Unimolecular decompositions, detailed

The desire to understand catalytic chemistry was one of the motivating forces underlying the development of surface science. In a catalytic reaction, the reactants first adsorb onto the surface and then react with each other to fonn volatile product(s). The substrate itself is not affected by the reaction, but the reaction would not occur without its presence. Types of catalytic reactions include exchange, recombination, unimolecular decomposition, and bimolecular reactions. A reaction would be considered to be of the Langmuir-Hinshelwood type if both reactants first adsorbed onto the surface, and then reacted to fonn the products. If one reactant first adsorbs, and the other then reacts with it directly from the gas phase, the reaction is of the Eley-Ridel type. Catalytic reactions are discussed in more detail in section A3.10 and section C2.8. 

Alkyl hydroperoxides give alkoxy radicals and the hydroxyl radical. r-Butyl hydroperoxide is often used as a radical source. Detailed studies on the mechanism of the decomposition indicate that it is a more complicated process than simple unimolecular decomposition. The alkyl hydroperoxides are also sometimes used in conjunction with a transition-metal salt. Under these conditions, an alkoxy radical is produced, but the hydroxyl portion appears as hydroxide ion as the result of one-electron reduction by the metal ion. ... 

Reactants AB+ + CD are considered to associate to form a weakly bonded intermediate complex, AB+ CD, the ground vibrational state of which has a barrier to the formation of the more strongly bound form, ABCD+. The reactants, of course, have access to both of these isomeric forms, although the presence of the barrier will affect the rate of unimolecular isomerization between them. Note that the minimum energy barrier may not be accessed in a particular interaction of AB+ with CD since the dynamics, i.e. initial trajectories and the detailed nature of the potential surface, control the reaction coordinate followed. Even in the absence (left hand dashed line in Figure 1) of a formal barrier (i.e. of a local potential maximum), the intermediate will resonate between the conformations having AB+ CD or ABCD+ character. These complexes only have the possibilities of unimolecular decomposition back to AB+ + CD or collisional stabilization. In the stabilization process,... 

At high temperatures and low pressures, the unimolecular reactions of interest may not be at their high-pressure limits, and observed rates may become influenced by rates of energy transfer. Under these conditions, the rate constant for unimolecular decomposition becomes pressure- (density)-dependent, and the canonical transition state theory would no longer be applicable. We shall discuss energy transfer limitations in detail later. 

To illustrate these issues better, the pressure at the center of fall-off (F ) is presented in Fig. 20. As seen from this figure, the unimolecular decompositions of small molecules are at their low-pressure limits at atmospheric pressure, and at process temperatures, = feo [M]- Decompositions of larger molecules, on the other hand, are closer to their high-pressure limits. It is important to recognize that the unimolecular decompositions of hydrocarbons from CH4 to CaHg exhibit differing degrees of fall-off under process conditions, and this must be properly accounted for in the development of accurate detailed chemical kinetic models. 

A subsequent study examined phenylperoxy radical in greater detail. Fadden et identified five possible unimolecular decomposition pathways for phenylperoxy radical (Fig. 10) via oxygen atom loss to form phenoxy radical (Fig. 10, route A), via a dioxiranyl radical species (Fig. 10, route B), via a dioxetanyl radical... 

Marcus and Rice6 made a more detailed analysis of the recombination from the point of view of the reverse reaction, the unimolecular decomposition of ethane, C2Ha - 2CH3. By the principle of microscopic reversibility the transition states must be the same for forward and reverse paths. Although they reached no definite conclusion they pointed out that a very efficient recombination of CH3 radicals would imply a very high Arrhenius A factor for the unimolecular rate constant of the C2H6 decomposition which in turn would be compatible only with a very "loose transition state. Conversely, a very low recombination efficiency would imply a very tight structure for the transition state and a low A factor for the unimolecular decomposition. 

A detailed quantum mechanical study of the mechanism of thermal decomposition of isoxazole has been conducted since previous theoretical predictions appeared to be inconsistent with the experimental results.33 It has been concluded that the mam unimolecular decomposition is through the sequence isoxazole —> NCCH2CHO —> CH3CN + CO and that the minor products, HCN and H2CCO, probably arise via a cyclic carbene as proposed in the experimental study. 

We conclude that collisional activation, preceding unimolecular decomposition of complex molecules, seems to occur with very high efficiency, but precisely how efficiently is not known in any one case161. A detailed examination of energy distributions may be found in recent papers by Rabinovitch and coworkers183. 

Although a vast majority of important chemical reactions occur primarily in liquid solution, the study of simple gas-phase reactions is very important in developing a theoretical understanding of chemical kinetics. A detailed molecular explanation of rate processes in liquid solution is extremely difficult. At the present time reaction mechanisms are much better understood for gas-phase reactions even so this problem is by no means simple. This experiment will deal with the unimolecular decomposition of an organic compound in the vapor state. The compound suggested for study is cyelopentene or di-i-butyl peroxide, but several other compounds are also suitable see, for example. Table XI.4 of Ref. 1. 

M is Br2 or any other gas that is present. By the principle of microscopic reversibility , the reverse processes are also pressure-dependent. A related pressure effect occurs in unimolecular decompositions which are in their pressure-dependent regions (including unimolecular initiation processes in free radical reactions). According to the simple Lindemann theory the mechanism for the unimolecular decomposition of a species A is given by the following scheme (for more detailed theories see ref. 47b, p.283)... 

A reaction-path based method is described to obtain information from ab initio quantum chemistry calculations about the dynamics of energy disposal in exothermic unimolecular reactions important in the initiation of detonation in energetic materials. Such detailed information at the microscopic level may be used directly or as input for molecular dynamics simulations to gain insight relevant for the macroscopic processes. The semiclassical method, whieh uses potential energy surface information in the broad vicinity of the steepest descent reaction path, treats a reaction coordinate classically and the vibrational motions perpendicular to the reaction path quantum mechanically. Solution of the time-dependent Schroedinger equation leads to detailed predictions about the energy disposal in exothermic chemical reactions. The method is described and applied to the unimolecular decomposition of methylene nitramine. 

Initiated by the chemical dynamics simulations of Bunker [37,38] for the unimolecular decomposition of model triatomic molecules, computational chemistry has had an enormous impact on the development of unimolecular rate theory. Some of the calculations have been exploratory, in that potential energy functions have been used which do not represent a specific molecule or molecules, but instead describe general properties of a broad class of molecules. Such calculations have provided fundamental information concerning the unimolecular dissociation dynamics of molecules. The goal of other chemical dynamics simulations has been to accurately describe the unimolecular decomposition of specific molecules and make direct comparisons with experiment. The microscopic chemical dynamics obtained from these simulations is the detailed information required to formulate an accurate theory of unimolecular reaction rates. The role of computational chemistry in unimolecular kinetics was aptly described by Bunker [37] when he wrote The usual approach to chemical kinetic theory has been to base one s decisions on the relevance of various features of molecular motion upon the outcome of laboratory experiments. There is, however, no reason (other than the arduous calculations involved) why the bridge between experimental and theoretical reality might not equally well start on the opposite side of the gap. In this paper... results are reported of the simulation of the motion of large numbers of triatomic molecules by... 

The random lifetime assumption is perhaps most easily tested by classical trajectory calculations (Bunker, 1962 1964 Bunker and Hase, 1973). Initial momenta and coordinates for the Hamiltonian of an excited molecule can be selected randomly, so that a microcanonical ensemble of states is selected. Solving Hamilton s equations of motion, Eq. (2.9), for an initial condition gives the time required for the system to reach the transition state. If the unimolecular dynamics of the molecule are in accord with RRKM theory, the decomposition probability of the molecule versus time, determined on the basis of many initial conditions, will be exponential with the RRKM rate constant. That is, the decay is proportional to exp[-k( )t]. The observation of such an exponential distribution of lifetimes has been identified as intrinsic RRKM behavior. If a microcanonical ensemble is not maintained during the unimolecular decomposition (i.e., IVR is slower than decomposition), the decomposition probability will be nonexponential, or exponential with a rate constant that differs from that predicted by RRKM theory. The implication of such trajectory studies to experiments and their relationship to quantum dynamics is discussed in detail in chapter 8. 

Further developments in the use of kinetic chemical activation for energy transfer studies will undoubtedly be based on more detailed attention to the energy dependence of the transition probabilities and more accurately defined initial product excitation functions. Each extension wall require that the unimolecular decomposition rate constant be calculated or measured as a function of energy. In cases where adequate... 

This matter has been discussed in some detail, because it leads directly to the consideration of unimolecular reactions, an example of which is in effect presented by the redissociation of the energized ethane. If the latter instead of retaining its energy from the process of formation, had received it in collisions, then the situation would have corresponded to an ordinary unimolecular decomposition. 

Although this discussion of gas-phase reactions can hardly be considered comprehensive, many important and general features of gas-phase mechanisms have been considered. Unimolecular decompositions are discussed in some detail in the next chapter, and some approaches to elementary reactions in the gas phase are considered in Chapters 5 and 6. 

The important role of both intramolecular and intermolecular energy transfer in gas-phase chemical reactions has been stressed in the discussions of unimolecular decompositions and molecular beam studies. In this chapter, intermolecular energy transfer and energy partitioning in chemical reactions is considered more explicitly. The dissociation of homonuclear molecules is discussed since the details of the energy distribution appear to play a major role in the reaction mechanism. The reaction... 

This is an unimolecular decomposition process of a hot n-propyl radical. This rate constant ke-2 can be estimated by RRKM theory. Details of the calculation are given in the appendix. 

The kinetic isotope effect observed on the overall rates of hydrogenolytic demethylation of propylene in the presence of deuterium was successfully interpreted in terms of a free radical chain mechanism. Little differences were inferred to exist between the rates of addition of H or D- to propylene and also between those of unimolecular decomposition of the produced hot n-propyl radicals, and thus the kinetic isotope effect was ascribed mainly to the difference between the steady state concentrations of [H-] in the presence of hydrogen and the concentrations of [D ] + [H ] in the presence of deuterium. In more detail, conversion of rather inactive allyl radical by metathesis with deuterium into an active D is relatively slow. This was concluded to be the main cause of the observed kinetic isotope effect, which agrees well with the calculated... 

In previously reported work, we ve looked for comparisons with other types of studies related to explosives. Experimental studies such as thermal decomposition, laser irradiation decomposition (LIMA), impact induced decomposition, and even unimolecular decomposition have been examined to see if there is a common thread between decomposition and detonation products. Almost all of the products that we observe, which of course are gaseous, are in the list of products that some of these other experiments report. But quantitatively we don t find much in common, although that may be partly because not all of their products were reported in enough detail for a good comparison. Water seems to be especially difficult to measure in some of the methods and is only reported as being present. We conclude that the product distributions that we find, and which we are certain are closely related to the chemistry driving the detonation process, are not well represented by any other process at work in these other experiments. 

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