Unimolecular transition state

In the event, treatment of a rapidly stirred solution of 3 and sodium acetate in MeOH-tbO at 38 °C with PdCl2 results in the fomation of carpanone (1) in 46% yield. The ordered unimolecular transition state for the oxidative coupling reaction furnishes putative bis(quinodimethide) 2 stereoselectively. Once formed, 2 readily participates in an intramolecular Diels-Alder reaction4 to give carpanone (1). Two new rings and all five contiguous stereocenters are created in this spectacular sequential transformation.5... 

Protonated amide / Unimolecular —Transition states-Bimoleciilar > Bimolecular... 

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

Considering equation (A3.6.3). if activity coefficients of reactant and transition state are approximately equal, for a imimolecular reaction one should observe This in fact is observed for many unimolecular... 

In the statistical description of ununolecular kinetics, known as Rice-Ramsperger-Kassel-Marcus (RRKM) theory [4,7,8], it is assumed that complete IVR occurs on a timescale much shorter than that for the unimolecular reaction [9]. Furdiemiore, to identify states of the system as those for the reactant, a dividing surface [10], called a transition state, is placed at the potential energy barrier region of the potential energy surface. The assumption implicit m RRKM theory is described in the next section. 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

In deriving the RRKM rate constant in section A3.12.3.1. it is assumed that the rate at which reactant molecules cross the transition state, in the direction of products, is the same rate at which the reactants fonn products. Thus, if any of the trajectories which cross the transition state in the product direction return to the reactant phase space, i.e. recross the transition state, the actual unimolecular rate constant will be smaller than that predicted by RRKM theory. This one-way crossing of the transition state, witii no recrossmg, is a fiindamental assumption of transition state theory [21]. Because it is incorporated in RRKM theory, this theory is also known as microcanonical transition state theory. 

Figure A3.12.9. Comparison of the unimolecular dissociation rates for HO2—>H+02 as obtained from the quantum mechanical resonances open circles) and from variational transition state RRKM step...

Detailed analyses of the above experiments suggest that the apparent steps in k E) may not arise from quantized transition state energy levels [110.111]. Transition state models used to interpret the ketene and acetaldehyde dissociation experiments are not consistent with the results of high-level ab initio calculations [110.111]. The steps observed for NO2 dissociation may originate from the opening of electronically excited dissociation chaimels [107.108]. It is also of interest that RRKM-like steps in k E) are not found from detailed quantum dynamical calculations of unimolecular dissociation [91.101.102.112]. More studies are needed of unimolecular reactions near tln-eshold to detennine whether tiiere are actual quantized transition states and steps in k E) and, if not, what is the origin of the apparent steps in the above measurements of k E). 

Chesnavich W J, Bass L, Su T and Bowers M T 1981 Multiple transition states in unimolecular reactions a transition state switching model. Application to C Hg" J. Chem. Rhys. 74 2228—46... 

Green W H, Moore C B and Polik W F 1992 Transition states and rate constants for unimolecular reactions Ann. Rev. Phys. Chem. 43 591-626... 

Ionov S I, Brucker G A, Jaques C, Chen Y and Wittig C 1993 Probing the NO2 —>NO+0 transition state via time resolved unimolecular decomposition J. Chem. Phys. 99 3420-35... 

Miller W H, Hernandez R, Moore C B and Polik W F A 1990 Transition state theory-based statistical distribution of unimolecular decay rates with application to unimolecular decomposition of formaldehyde J. Chem. Phys. 93 5657-66... 

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

Unimolecular (Section 4 8) Describing a step in a reaction mechanism in which only one particle undergoes a chemi cal change at the transition state... 

Unimolecular reactions that take place by way of cyclic transition states typically have negative entropies of activation because of the loss of rotational degrees of freedom associated with the highly ordered transition state. For example, thermal isomerization of allyl vinyl ether to 4-pentenal has AS = —8eu. ... 

As depicted, the E2 mechanism involves a bimolecular transition state in which removal of a proton to the leaving group is concerted with departure of the leaving group. In contrast, the rate-determining step in the El mechanism is the unimolecular ionization of... 

The major difference between the two mechanisms is the second step. The second step in the reaction of tcrt-butyl alcohol with hydrogen chloride is the unimolecular dissociation of tcrt-butyloxonium ion to tcrt-butyl cation and water. Heptyloxonium ion, however, instead of dissociating to an unstable primar y car bocation, reacts differently. It is attacked by bromide ion, which acts as a nucleophile. We can represent the transition state for this step as ... 

Section 4.9 The potential energy diagrams for separate elementary steps can be merged into a diagram for the overall process. The diagram for the reaction of a secondary or tertiary alcohol with a hydrogen halide is characterized by two intermediates and three transition states. The reaction is classified as a unimolecular- nucleophilic substitution, abbreviated as SnI. 

The first step, which is rate determining, is an ionization to a carbocation (carbonium ion in earlier terminology) intermediate, which reacts with the nucleophile in the second step. Because the transition state for the rate-determining step includes R-X but not Y , the reaction is unimolecular and is labeled S l. First-order kinetics are involved, with the rate being independent of the nucleophile identity and concentration. 

Electrocyclic reaction (Section 30.3) A unimolecular peri-cyclic reaction in which a ring is formed or broken by a concerted reorganization of electrons through a cyclic transition state. For example, the cyciization of 1,3.5-hexatriene to yield 1,3-cyclohexadiene is an electrocyclic reaction. 

It is possible to take advantage of the differing characteristics of the periphery and the interior to promote chemical reactions. For example, a dendrimer having a non-polar aliphatic periphery with highly polar inner branches can be used to catalyse unimolecular elimination reactions in tertiary alkyl halides in a non-polar aliphatic solvent. This works because the alkyl halide has some polarity, so become relatively concentrated within the polar branches of the dendrimer. This polar medium favours the formation of polar transition states and intermediates, and allows some free alkene to be formed. This, being nonpolar, is expelled from the polar region, and moves out of the dendrimer and into the non-polar solvent. This is a highly efficient process, and the elimination reaction can be driven to completion with only 0.01 % by mass of a dendrimer in the reaction mixture in the presence of an auxiliary base such as potassium carbonate. 

By ab initio MO and density functional theoretical (DPT) calculations it has been shown that the branched isomers of the sulfanes are local minima on the particular potential energy hypersurface. In the case of disulfane the thiosulfoxide isomer H2S=S of Cg symmetry is by 138 kj mol less stable than the chain-like molecule of C2 symmetry at the QCISD(T)/6-31+G // MP2/6-31G level of theory at 0 K [49]. At the MP2/6-311G //MP2/6-3110 level the energy difference is 143 kJ mol" and the activation energy for the isomerization is 210 kJ mol at 0 K [50]. Somewhat smaller values (117/195 kJ mor ) have been calculated with the more elaborate CCSD(T)/ ANO-L method [50]. The high barrier of ca. 80 kJ mol" for the isomerization of the pyramidal H2S=S back to the screw-like disulfane structure means that the thiosulfoxide, once it has been formed, will not decompose in an unimolecular reaction at low temperature, e.g., in a matrix-isolation experiment. The transition state structure is characterized by a hydrogen atom bridging the two sulfur atoms. 

It is worthwhile to first review several elementary concepts of reaction rates and transition state theory, since deviations from such classical behavior often signal tunneling in reactions. For a simple unimolecular reaction. A—>B, the rate of decrease of reactant concentration (equal to rate of product formation) can be described by the first-order rate equation (Eq. 10.1). 

Hesse691 has shown that the unimolecular chemistry of cation radicals of di- or polyfunctionalized alkanes is strongly dependent upon the interaction of the functional groups, mainly via neighbouring group participation in the transition states and the... 

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