Unimolecular Conversion

Further development of the statistical theory introduced an additional constraint imposed by the conservation of the molecular angular momentum [339] by a more precise specification of the transition complex structure [486] along with the elucidation of the limitations of statistical approximation [179]. 

The general RRKM theory gives the following expression for the microscopic rate constant k(E) 

Here w (E — Ea) is the number of quantum states of the activated complex for all energies up to E — Ea and p(E) the density of the active molecule quantum states. Thus, in terms of the statistical theory, the calculation of k(E) reduces to the calculation of the characteristics of the active molecule and of the activated complex spectra (for detail see [142, 391, 397, 398]). 

One of the versions of the RRKM theory is based on the harmonic model of the molecule. The active molecule is represented by a system of s harmonic oscillators with frequencies 

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The next step in a catalytic cycle after adsorption of the reactant molecules is a surface reaction, the simplest of which is the unimolecular conversion of an adsorbed species into a product molecule. For example, the following two-step sequence represents the conversion of A into products through the irreversible surface reaction of A ... 

The aliphatic nitrogen mustards act similarly after formation of a cyclic immonium ion. The unimolecular conversion to the immonium ion is relatively fast and once formed it reacts by an, Sy2 mechanism at a rate dependent on the concentration of nucleophilic centres ... 

The model of Lebedev assumes that the chemical reaction of A and B begins only when they are in some active volume, v, given by 7X3 where X is the permanent crystal lattice parameter and 7 is a coefficient which depends on the nature of the matrix and which usually differs little from unity. Initially, no more than one particle is located in the cell. The particles can transfer from one cell to another with an average frequency, km, so that the diffusion coefficient Def = km /6X2. Particles appearing in the active volume, v, are in thermal equilibrium with the surrounding medium for a period l/ftm during which the probability of reaction is proportional to k, the rate coefficient of the unimolecular conversion (A. . . B) - AB. The probability of the reaction occurring in the cell is... 

Consider the system in which an electrode reaction is followed by a unimolecular conversion ... 

Subsequently, 2-methylazulene was shown to give nearly a 2 1 mixture of j8-methyl and a-methylnapthalene, but more importantly, it was found the reaction had an induction period suggesting that it was a radical chain process. Further, shock wave pyrolysis of azulene allowed determination of log k = 12.93 — 63 000/23RT for its unimolecular conversion to naphthalene. Furthermore, the rate constant calculated at the temperatures involved in the initial reports makes it clear that the unimolecular process is 10 000 times slower than what was observed. So radical chemistry is most likely involved in the early reports. 

In HAB molecules the potential surface involves three variables, the molecular angle, the AB distance and the H-AB separation if internal coordinates are chosen. Alternatively a representation is often taken in which, in addition to the AB separation, the H atom is described by its separation from a point on the AB axis (midpoint or center of mass) and the corresponding angle, sometimes referred to as scattering coordinates. Depending on the problem to be solved, the entire three-dimensional surface (very seldom) or a representative section thereof is calculated in ab initio work. The most interesting questions in an HAB study are (1) is the system bent or linear in the various states, (2) what is the energy difference for the two isomers HAB and ABH and what is the barrier to possible unimolecular conversion, and (3) how is the stability situation in the excited states ... 

It will be noted that in the initial Lindemann scheme the notion of the activated molecule was absent. It has been introduced later to account for the fact that unimolecular conversion will take place only if the energy of the active molecule is concentrated on definite degrees of freedom. 

It will be borne in mind that the concepts described above have been adopted before the tunnelling reactions were discovered. For these reactions, it is impossible to determine a sharp energy boundary between molecules capable of participating, with a certain probability, in unimolecular conversions and inactive molecules. However, since the corrections for tunnelling are often small, the definitions given above can be retained. 

It follows from vast experimental data that all processes of unimolecular conversions can be divided into two classes, depending on the relation between the activation energy E and the reaction heat. One class comprises processes with an activation energy higher than the reaction heat (Fig. 28). Such are the reactions of cis-trans isomerization with their activation energies of tens of kj at a reaction heat of about 10 kJ. 

If the overall reaction can be described as a fast pre-equilibrium followed by a slow unimolecular conversion, then in a temperature-jump experiment two relaxation times are expected, the faster of which is not observed, while the slower, which is observed and is of the order of milliseconds, is given by ... 

Later DFT studies (Table 3.1) present a consistent picture the vinyiidene complex is always the global minimum and the unimolecular conversion ofthe alkynyl hydride complex to the vinyiidene is the rate-controlling step, although the energy difference between the two competing transition states (TSj 2 and TS2 3) is quite small. The largest outlier is the study by Hall, entry 3 [50], which puts TSj 2 at just 3 kcal mol , but it appears that what is reported as TSj 2 maybe the C-H o-complex that precedes formal oxidative addition and not the transition state itself. 

Chain uncoiling, and the converse process of coiling, is conveniently considered as a unimolecular chemical reaction. It is assumed that the rate of uncoiling at any time after application of a stress is proportional to the molecules still coiled. The deformation Dhe(0 at tinie t after application of stress can be shown to be related to the equilibrium deformation Dhe( ) by the equation... 

Since an elementary reaction occurs on a molecular level exactly as it is written, its rate expression can be determined by inspection. A unimolecular reaction is first-order process, bimolecular reactions are second-order, and termolecular processes are third-order. However, the converse statement is not true. Second-order rate expressions are not necessarily the result of an elementary bimolecular reaction. While a... 

The rate constant ke corresponds to the reciprocal of the lifetime of the excited state. Internal conversion The excited state can do other things, such as convert some of the original electronic excitation to a mixture of vibration and a different electronic state. These are also treated as unimolecular processes with associated rate constants ... 

Fig. 11.16. Representation of three tandem mass spectrometry (MS/MS) scan modes illustrated for a triple quadrupole instrument configuration. The top panel shows the attributes of the popular and prevalent product ion CID experiment. The first mass filter is held at a constant m/z value transmitting only ions of a single mlz value into the collision region. Conversion of a portion of translational energy into internal energy in the collision event results in excitation of the mass-selected ions, followed by unimolecular dissociation. The spectrum of product ions is recorded by scanning the second mass filter (commonly referred to as Q3 ). The center panel illustrates the precursor ion CID experiment. Ions of all mlz values are transmitted sequentially into the collision region as the first analyzer (Ql) is scanned. Only dissociation processes that generate product ions of a specific mlz ratio are transmitted by Q3 to the detector. The lower panel shows the constant neutral loss CID experiment. Both mass analyzers are scanned simultaneously, at the same rate, and at a constant mlz offset. The mlz offset is selected on the basis of known neutral elimination products (e.g., H20, NH3, CH3COOH, etc.) that may be particularly diagnostic of one or more compound classes that may be present in a sample mixture. The utility of the two compound class-specific scans (precursor ion and neutral loss) is illustrated in Fig. 11.17.

This paper is about a reinterpretation of the cationic polymerizations of hydrocarbons (HC) and of alkyl vinyl ethers (VE) by ionizing radiations in bulk and in solution. It is shown first that for both classes of monomer, M, in bulk ([M] = niB) the propagation is unimolecular and not bimolecular as was believed previously. This view is in accord with the fact that for many systems the conversion, Y, depends rectilinearly on the reaction time up to high Y. The growth reaction is an isomerization of a 7t-complex, P +M, between the growing cation PB+ and the double bond of M. Therefore the polymerizations are of zero order with respect to m, with first-order rate constant k p]. The previously reported second-order rate constants kp+ are related to these by the equation... 

The proof is based on the fact that the reaction between acetone and bromine is recognised as being unimolecular and not, as would be expected, bimolecular. In the determination of the velocity of reaction, therefore, the (slow) conversion of the ketone into the enol is measured, whilst the addition of the bromine occurs with immeasurable rapidity. 

Scheme 1 illustrates the design of an experiment that could be used to determine the rate constant for H-atom abstraction from a group 14 hydride. Radical A- reacts with the hydride to give product A-H. In competition with this reaction, radical A- gives radical B- in a unimolecular or bimolecular reaction with a known rate constant, and product radical B- also reacts with the hydride, giving B-H. The rate constant for reaction of A- with the metal hydride can be determined from the product distribution, the known rate constant for conversion of A- to B-, and the concentrations... 

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