 

The Davis-Gray theory teaches us that by retaining the most important elements of the nonhnear reaction dynamics it is possible to accurately locate the intramolecular bottlenecks and to have an exact phase space separatrix as the transition state. Unfortunately, even for systems with only two DOFs, there may be considerable technical difficulties associated with locating the exact bottlenecks and the separatrix. Exact calculations of the fluxes across these phase space structures present more problems. For these reasons, further development of unimolecular reaction rate theory requires useful approximations. 

The intercept of Eq. (3) is the unimolecular rate constant k(E) for a microcanonical ensemble of reactant states. Bunker found that k(E) is well represented by the RRKM expression in Eq. (1) if anharmonicity effects are included for N E) and p( ) and if variational effects are included in identifying the transition state for reactions which do not have a barrier for the reverse association reaction [37-40]. Each of these two findings motivated extensive future studies [41-47]. 

In this spirit, we will also briefly describe the basis for some of the microscopic kinetic theories of unimolecular reaction rates that have arisen from nonlinear dynamics. Unlike the classical versions of Rice-Ramsperger-Kassel-Marcus (RRKM) theory and transition state theory, these theories explicitly take into account nonstatistical dynamical effects such as barrier recrossing, quasiperiodic trapping (both of which generally slow down the reaction rate), and other interesting effects. The implications for quantum dynamics are currently an active area of investigation. 

Furthermore, these results indicate that the transition state governing the rate of reaction involves only molecules of tert-huty chloride, and not water or hydroxide ions. The reaction is said to be unimolecular (first-order) in the rate-determining step, and we call it an S , reaction (substitution, nucleophilic, unimolecular). In Section 6.15 we shall see that elimination reactions can compete with S l reactions, leading to the formation of alkenes, but in the case of the conditions used above for the experiments with tert-huty chloride (moderate temperature and dilute base), S l is the dominant process. 

Unimolecular reaction A reaction in which only one species is involved in the reaction leading to the transition state of the rate-determining step. 

Before considering how the intramolecular dynamics determines the absolute value of the unimolecular reaction rate, and how van der Waals molecules can serve as a vehicle for the study of those intramolecular processes that compete with reaction, we ask if the characteristic features of the fragmentation reactions described in this section can be interpreted using perturbation theory. This approach is at the opposite end of the spectrum from the statistical theory of unimolecular reaction rate, since it focuses attention on state-to-state transitions. We shall see that such an analysis has some successes and some failures. 

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