Transition-state control

The idea that an activated complex or transition state controls the progress of a chemical reaction between the reactant state and the product state goes back to the study of the inversion of sucrose by S. Arrhenius, who found that the temperature dependence of the rate of reaction could be expressed as k = A exp (—AE /RT), a form now referred to as the Arrhenius equation. In the Arrhenius equation k is the forward rate constant, AE is an energy parameter, and A is a constant specific to the particular reaction under study. Arrhenius postulated thermal equilibrium between inert and active molecules and reasoned that only active molecules (i.e. those of energy Eo + AE ) could react. For the full development of the theory which is only sketched here, the reader is referred to the classic work by Glasstone, Laidler and Eyring cited at the end of this chapter. It was Eyring who carried out many of the... 

SCHEME 50. Postulated transition states controlling the site selectivity in the intrazeolite photooxygenation of isobutenylarenes... 

Fig. 8. Standard free energy diagram for a two-step electron transfer reaction at an electrode with variation of the transition state with potential, (a) At Ej, the rds corresponds to transition state 1. (c) At E2, the transition state controlling the kinetics is 2. (b) corresponds to E. ...

Figure 2. Models for the transition states controlling asymmetric induction in the hydrocarbonylation of olefins...

The fact that a model for the transition state controlling asymmetric induction based on steric interactions allows us to correctly predict the type of prevailing regio- and stereoisomer for about 85% of the asymmetric hydrocarbonylation experiments (including hydroformylation and hydrocarbalkoxylation) is an indication that asymmetric induction in these catalytic reactions is based mainly on steric interactions. The data obtained so far do not allow us to establish whether the more stable or the less stable 7r-olefin complex intermediate is the one that reacts preferentially. However, the regularities that we observed indicate that the kinetic features are the same, at least in most of the experiments. 

A Model for the Diastereomeric Transition States Controlling Asymmetric Induction in Hydroformylation... 

The prevalence of the (S) or (R) antipode of the product gives a qualitative idea of the relative energy of the transition states controlling asymmetric induction. However, the values of the enantiomeric excess do not necessarily indicate the extent but only a minimum value of the free energy differences between the above transition states (e.g. the reaction product could racemize after its formation). On this basis the already discussed model for the transition state controlling asymmetric induction has been formulated (Sect. 4.). 

D.C. Chatfield, S.L. Mielke, T.C. Allison, D.G. Truhlar, Quantum dynamical bottlenecks and transition state control of the reaction of D with H2 Effect of varying the total angular momentum, J. Chem. Phys. 112 (2000) 8387. 

Transition-State Analogs. As a chemical reaction proceeds from substrates to products, it will pass through one or more transition states. The energy barrier imposed by the highest energy transition state controls the overall rate of the reaction. Enzymes bring about rate enhancements of (123)... 

One important component of practical epoxidation catalysis for which many questions remain open is the role of promoters. Industrially, both Cs and Cl are used as promoters.76 Saravanan et al. used cluster DFT calculations to examine the interactions between adsorbed Cs and oxametallacycles on Ag(lll).77 These calculations suggested that both neutral Cs and Cs+ gave similar outcomes and that the promoter atom made the formation of a surface oxametallacycle less energetically favorable than on the bare Ag surface. More recently, Linic and Barteau used plane wave DFT calculations to probe the effect of adsorbed Cs on the transition states controlling the formation of EO and acetaldehyde from oxametallacycles on Ag(lll).78 The role of Cs was... 

The high regioselectivity of these reactions follows the same pattern as those of 2- and 3-substituted cyclohexanones when converted to enamines.9 Apparently, A<1-2) and Af1-3) strain in the transition state controls the regiochemistry. The additive... 

The activity of zeolites for alk3dation of toluene with 1-heptene depends on then-acidity and on the ease of desorption of alkjiates. Thus average pore size zeolites such as HMFI and monodimensional laigc pore zeolites are practically inactive. Extraframework aluminium species which limit the product desorption have a negative effect, while mesopores (in particular with monodimensional zeolites such as HMOR) have a positive effect. EEMOR zeolites are more selective for 2-phenylalkanes than HFAU zeolites. This is mainly due to shape selective preference via transition state control. 

The excellent agreement between the quantal and synthetic densities of reactive states in Fig. lb demonstrates that quantized transition states globally control the chemical reactivity. All of the reactive flux, up to an energy of 1.6 eV, can be attributed to contributions from the energy levels of the transition state i.e., there is no noticeable background. Thus, this study (and ones to follow) provides a strong validation for approximate transition state theories that postulate the existence of transition states controlling the reaction dynamics. 

Fitting the quantal density by a sum of terms KTpT( ) is difficult because of the large number of transition states for 7 = 4. However, quantized transition state control of chemical reactivity can be assessed for 7 = 4 without identifying all of the individual contributions to the total density by comparing the accurate values of N4(E) with those in the next to last column of Table 4. If the transition states were ideal (kt = 1), the two numbers would be equal. Up to 1.228 eV, the energy of the sixth peak, the numbers are very close at 1.228 eV the accurate value of N4(E) is 24. Thus, the quantized transition states up to 1.228 eV are nearly ideal dynamical bottlenecks. Above 1.228 eV the quantal N4(E) is somewhat smaller than the predicted value, but even at 1.570 eV the difference is only 15%. This difference may be due to the inaccuracy of Eq. (25) at high v2 or to... 

The accurate density of reactive states O + H2, J = 0 is shown in the top left panel of Fig. 5, and results of the quantized transition state theory fit are in Table 6, along with assignments discussed below. The quantal and fitted densities are indistinguishable to plotting accuracy (14), indicating that quantized transition states control the chemical reactivity. The density closely resembles that for the reaction of H with H2 up to about 1.3 eV. Analogous features are associated with the same sets of quantum numbers through the [06°] transition state at 1.218 ev. 

The hydrogen transfer reactions Cl + HC1, I + HI, and I + DI present a more difficult test of quantized transition state control of chemical reactivity. In contrast to the H + H2, D + H2, O + H2, and F + H2 reactions, the quantized transition state structure in the accurate dynamics of these reactions is almost completely obscured by features that have been attributed to trapped-state resonances and rotational thresholds (17-19). Al-... 

A study with camphoroquinone (CQ) also supported the idea that the dipole-dipole interaction between the substrate and the amide moiety in Me2PNPH at the transition state controls the stereochemistry in... 

To illustrate the influence of pre-transition-state control for a zeolite-catalyzed reaction, we describe the results of a quantum-chemical study of the alkylation of toluene by methanoll l. The selectivities to produce ortho-, meta- or pora-xylene in the channel of the Mordenite zeolite are studied. The study illustrates the effect of the spatial constraint induced by the one-dimensional 12-ring micropore channel dimension on the selectivity of the zeolite catalyzed-reaction. 

The dissection of medium effects on reaction rates into initial state and transition state contributions leads to the development of a systematic approach to classify reaction types. The resulting classification is shown in Table I, which presents all possible outcomes of medium change rate acceleration, rate retardation and no change. Thus we have classified reaction types as balanced, re-infor-ced, positive or negative, initial state or transition state controlled, ans so on. Not all of these situations have been observed so far and it would be intriguing to design appropriate systems which would complete this classification. The studies to be described forthwith serve to illustrate some of these reaction types. 

In A we have two neutral reactant molecules which are not appreciably solvated, hence will not be appreciably affected by the change in medium from protic to dipolar aprotic, so that the initial state is coincident in the two media. However, the polarizable transition state will be more solvated in a dipolar aprotic medium such as DMF, so there should normally be a rate enhancement on changing to a dipolar aprotic medium (6h is negative). This is the Menschutkin type reaction which is discussed in detail by Professor Abraham(36), who has observed cases in which the realation-ship of the coincident initial states in the two media does not hold(31). However this relationship does hold for this particular reaction and we selected it so as to contrast with the other reaction types shown in this Figure, in which the initial state is not coincident in the two media. It may perhaps be emphasized that this is the only case, of the systems illustrated here, in which changes in the transition state solvation are solely responsible for the medium effect on the reaction rate. In terms of the classification in Table I we can describe this as a "positive transition state control" reaction type. 

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