Unimolecular thermal reactions

The system of coupled differential equations that result from a compound reaction mechanism consists of several different (reversible) elementary steps. The kinetics are described by a system of coupled differential equations rather than a single rate law. This system can sometimes be decoupled by assuming that the concentrations of the intennediate species are small and quasi-stationary. The Lindemann mechanism of thermal unimolecular reactions [18,19] affords an instructive example for the application of such approximations. This mechanism is based on the idea that a molecule A has to pick up sufficient energy... 

Gilbert R G, Luther K and Troe J 1983 Theory of thermal unimolecular reactions in the fall-off range. II. Weak collision rate constants Ber. Bunsenges. Phys. Chem. 87 169-77... 

Troe J 1977 Theory of thermal unimolecular reactions at low pressures. I. Solutions of the master equation J. Chem. Phys. 66 4745-57... 

Nitrosoimines can undergo thermal reaction, a unimolecular, two-step mechanism has been proposed, as shown in Scheme 3.22 [193]. In this mechanism, a concerted electrocyclization is envisioned to form the strained four-membered ring in 41, followed by a presumably forbidden, but highly exothermic, deazetization to give 41. The electrocyclic ring closure is, at first glance, a 4-electron process, analogous to the cyclization of butadiene [194] or acrolein [194, 195]. This would be expected to involve rotation around the C=N bond coupled with C-O bond formation. 

Two likely paths exist for the thermal unimolecular decomposition of silane. The first reaction path involves the scission of the SiHs-H bond, with a stretched or loose transition state ... 

Conventional wisdom concerning thermal unimolecular reactions would seem to dictate that this must then be a Lindemann-type collisionally activated dissociation reaction scheme such as is in Equation (17). Application of the steady-state... 

Troe, J., Theory of Thermal Unimolecular Reactions in the Fall-Off Range. Strong Collision Rate Constants, Her. Bunsenges. Phys. Chem., 87, 161-169 (1983). 

Pericyclic reactions are unimolecular, concerted, uncatalyzed transformations. They take place in a highly stereoselective manner governed by symmetry proper-ties of interacting orbitals. - Characteristic of all these rearrangements is that they are reversible and may be effected thermally or photochemically. The compounds in equilibrium are usually interconverted through a cyclic transition state,224 although biradical mechanisms may also be operative. A few characteristic examples of pericyclic rearrangements relevant to hydrocarbon isomerizations are presented here. 

J. Troe. Theory of Thermal Unimolecular Reactions at Low Pressures. II. Strong Collision Rate Constants. Applications. J. Chem. Phys., 66(11) 4758—4775,1977. 

From a structural point of view, mechanism in a single crystal can be much closer to a set of identical atomic trajectories than to the kind of fuzzy statistical average with which one must be content in solution. It is not surprising that with this kind of structural uniformity the site problems that plague kinetic studies in rigid glasses disappear. Adherence to first-order rate laws can be as close in single crystals as it is in fluids, and equally valid activation parameters can be obtained for thermal unimolecular reactions of reaction intermediates [12]. 

The kinetics of formation of ketene and acetic acid on thermal unimolecular decomposition of acetic anhydride at 750-980 K have been reported and used to reevaluate the Arrhenius equation as k = 10122exp(—145 kJ mol l/RT) s-1 for the temperature range 470-980 K.54 Results of ah initio MO calculations suggest that the reaction proceeds by concerted elimination through a six-centre transition state, with potential barrier height 156 kJ mol-1. 

A series of cyano(arylcarbamoyl)phosphorus ylides (6) and cyano(arylthiocarbamo-yl)phosphorus ylides (7) have been prepared and fully characterized.33 Pyrolytic reaction products obtained by FVP have shown that thermal extrusion of PI13PO or PI13PS occurs (Scheme 5). Kinetic study of the gas-phase pyrolysis of each ylide by a static method showed that these reactions are unimolecular and first order with no significant substituent effect, but the thiocarbamoyl ylides (7) react 40-65 times more rapidly than their carbamoyl analogues (6). 

N. S. Snider, J. Phys. Chem., 90, 4366 (1986). Model Dependence of Collision Efficiencies for Thermal Unimolecular Reactions. 

In principle, one can induce and control unimolecular reactions directly in the electronic ground state via intense IR fields. Note that this resembles traditional thermal unimolecular reactions, in the sense that the dynamics is confined to the electronic ground state. High intensities are typically required in order to climb up the vibrational ladder and induce bond breaking (or isomerization). The dissociation probability is substantially enhanced when the frequency of the field is time dependent, i.e., the frequency must decrease as a function of time in order to accommodate the anharmonicity of the potential. Selective bond breaking in polyatomic molecules is, in addition, complicated by the fact that the dynamics in various bond-stretching coordinates is coupled due to anharmonic terms in the potential. 

Thermal unimolecular reactions usually exhibit first-order kinetics at high pressures. As pointed out originally by Lindemann [1], such behaviour is found because collisionally energised molecules require a finite time for decomposition at high pressures, collisional excitation and de-excitation are sufficiently rapid to maintain an equilibrium distribution of excited molecules. Rice and Ramsperger [2] and, independently, Kassel [3] (RRK), realised that a detailed theory must take account of the variation of decomposition rate of an excited molecule with its degree of internal excitation. Kassel s theory is still widely used and is valid for the chosen model of a set of coupled, classical, harmonic oscillators. 

In addition to the chemical activation non-equilibrium systems, the thermally induced decomposition of hydrocarbons and hydrocarbon radicals has also been widely encountered. The earliest hydrocarbon reactions to be studied were the thermal unimolecular decompositions of alkanes10 and alkyl radicals11 in which mirror removal techniques were used to demonstrate the actual presence of the radicals. These thermal reaction systems tend to be complex and, despite continued investigation, 12-13 many are not fully understood. 

Combined Primary and Secondary Unimolecular Isotope Effects in Thermal Activation Systems. Thermal unimolecular reactions offer a number of interesting combinations of primary and secondary inter-molecular effects and their variation with pressure. 

Although the theory was initially developed in 1952 and had been partly prompted by my prior experimental work, there were very few experimental data to which it could be applied. Around 1959 and subsequent years, B.S. Rabinovitch and coworkers used this theory to interpret their data on chemical activation [62, 69]. It may be recalled that chemical activation produced a narrower energy distribution of dissociating molecules than that in thermal unimolecular reactions and, hence, is better for testing the theory. 

As soon as the reactant molecule includes numerous atoms (as is often the case in Organic Chemistry) one just cannot study the overall dynamics of the reaction. In particular, if one must renounce the investigation of the activation phase of the reaction, one must also renounce the attribution of statistical weights to individual trajectories. Then one must postulate, on the basis of either experimental information or physical intuition, initial activated states of the reactant system and study only its subsequent dynamical evolution. Thus the work is restricted to sample in a random way all the possible initial conditions with no attempt to obtain at the end theoretical values of experimental quantities. Nevertheless, this context is not too restrictive. The trajectory study of thermal unimolecular reactions allows one... 

J. Troe, Theory of multichannel thermal unimolecular reactions. 2. Application to the thermal dissociation of formaldehyde, /. Phys. Chem. A109 (37) (2(X)5) 8320-8328. 

E2 elimination reactions occur preferentially when the leaving groups are in an anti copla-nar arrangement in the transition state. However, there are a few thermal, unimolecular sy -eliminations that produce alkenes. For example, pyrolysis of several closely related amine oxides, sulfoxides, selenoxides, acetates, benzoates, carbonates, carbamates and thio-carbamates gives alkenes on heating (Scheme 4.10). The syn character of these eliminations is enforced by a five- or six-membered cyclic transition states by which they take place. 

Hawton and Semeluk have studied the thermal unimolecular trans-cis-i o-merisation of 1,2-dichloroethene using a toluene vapour-flow technique. Earlier attempts to study this reaction were complicated by concurrent radical and heterogeneous processes. Table 6 summarises the results of kinetic studies of some thermally induced unimolecular isomerisations of chlorinated and brominated hydrocarbons. 

The thermal unimolecular cyclization of 3-diazoalkenes to pyrazoles appears to be an intramolecular 1,3-dipolar cycloaddition and the first-order rate coefficients of four substituted // art5-3-diazo-l-phenylpropenes fit the Hammett equation (p = — 0.40). The small value of p, indicating a lack of sensitivity of the cyclization rate to the electronic nature of the substituents supports the belief that the reaction involves a synchronous, cyclic electron shift. Table 11 lists the measured rate coefficients. 

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