Unimolecular isomerization reaction

Example 11.7 Unimolecular isomerization reaction One of the simplest biochemical reactions is a unimolecular 

To simulate a biological metabolic network, consider a special controlling mechanism so that the concentrations of S and P are maintained at prescribed levels. Therefore, the chemical system is at steady state since concentrations remain unchanged with time. However, the system in not at an equilibrium state and the reaction velocity (flow) is not zero  

We can determine the affinity of the reaction as the driving force for the chemical system 

Introducing chemical potentials for biochemical substrates needs to be done with caution when considering, for example, molecular crowding and signaling molecules with limited copy numbers (Parsegian et al., 2000). This simple chemical system is for cellular metabolic networks, and concentrations replace activities in ideal solutions. 

Equation (11.3) can be transformed to describe the amount of work done by the controlling mechanism, which pumps reactant S and product P to maintain nonequilibrium steady-state conditions 

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Thus our unimolecular isomerization reaction actually occurs by a sequence of steps and is therefore a multiple-reaction system We need a simplified expression for the overall rate of this rate in terms of Ca alone because zl is an intermediate whose concentration is always very small just as for the free-radical intermediates and dimers in the previous examples. 

In this problem we will consider the kinetics of this unimolecular isomerization reaction in a nitrogen bath gas at 1500 K, using several different theoretical treatments. The high-pressure Arrhenius coefficients for this reaction are A00 = 1 x 1014 s-1 and E0 = 45 kcal/mol. 

Several kinds of thermal unimolecular isomerization reactions of disilenes are now known. 

The ability of both pulsed and cw infrared lasers to induce chemical reactions is well known. CO2 lasers are now common equipment in many laboratories. The infrared laser-induced process studied most extensively is multiplephoton excitation of molecules (using megawatt COj laser radiation) to high vibrational states from which reaction, usually dissociation, may occur. This field is the subject of intense effort by many research groups, and a number of excellent review articles have been written about multiplephoton excitation. At lower laser intensities it is possible to prepare molecules in specific initial vibrational states below the dissociation threshold and to study their subsequent bimolecular and unimolecular (isomerization) reactions. In this chapter we shall restrict ourselves to considering only the results of low-level vibrational excitation on chemical reactions. 

Sigmatropic rearrangements are the unimolecular isomerization reactions in which a a-bond moves from one position to another over an unsaturated system. In such reactions, rearrangement of the Tt-bonds takes place to accommodate the new a-bond, but the total number of Tt-bonds remains the same. 

Figure A3.4.6. Potential energy along the reaction coordinate r for an unimolecular isomerization (left) and a...

From stochastic molecnlar dynamics calcnlations on the same system, in the viscosity regime covered by the experiment, it appears that intra- and intennolecnlar energy flow occur on comparable time scales, which leads to the conclnsion that cyclohexane isomerization in liquid CS2 is an activated process [99]. Classical molecnlar dynamics calcnlations [104] also reprodnce the observed non-monotonic viscosity dependence of ic. Furthennore, they also yield a solvent contribntion to the free energy of activation for tlie isomerization reaction which in liquid CS, increases by abont 0.4 kJ moC when the solvent density is increased from 1.3 to 1.5 g cm T Tims the molecnlar dynamics calcnlations support the conclnsion that the high-pressure limit of this unimolecular reaction is not attained in liquid solntion at ambient pressure. It has to be remembered, though, that the analysis of the measnred isomerization rates depends critically on the estimated valne of... 

Direct photochemical excitation of unconjugated alkenes requires light with A < 230 nm. There have been relatively few studies of direct photolysis of alkenes in solution because of the experimental difficulties imposed by this wavelength restriction. A study of Z- and -2-butene diluted with neopentane demonstrated that Z E isomerization was competitive with the photochemically allowed [2tc + 2n] cycloaddition that occurs in pure liquid alkene. The cycloaddition reaction is completely stereospecific for each isomer, which requires that the excited intermediates involved in cycloaddition must retain a geometry which is characteristic of the reactant isomer. As the ratio of neopentane to butene is increased, the amount of cycloaddition decreases relative to that of Z E isomerization. This effect presumably is the result of the veiy short lifetime of the intermediate responsible for cycloaddition. When the alkene is diluted by inert hydrocarbon, the rate of encounter with a second alkene molecule is reduced, and the unimolecular isomerization becomes the dominant reaction. 

Like fragmentations, unimolecular rearrangements are always uphill at the beginning of the process, because a bond breaks. Unlike fragmentations, rearrangements are downhill at the end as a new bond forms. An example of this kind of energy profile for the Isomerization reaction of ds-2-butene appears in Figure 15-14Z). 

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,... 

In general, intramolecular isomerization in coordinatively unsaturated species would be expected to occur much faster than bimolecular processes. Some isomerizations, like those occurring with W(CO)4CS (47) are anticipated to be very fast, because they are associated with electronic relaxation. Assuming reasonable values for activation energies and A-factors, one predicts that, in solution, many isomerizations will have half-lives at room temperature in the range 10 7 to 10 6 seconds. The principal means of identifying transients in uv-visible flash photolysis is decay kinetics and their variation with reaction conditions. Such identification will be difficult if not impossible with unimolecular isomerization, particularly since uv-visible absorptions are not very sensitive to structural changes (see Section I,B). These restrictions do not apply to time-resolved IR measurements, which should have wide applications in this area. 

A second example of an inverse statistical weight isotope effect is that of the secondary H/D KIE on C-C bond rupture during the gas phase unimolecular isomerization of cyclopropane to propene. Theory and experiment are compared in Fig. 14.2 for reactions 14.37 and 14.38. 

The cis-trans isomerization of cyclopropanes is not restricted to the deuterium-substituted molecules, cis- and traws-l,2-Dimethylcyclo-propane have been shown to imdergo reversible geometrical isomerization as well as slower structural isomerization. All the processes are homogeneous and kinetically first order, and almost certainly unimolecular. The reaction scheme is shown below. 

Isomerizations are important unimolecular reactions that result in the intramolecular rearrangement of atoms, and their rate parameters are of the same order of magnitude as other unimolecular reactions. Consequently, they can have significant impact on product distributions in high-temperature processes. A large number of different types of isomerization reactions seem to be possible, in which stable as well as radical species serve as reactants (Benson, 1976). Unfortunately, with the exception of cis-trans isomerizations, accurate kinetic information is scarce for many of these reactions. This is, in part, caused by experimental difficulties associated with the detection of isomers and with the presence of parallel reactions. However, with computational quantum mechanics theoretical estimations of barrier heights in isomerizations are now possible. 

Case 1. Unimolecular Isomerization Consider a simple chemical reaction between species A and B at dynamic equilibrium ... 

NONEQUILIBRIUM THERMODYNAMICS A PRIMER UNIMOLECULAR CHEMICAL KINETICS MOLECULARITY ORDER OF REACTION ELEMENTARY REACTIONS Unimolecular forward/bimolecular reverse, CHEMICAL KINETICS Unimolecular isomerization,... 

In longer chain hydrocarbon radicals, isomerization reactions become more important these pathways compete with bimolecular oxidation reactions and can impact ignition rates at low temperatures. For instance, -propylperoxy radical can undergo several unimolecular dissociations/rearrangements ... 

The formation of oxidation products a-c in a range of G values (0.7-3.8) during the 7-R of S in 02-saturated DCE suggests that a-c would be produced from complicated reactions of peroxy radicals with S (Table 5). On the other hand, the regioselective formation of 3d with large G values (2.6-3.0) in oxidation of 3 with O2 is explained by spin localization on the p-olefinic carbon because of the contribution of (B) in 3. The results of products analyses are essentially identical with prediction based on k and ko for S measured with PR. It should be emphasized that the reactivities of c-t unimolecular isomerization and reaction of S with O2 can be understood in terms of charge-spin separation induced by p-MeO. 

Achieving control over microscopic dynamics of molecules with external fields has long been a major goal in chemical reaction dynamics. This goal stimulated the development of quantum control schemes, which have been applied with spectacular results to unimolecular reactions, such as photodissociation or isomerization reactions. Attaining control over bimolecular reactions in a gas has proven to be a much bigger challenge. 

When the commodity chemical propylene oxide is heated to high temperature in the gas phase in a shock tube, unimolecular rearrangement reactions occur that generate the CsHgO isomers allyl alcohol, methyl vinyl edier, propanal, and acetone (Figure 15.9). Dubnikova and Lifshitz carried out a series of calculations to determine the mechanistic pathway(s) for each isomerization, with comparison of activation parameters to those determined from Arrhenius fits to experimental rate data to validate the theoretical protocol. 

Biradicals are frequently postulated to arise as intermediates in a number of chemical reactions and unimolecular isomerizations. Sometimes there are reasonable alternative concerted mechanisms in which the intermediate (or transition-state complex) is not a biradical. Such a case of much interest37,61 involves the reactions of singlet [5] and triplet [7] methylenes with olefins. We note that the permutational symmetry does not determine whether or not a reaction is concerted rather it is determined by the shapes of the intermolecular potential surfaces.78 The lowest 1Ai methylene is expected to react by a concerted mechanism, since it correlates with the ground state of the product cyclopropane higher excited singlets need not react via a concerted mechanism. 

The major reaction in the thermal decomposition of 2,3-dihydrofuran (9) is a unimolecular isomerization to cyclopropanecarboxaldehyde (89JPC-1139). In an analogous [1,3] sigmatropic reaction, the isomerization of 2-methyl-4,5-dihydrofuran (10) leads to acetylcyclopropane, which can rearrange to 3-penten-2-one (94JPC2341). The latter product may also be formed directly from 10. 

The stilbenes have played a crucial role in the development of modern photochemistry. Direct or triplet sensitized irradiation of trans-stilbene (t-1) in dilute solution results in isomerization to cis-stilbene (c-1) as the exclusive uni-molecular photochemical reaction (1-3). Direct irradiation of c-1 results in isomerization to both t-1 and trans-4a,4b-di-hydrophenanthrene (2), which revert to c-1 both thermally and photochemically and can be trapped by oxidants such as iodine or oxygen to yield phenanthrene (3) (4-6). Triplet sensitized irradiation of c-1 yields only t-1. These unimolecular isomerization pathways are summarized in eq. 1. 

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