Unimolecular reactions, isotope effects

Collisions at low ion energies (where Equation 1 can be applied) lead to a short-lived complex between the ion and the molecule—i.e., both collision partners move with the same linear velocity in the direction of the incident ion. The decay of the complex may be described by the theory of unimolecular rate processes if its excess energy can fluctuate between the various internal degrees of freedom. For example, the isotope effect in the reaction of Ar+ with HD may be explained by the properties of... 

Labelling experiments provided the evidence that the Fe1- and Co1-mediated losses of H2 and 2H2 from tetralin are extremely specific. Both reactions follow a clear syn- 1,2-elimination involving C(i)/C(2) and C(3)/C(4), respectively. In the course of the multistep reaction the metal ions do not move from one side of the rr-surface to the other. The kinetic isotope effect associated with the loss of the first H2 molecule, k( 2)/k(Y)2) = 3.4 0.2, is larger than the KIE, WFLj/ATHD) = 1.5 0.2, for the elimination of the second H2 molecule. A mechanism of interaction of the metal ion with the hydrocarbon n-surface, ending with arene-M+ complex 246 formation in the final step of the reaction, outlined in equation 100, has been proposed241 to rationalize the tandem MS studies of the unimolecular single and double dehydrogenation by Fe+ and Co+ complexes of tetraline and its isotopomers 247-251. 

Abstract The theoretical framework needed for interpretation of kinetic isotope effects on unimolecular reactions is reviewed. Application to the satisfactory rationalization of the theoretically puzzling mass independent isotope effect observed for oxygen isotope fractionation in extraterrestrial samples is described. 

As is implied by the name, a unimolecular reaction is one in which a single molecule of reactant decomposes or rearranges to give rise to product molecules. Ordinary thermal reactions can be modeled by a process which considers the reactant to be in thermal equilibrium with a transition state which then decomposes (rearranges) to give products. One can theoretically describe the process and its isotope effects using transition state theory. For unimolecular reactions, on the other hand, while there is still a transition state, it is not in thermal equilibrium with the reactant except for systems at high pressure. Consequently, a more elaborate theoretical framework is required to understand unimolecular reactions and their isotope effects. 

In the following section, the RRKM mechanism for gas phase unimolecular reactions will be introduced and the corresponding theoretical framework, including isotope effects, will be outlined. Subsequent sections will deal with some applications of this theoretical framework to systems which have been studied experimentally. 

As pointed out before kuni is a pseudo first order rate constant. Since kuni/[M] is independent of [M], kuni/[M] is a second order rate constant at low pressure. It is significant and important for consideration of isotope effects that this second order rate constant for unimolecular reactions depends only on the energy levels of reactant molecules A and excited molecules A, and on the minimum energy Eo required for reaction. It does not depend on the energy levels of the transition state. There will be further discussion of this point in the following section. 

Our interest in thermally activated unimolecular reactions is in the change of kuni with pressure from the high to the zero pressure limit, and in the pressure dependence of the isotope effect over that range. One particularly interesting study carried out by Rabinovitch and Schneider (reading list) focused on the isomerization of methyl isocyanide, CH3NC, to methyl cyanide, CH3CN... 

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 formalism for treating primary isotope effects on unimolecular processes follows analogously to the development above, once due account is taken of the difference in zero point energies on isotope substitution at the reaction site (which is reflected in an isotopic difference in the threshold energy Eo). For thermal activation the rate ratio in the high pressure limit is straightforwardly obtained from Equation 14.25. For H/D effects... 

Recently, some attempts were nndertaken to uncover the intimate mechanism of cation-radical deprotonation. Thns, the reaction of the 9-methyl-lO-phenylanthracene cation-radical with 2,6-Intidine (a base) was stndied (Ln et al. 2001). The reaction proceeds through two steps that involve the intermediary formation of a cation-radical/base complex before unimolecular proton transfer and separation of prodncts. Based on the value of the kinetic isotope effect observed, it was concluded that extensive proton tnnneling is involved in the proton-transfer reaction. The assumed structure of the intermediate complex involves n bonding between the unshared electron pair on nitrogen of the Intidine base with the electron-deficient n system of the cation-radical. Nonclassical cation-radicals wonld also be interesting reactants for snch a reaction. The cation-radical of the nonclassical natnre are known see Ikeda et al. (2005) and references cited therein. 

Entropies and volumes of activation,74 though less reliable criteria, are in the range usually found for unimolecular reactions and do not agree with values expected for the A-2 process. Solvent isotope effects also are in agreement with the A-l mechanism.75... 

A study of the decomposition of /f-hydroxy-/V-chloroamines in aqueous medium has established that pre-equilibrium formation of the conjugate alcoholate is a prerequisite feature of the competing fragmentation and intramolecular elimination paths (Scheme 13).98 A very high effective molarity (EM = 2 x 105 M) has been estimated for the intramolecular process, which cannot occur in the case of (/V-chloro)butylethanolaminc. For reaction of (A-c h I o ro )ct hy I cth an o I am i nc kmln/k g = 6.1 and the solvent isotope effect ( oh- /koo- )obs = 0.68 is consistent with pre-equilibrium deprotonation followed by a unimolecular reaction in which there is no participation by solvent. 

Experimental rate constants, kinetic isotope effects and chemical branching ratios for the CF2CFCICH3-do, -d, -d2, and -d2 molecules have been experimentally measured and interpreted using statistical unimolecular reaction rate theory.52 The structural properties of the transition states needed for the theory have been calculated by DFT at the B3PW91 /6-31 G(d,p/) level. 

Investigation of this reaction isolated in an N2 matrix at 10-20 K has shown that the apparent activation energy is smaller than 0.11 kcal/mol the unimolecular rate constant for N0-03 reactant complexes prepared in this way is 1.4 x 10-5 s-1 at 12 K. Experiments carried out using ozone enriched with 180 have revealed no observable isotope effect. 

Isotopic substitution affects rates of ionic decompositions and isomerisations in essentially the same ways as isotopic substitution affects rates of thermal reactions [360, 608, 654, 764, 905, 925]. Mass spectrometry does, however, own a few idiosyncracies in this area and it is important to distinguish clearly the different sorts of isotope effects involved. The term kinetic isotope effects in this review will be restricted to effects of isotopic substitution on the values of rate coefficients, k(E). Kinetic isotope effects on unimolecular gas-phase... 

The work is divided into several parts. Part A in Sec. II briefly sets out the relevant aspects of the RRKM formulation14 for unimolecular reactions. Rather than repeat the derivation of the equations, emphasis is placed upon the present status of the theory, and the best techniques for carrying out computations simply. In Sec. II-B, characteristics of various model hydrocarbon-type molecular species are outlined and are used in Sec. II-C for theoretical calculations that illustrate various aspects of the theory. Some related aspects of kinetic isotope effects are... 

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