Collision complexes Unimolecular reactions

The introductory remarks about unimolecular reactions apply equivalently to bunolecular reactions in condensed phase. An essential additional phenomenon is the effect the solvent has on the rate of approach of reactants and the lifetime of the collision complex. In a dense fluid the rate of approach evidently is detennined by the mutual difhision coefficient of reactants under the given physical conditions. Once reactants have met, they are temporarily trapped in a solvent cage until they either difhisively separate again or react. It is conmron to refer to the pair of reactants trapped in the solvent cage as an encounter complex. If the unimolecular reaction of this encounter complex is much faster than diffiisive separation i.e., if the effective reaction barrier is sufficiently small or negligible, tlie rate of the overall bimolecular reaction is difhision controlled. 

In a termolecular reaction, three chemical species collide simultaneously. Termolecular reactions are rare because they require a collision of three species at the same time and in exactly the right orientation to form products. The odds against such a simultaneous three-body collision are high. Instead, processes involving three species usually occur in two-step sequences. In the first step, two molecules collide and form a collision complex. In a second step, a third molecule collides with the complex before it breaks apart. Most chemical reactions, including all those introduced in this book, can be described at the molecular level as sequences of bimolecular and unimolecular elementary reactions. 

The Lindemann kinetics for unimolecular reactions [185] can be formally recovered if one subsumes the formation of a collision complex with the precursor complex steps R1-R2 <—> APC) into one corresponding to the excited reactant Rl. The excited... 

Not all ionization methods rely on such strictly unimolecular conditions as El does. Chemical ionization (Cl, Chap. 7), for example, makes use of reactive collisions between ions generated from a reactant gas and the neutral analyte to achieve its ionization by some bimolecular process such as proton transfer. The question which reactant ion can protonate a given analyte can be answered from gas phase basicity (GB) or proton affinity (PA) data. Furthermore, proton transfer, and thus the relative proton affinities of the reactants, play an important role in many ion-neutral complex-mediated reactions (Chap. 6.12). 

We have seen that neither the requirements for activation energy nor the fact that the rates of unimolecular reactions are independent of collision frequency can be explained on the basis of the simple collision hypothesis or the radiation hypothesis. The elaborated collision hypothesis is able to explain them on the assumption of a time-lag in complex molecules between activation and decomposition. In this way a single molecule can collect energy from many successive collisions and store up a sufficient amount for activation. Just because a given hypothesis accounts for the facts, is no reason to consider that the hypothesis has been proved. There may be other hypotheses which will account equally well for the facts. The hypothesis of chain reaction offers a competing hypothesis which up to the present time has been increasing in favor. 

It has been mentioned that phase space theory, i.e. assuming a loose transition state, has been able to explain the translational energy releases in the decomposition of certain ion—molecule collision complexes [485] and in some unimolecular decompositions measured by PIPECO (see Sect. 8.2). There is a larger number of translational energy releases from PIPECO and a body of data as to translational energy releases in source reactions of positive ions formed by El [162, 310] (Sect. 8.3.1) with which the predictions of phase space theory are in poor agreement. The predicted energy releases are too low. 

In the case of a unimolecular reaction, the activated complex is a single molecule which has gained the necessary energy by collision with other molecules.7,15,16 The generally accepted mechanism of the thermal dissociation of a molecule AB... 

The statistical dissociation rate constant can be calculated from the point of view of the reverse reaction, namely the recombination of the products to form a complex. This approach, commonly referred to as phase space theory (PST) (Pechukas and Light, 1965 Pechukas et al., 1966 Nikitin, 1965 Klots, 1971, 1972) is limited to reactions with no reverse activation energy, that is, reactions with very loose transition states. PST assumes the decomposition of a molecule or collision complex is governed by the phase space available to each product under strict conservation of energy and angular momentum. The loose transition state limit assumes that the reaction potential energy surface is of no importance in determining the unimolecular rate constant. 

The most favored decomposition reaction is the cleavage of SiCU, which, after numerous repetitions, should lead to Si02 and SiCU. Considering the discussed decomposition reactions from a molecular view point (kinetic aspect) also leads to a clear preference for decomposition reaction (a) For reaction (a) to occur, only the necessary activation energy from a collision with an energy-rich molecule or the (hot) wall of the reaction vessel has to be supplied. For reactions (b) and (c) to become operative, however, a collision of two molecules of equal composition is necessary. This is rather improbable in the complex reaction mixture. Unimolecular reactions which lead to products under (b) or (c) are not conceivable. 

Now, let us find a little flaw in the theory equation (2-86) predicts only first-order behavior for the unimolecular reaction, something we know in fact is not true at low pressures. The reason for this failure in TST is the assumption of universal equilibrium between reactants and the transition state complex. At low pressures the collisional deactivation process becomes very slow, since collisions are infrequent, and the rate of decomposition becomes large compared to deactivation. In such an event, equilibrium cannot be established nearly every molecule which is activated will decompose to product. However, the magnitude of the rate of decomposition of the transition complex is much larger than the decomposition of the activated molecule in the collision theory scheme, so one must resist the temptation to equate the two. Since the transition state complex represents a configuration of the reacting molecule on the way from reactants to products, the activated molecule must be a precursor of the transition state complex. 

The discovery of the unimolecular reactions which depend upon collisions blurred the classification in terms of orders, and the complex kinetics of chain reactions stiU further lessened its utility as a... 

A most interesting recent development is the work of Augustin and Rabitz, who obtained a transition between statistical and perturbation theories for any type of collision, not only complex-forming ones. More general stochastic aspects of unimolecular reactions have been discussed by Sole and Widom. An application of a phase-space model to electronic transitions in atomic collisions has been reported, as well as a simple RRKM model for electronic to vibrational energy transfer in 0( Z)) -I- Nj collisions. ... 

Our treatment, based on both the collision and the statistical formulations of reaction rate theory, shows that there exist two possibilities for an interpretation of the experimental facts concerning the Arrhenius parameter K for unimolecular reactions. These possibilities correspond to either an adiabatic or a non-adiabatic separation of the overall rotation from the internal molecular motions. The adiabatic separability is accepted in the usual treatment of unimolecular reactions /136/ which rests on transition state theory. To all appearances this assumption is, however, not adequate to the real situation in most unimolecular reactions.The nonadiabatic separation of the reaction coordinate from the overall rotation presents a new, perhaps more reasonable approach to this problem which avoids all unnecessary assumptions concerning the definition of the activated complex and its properties. Thus, for instance, it yields in a simple way the rate equations (7.IV), corresponding to the "normal Arrhenius parameters (6.IV), which are both direct consequences of the general rate equation (2.IV). It also predicts deviations from the normal values of the apparent frequency factor K without any additional assumptions, such that the transition state (AB)" (if there is one) differs more or less from the initial state of the activated molecule (AB). ... 

In recent years the semiclassical "statistical theory of RICE, RAMSPERGER, KASSEL, and MARCUS /136/ has made great progress in its development. The computational techniques of this theory provide the possibility of calculating the velocities of unimolecular reactions using suitable, models for the activated complex. This approach is certainly very useful for a correlation of the experimental facts and a description of various aspects of the observed phenomena. The success of such applications of the RRKM-theory does not at all preclude an alternative treatment based on the collision theory of... 

For reactions treated in this work, where one observes second-order intermolecular ET between freely diffusing small donor and acceptor molecules in homogeneous solution, ET is assumed to be preceded by the diffusion-controlled formation of a donor-acceptor collision complex. When formation and disassociation occur at or near diffusion control and are rapid relative to ET, the observed second-order ET rate constant, fc(obsvd)> is the product of the equilibrium constant for collision complex formation, K, and the unimolecular rate constant from Eq. (10.4) for ET from within the precursor complex (Eq. (10.6) [32, 33b] ... 

The collision theory is a useful one not only in the sense that it has provided insight into the nature of chemical reactions, but also because it is a theory that can be readily tested. The mark of a scientific theory is that it can be tested and falsified. So far, collision theory has been supported by experimental evidence, but if new data were produced that could not be explained using the collision theory then it would need to be modified or dismissed in favour of a new theory that did explain all the evidence. Currently collision theory is the best explanation of the experimental data produced so far (at this working level). It should be noted here that we have not begun to distinguish between elementary and complex, multi-step reactions. That discussion is developed in Chapter 16 with the introduction of the idea of the rate-determining step in a sequence of stages. This is an example of how the theory is modified to explain more complex situations. Note that unimolecular reactions are an apparent exception which require special treatment. 

The first of the theoretical chapters (Chapter 9) treats approaches to the calculation of thermal rate constants. The material is familiar—activated complex theory, RRKM theory of unimolecular reaction, Debye theory of diffusion-limited reaction—and emphasizes how much information can be correlated on the basis of quite limited models. In the final chapt, the dynamics of single-collision chemistry is analyzed within a highly simplified framework the model, based on classical mechanics, collinear collision geometries, and naive potential-energy surfaces, illuminates many of the features that account for chemical reactivity. 

Figure 1 Schematic potential profiles for (a) direct bimolecular reaction, and (b) collision-complex-forming bimolecular reaction and unimolecular dissociation reaction...

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