Activated complex or transition state

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

The case of m = Q corresponds to classical Arrhenius theory m = 1/2 is derived from the collision theory of bimolecular gas-phase reactions and m = corresponds to activated complex or transition state theory. None of these theories is sufficiently well developed to predict reaction rates from first principles, and it is practically impossible to choose between them based on experimental measurements. The relatively small variation in rate constant due to the pre-exponential temperature dependence T is overwhelmed by the exponential dependence exp(—Tarf/T). For many reactions, a plot of In(fe) versus will be approximately linear, and the slope of this line can be used to calculate E. Plots of rt(k/T" ) versus 7 for the same reactions will also be approximately linear as well, which shows the futility of determining m by this approach. 

Transition state theory complements collision theory. When particles collide with enough energy to react, called the activation energy, Ea, the reactants form a short-lived, high energy activated complex, or transition state, before forming the products. The transition state also could revert back to the reactants. 

The idea that an activated complex or transition state controls the progress of a chemical reaction between the reactant state and the product state goes back to the study of the inversion of sucrose by S. Arrhenius, who found that the temperature dependence of the rate of reaction could be expressed as k = A exp (—AE /RT), a form now referred to as the Arrhenius equation. In the Arrhenius equation k is the forward rate constant, AE is an energy parameter, and A is a constant specific to the particular reaction under study. Arrhenius postulated thermal equilibrium between inert and active molecules and reasoned that only active molecules (i.e. those of energy Eo + AE ) could react. For the full development of the theory which is only sketched here, the reader is referred to the classic work by Glasstone, Laidler and Eyring cited at the end of this chapter. It was Eyring who carried out many of the... 

The Eyring activated-complex (or transition-state) treatment relates the observed rate constant k to multiplied by the frequency factor k TIh, where k is the Boltzmann constant, T is the absolute temperature, and h is Planck s constant ... 

Absolute Reaction Rate Theory of Eyring Activated Complex- or Transition State- Theory. See "Absolute Rate Theory in Vol 1 of Encycl, p A4-R and in Ref 96, p 134... 

As two reactant species approach each other along a reaction path, their potential energy increases. At some maximum potential energy, they are combined in an unstable form, called an activated complex or transition state. Activation energy can also be defined as the minimum energy that reacting particles must possess in order to be able to form an activated complex prior to becoming products. 

When a collision with the proper orientation and sufficent activation energy occurs, an intermediate state exists before the products arc formed piis intermediate state, also called an activated complex or transition state, as neither the reactant or product, but rather a highly unstable combination of bbth as represented in Figure 1.13 for the decomposition of HI. 

Figure 1.14 shows the potential energy diagram for the decomposition of HI. As can be seen, in-order to reach the activated complex or transition state the proper orientaion (and JsufFicent collision energy must be achieved. Once these requirements/areyiCnieved the reaction continues on to completion and the products are fc... 

We are often interested in the activated complex or transition state of a reaction—that is, the halfway point beyond which the system becomes more likely to progress to the products than return to the reactants. Similarly important are the reaction intermediates, species formed during the course of the reaction, which exist for a significant time interval, but which are ultimately consumed. Reaction intermediates often may be detected physically or chemically. Of the many methods for studying reaction mechanisms, the most important is the determination of the rate law, the quantitative relationship between the reaction speed at a fixed temperature and the concentrations of the reagents. The rate law will often indicate the species that participate in the ratedetermining step of the reaction. 

We can envision the reaction progress as shown in Fig. 15.11. The arrangement of atoms found at the top of the potential energy hill, or barrier, is called the activated complex, or transition state. The conversion of BrNO to NO and Br2 is exothermic, as indicated by the fact that the products have lower energy than the reactant. However, AE has no effect on the rate of the reaction. Rather, the rate depends on the size of the activation energy a. 

According to the theory of absolute reaction rates [4-9], the rate is the product of a universal frequency factor and the concentration of the activated complex or transition state, M (the system in the transient state of highest potential energy), crossing the energy barrier in the direction toward the products. The activated complex, in turn, is postulated to be in equilibrium with the reactants. Say, for a single-step reaction A + B — P ... 

The repulsion of c from ah (owing to the transfer of electrons i and 3) increases as c approaches ab Simultaneously the state a—he becomes more probable and resonance between the states a—he and ah—c somewhat decreases the energy of repulsion. Thus, although it is necessary to expend energy as translational energy in order to bring atom c up to the molecule ah there may ultimately be attained a state in which h is equally joined to both a and c. This active complex or transitional state may be represented as... 

Ground-state reactions are easily modeled using the absolute reaction-rate theory and the concept of the activated complex. The reacting system, which may consist of one or several molecules, is represented by a point on a potential energy surface. The passage of this point from one minimum to another minimum on the ground-state surface then describes a ground-state reaction, and the saddle points between the minima correspond to the activated complexes or transition states. 

The activated complex or transition state is the configuration of the system with the highest potential energy. The energy difference between the reactants and the transition state is the activation energy for the reaction. Only those molecules with enough energy to surmount the barrier will react. 

The essential postulate is that an activated complex (or transition state) is formed from the reactant, and that this subsequently decomposes to the products. The activated complex is assumed to be in thermodynamic equilibrium with the reactants. Then the rate-controlling step is the decomposition of the activated complex. The concept of an equilibrium activation step followed by slow decomposition is equivalent to assuming a time lag between activation and decomposition into the reaction products. It is the answer proposed by the theory to the question of why all collisions are not effective in producing a reaction. 

In a bimolecular solution reaction, the reactants A and B diffuse to a point close to one another at which reaction is possible. This process is called formation of the precursor complex. At this point, rearrangement of bond lengths and bond angles in the two reactants, and of the surrounding solvent molecules, can occur to form an activated complex or transition state between the reactants and products. As one would expect, the nature of this process depends on the specific reaction involved. It is the focus of the development of the theory of the elementary step in the reaction and the associated energy requirements. In some cases it has been studied experimentally using very fast laser spectroscopic techniques which provide time-resolved information about the elementary step in the femtosecond range. 

Figure 3.1.2 Free energy changes during a reaction. The activated complex (or transition state) is the configuration of maximum free energy.

The first step in the above reaction is the formation of a transient complex, called the activated complex or transition state ... 

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