Unimolecular reactions chemical activation

In a true unimolecular reaction, the activation is done by exposing the molecules to electromagnetic radiation, whereas activation is accomplished by inelastic collisions with other molecules in an apparent unimolecular reaction. The condition for the latter process to be unimolecular is that the time scales of the activation process and the chemical reaction are very different, so that the chemical reaction is much slower than the activation process. 

Commonly used reaction mechanisms for atmospheric or combustion systems contain a significant fraction of unimolecular and chemically activated reactions. Each of these reactions is in principle both temperature and pressure dependent, although the pressure dependence might vanish under certain conditions. Consequently, in order to achieve accurate kinetic predictions of complex chemical systems, it is necessary to incorporate this pressure and temperature dependence into kinetic models. This leads to the need to develop tools which allow the kineticist to analyze these types of reactions and which yield apparent time-independent rate constants that can be used in modeling studies. 

There are three methods for the formation of active molecules A (s > Eq), which could participate in the unimolecular reaction thermal activation, chemical activation, and photoactivation. Let us consider unimolecular reaction taking into account the method of activation. 

To detect tlie initial apparent non-RRKM decay, one has to monitor the reaction at short times. This can be perfomied by studying the unimolecular decomposition at high pressures, where collisional stabilization competes with the rate of IVR. The first successful detection of apparent non-RRKM behaviour was accomplished by Rabinovitch and co-workers [115], who used chemical activation to prepare vibrationally excited hexafluorobicyclopropyl-d2 ... 

Eyring H 1935 The activated complex in chemical reactions J. Chem. Phys. 3 107-15 Hofacker L 1963 Quantentheorie chemischer Reaktionen Z. Naturf. A 18 607-19 Robinson P J and Holbrook K A 1972 Unimolecular Reactions (New York Wiley)... 

It is convenient initially to classify elementary reactions either as energy-transfer-limited or chemical reaction-rate-limited processes. In the former class, the observed rate corresponds to the rate of energy transfer to or from a species either by intermolecular collisions or by radiation, or intramolecular-ly due to energy transfer between different degrees of freedom of a species. All thermally activated unimolecular reactions become energy-transfer-limited at high temperatures and low pressures, because the reactant can receive the necessary activation energy only by intennolecular collisions. 

The QRRK approach illustrated above also constitutes the basis to analyze the behavior of the reverse, i.e., association, reactions that proceed through chemically activated transition states. Recently Dean (1985) reformulated the unimolecular quantum-RRK method of Kassel and devised a practical method for the proper description of the fall-off behavior of bimolecular reactions, including reactions when multiple product channels are present. The method developed was shown to describe the behavior of a large variety of bimolecular reactions with considerable success (Dean and Westmoreland, 1987 Westmoreland et ai, 1986). 

Current studies of unimolecular reactions can be broadly divided into three categories, based on different methods of activation of the decomposing species. The first, most classical, method is that of thermal activation of the type first envisioned by Lindemann to explain unimolecular dissociation phenomena brought about by heat energy. The second method involves chemical activation, ... 

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

Figure 16. Metastable ion cyclotron resonance (MICR) spectra for the unimolecular dissociation of the chemically activated adduct ion derived from association of the methoxymethyl cation with pivaldehyde during a 2-s reaction delay at a pressure of pivaldehyde of 1.0 x 10 torr. The three spectra correspond to values of rf amplitude appropriate to eject transient intermediates with lifetimes longer than (a) 60 ps, (b) 80 ps, and (c) 1 70 ps. A partial pressure of CH4 of 1.0 x 10 torr was also present to thermalize ions. The peak at m/z 125 is a secondary reaction product of m/z 85.

These, and similar data for other systems, demonstrate the tremendous potential that the MICR technique has for the qualitative elucidation of potential energy surfaces of relatively complex organic reactions. Once implementation of the quadrupolar excitation technique has been effected to relax ions to the cell center, the technique will become even more powerful, in that the determination of highly accurate unimolecular decomposition lifetimes of chemically activated intermediates will also become possible. No other technique offers such a powerful array of capabilities for the study of unimolecular dissociation mechanisms and rates. 

A major source of acceleration in enzymic reactions is approximation, that is to say, the bringing together of two or more reactants in the active site. Once the reagents are in contact, the subsequent reaction is intra- rather than intermolecular. Comparisons of the rates of intermolecular and intramolecular reactions are, however, difficult because the rate constants for bimolecular reactions have the units of M "1 s-1, whereas rate constants for unimolecular reactions have the units of s l. The best one can do in comparing them is to state the molarity at which the reactants would have to be present in the bimolecular reaction to achieve the rate of the unimolecular process when the effective molarity is large-say 1000 M or more-one has some measure of the power of approximation to accelerate chemical reaction. 

The theoretical analysis of chemical activation reactions is similar to the Lindemann theory of unimolecular and association reactions. There are a number of competing reaction pathways. Depending on total pressure, concentrations of the participating species, and temperature, the outcome of the competition can change. 

In reaction 9.132, molecules A and B form the excited (energized) reactive intermediate species C. Translational energy of the reactant molecules from their relative motion before collision is converted to internal (vibrational, rotational) energy of C. Reaction 9.132 provides a chemical activation (excitation) of the unstable C, with rate constant ka. Note that 9.132 does not involve a third body M for creation of the excited intermediate species, which differs from the unimolecular initiation event in Eq. 9.100. 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

Transition-state theory is based on the assumption of chemical equilibrium between the reactants and an activated complex, which will only be true in the limit of high pressure. At high pressure there are many collisions available to equilibrate the populations of reactants and the reactive intermediate species, namely, the activated complex. When this assumption is true, CTST uses rigorous statistical thermodynamic expressions derived in Chapter 8 to calculate the rate expression. This theory thus has the correct limiting high-pressure behavior. However, it cannot account for the complex pressure dependence of unimolecular and bimolecular (chemical activation) reactions discussed in Sections 10.4 and 10.5. 

Pressure effects are also seen in a class of bimolecular reactions known as chemical activation reactions, which were introduced in Section 9.5. The treatment in that chapter was analogous to the Lindemann treatment of unimolecular reactions. The formulas derived in Section 9.5 provide a qualitative explanation of chemical activation reactions, and give the proper high- and low-pressure limits. However, that simple treatment neglected many quantum mechanical effects, namely the energy dependence of various excitation/de-excitation steps. 

This section treats the theory of chemical activation reactions more rigorously, at the same level of approximation as in the discussion of unimolecular reactions in Section 10.4.4. That is, the QRRK theory of chemical activation reactions is developed here. This theory for bimolecular reactions was set out by Dean and coworkers [93,428],... 

Reaction 10.178 is a chemical activation process. Note that this reaction does not involve a third body M for creation of the excited intermediate species, which differs from the unimolecular initiation event in Eq. 10.99. 

Another mechanism has been suggested by Christiansen and Kramers in which activation is by collision and yet there is an apparently unimolecular reaction. It depends upon the possibility that the products of reaction, possessing the energy corresponding to the chemical heat of reaction as well as the original heat of activation, are able immediately to activate fresh molecules of reactant. In this way reaction-chains are set up. The assumption is made that every molecule of product can at once activate by collision a fresh molecule of the reactant. In this way each activated molecule removed from the system by chemical transformation is replaced by a new activated molecule. 

Perrin s argument that the very nature of a unimolecular reaction demands independence of collisions, and therefore dependence on radiation, is adequately met both by the theory of Lindemann and by that of Christiansen and Kramers. Both these theories have the essential element in common that the distribution of energy among the molecules is not appreciably disturbed by the chemical transformation of the activated molecules thus the rate of reaction is proportional simply to the number of activated molecules and therefore to the total number of molecules, sinc in statistical equilibrium the activated molecules are a constant fraction of the whole. Thus the radiation theory is not necessary to explain the existence of reactions which are unimolecular over a wide range of pressures. 

If activation by collision is assumed two questions arise (i) how the velocity constant of the unimolecular reaction remains independent of pressure, and (ii) whether the number of collisions taking place in the gas is great enough to activate molecules sufficiently fast to account for the observed rate of chemical change even at the lowest pressures. 

The unimolecular 1,2-HF and 2,3-HF elimination reactions of CF3CHFCH3 have been characterized using the chemical activation technique for an average vibrational energy of 97 kcalmol-1.36 The transition state for 1,2-HF elimination has a two-fold larger pre-exponential factor than that for 2,3-HF elimination, because three F atoms attached to carbon atoms of the four-membered ring have lower frequencies than those in a CF3 group. 

In Sect. 7, we raised the question of what were the chemical stimuli to which the reactivity indices defined in Sect. 6, the softness kernels, were presumed to be the responses, our seventh issue. Now there are various broad categories of reactions to be considered, unimolecular, bimolecular, and multimolecular. The former occur via thermal activation over a barrier, tunneling through the barrier, or some combination of both. There is no stimulus, and the softness kernels defined as responses of the electron density to changes in external or nuclear potential are irrelevant. For the study of unimolecular reactions, one needs only information about the total energy in the relevant configuration space of the molecule. 

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