Position of the transition state

This effect starts to be even more important when the kinetic and thermodynamic products of a reaction are different diastereoisomers. Three examples of this type 

Indeed, early transition states favor the kinetic trans compound (reactive radical trap such as dimethyl fumarate). When later transition states are involved (octene case), the stability of the final products starts to influence the stereochemical outcome, and since the cis product is more stable than the trans, the diastereoselectivity of the process becomes lower. The same interpretation could also be used to rationalize the results depicted in equation 18.2 [41a]. Indeed, the allylation reaction is occurring via a relatively late transition state. Therefore, when R = H the stereoselectivity is low because the cis final product is more stable than the trans. When R = Me, the cis and trans products have almost the same stability, therefore the influenee of the transition state position on the stereochemical outcome vanishes and the diastereoselectivity is higher. 

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As a result of possible recrossings of the transition state, the classical RRKM lc(E) is an upper bound to the correct classical microcanonical rate constant. The transition state should serve as a bottleneck between reactants and products, and in variational RRKM theory [22] the position of the transition state along q is varied to minimize k E). This minimum k E) is expected to be the closest to the truth. The quantity actually minimized is N (E - E ) in equation (A3.12.15). so the operational equation in variational RRKM theory is... 

The next step will determine optimization convergence. If the criteria are satisfied, HyperChem will stop at this point, having found the position of the transition state. If convergence criteria are not... 

This equation implies that the relative reactivity is independent of the specific nucleophile and that relative reactivity is insensitive to changes in position of the transition state. Table 8.4 lists the B values for some representative ketones. The parameter B indicates relative reactivity on a log scale. Cyclohexanone is seen to be a particularly reactive ketone, being almost as reactive as cyclobutanone and more than 10 times as reactive as acetone. 

According to this very simple derivation and result, the position of the transition state along the reaction coordinate is determined solely by AG° (a thermodynamic quantity) and AG (a kinetic quantity). Of course, the potential energy profile of Fig. 5-15, upon which Eq. (5-60) is based, is very unrealistic, but, quite remarkably, it is found that the precise nature of the profile is not important to the result provided certain criteria are met, and Miller " obtained Eq. (5-60) using an arc length minimization criterion. Murdoch has analyzed Eq. (5-60) in detail. Equation (5-60) can be considered a quantitative formulation of the Hammond postulate. The transition state in Fig. 5-9 was located with the aid of Eq. (5-60). 

Several lines of evidenee led to the eonclusion that the reaetion is eoneerted. Experimental values of the sensitivity eoeffieients were aHA = —0.54 and 3 uc = 0.63. These values are plotted in Fig. 5-23 to define the position of the transition state, which probably has the following charge distribution, where the net charge is — 1, and bond formation from the nueleophile to carbon is well advanced. 

The position of the transition state on the reaetion eoordinate, a, is given by... 

The reader may now recall the discussion in Section 5.3, Position and Height of the Energy Barrier, on correlations of rates and equilibria of the same reactions and the interpretation of the slope a from such LEER as a measure of the position of the transition state along the reaction coordinate. It will now be apparent why the term Breasted coefficient is applied both to this quantity and also to the slope of LEER according to Eqs. (7-58) and (7-59). The interpretation of a and P from Eqs. (7-58) and (7-59) as measures of fractional progress along a reaction coordinate may be misleading when the reaction is complex, and caution is appropriate. - pp- 38-41... 

Support for the hypothesis that the relative position of the transition state is responsible for the dominant (kinetic) formation of either the (Z)- or the (ii)-isomer comes from a comparison of Hammett /7-values for rates of addition of nucleophiles with p-values for the corresponding equilibria. 

Effect of the Position of the Transition State Along the Reaction Coordinates... 

The position of the transition state along the reaction coordinates in relation to the well-known Hammond postulate [53] will now be considered. If the activation energy, AG+, of a reaction is only small the TS looks like the GS (it is depicted as a reactant-like transition state ). Consequently, the polarity is only slightly modified between the GS and TS during the course of the reaction and only weak specific micro-wave effects can be foreseen under these conditions. 

Numerous p-values for various electrophilic additions to styrene itself are available (Schmid and Garratt, 1977). Strictly speaking, the reaction constants measure only the sensitivity of the reaction to substituent effects they depend at the same time on the solvent, on the position of the transition state on the reaction coordinate (charge magnitude) and on the way in which substituent effects are transmitted (charge location). In particular, the observed trend of p-values for the chlorination ( — 3.22 Yates and Leung, 1980), bromination (—5.7 Ruasse et al, 1978) and sulfenylation ( — 2.41 ... 

This result, associated with those on substituent effects, supports previous conclusions to the effect that the position of the transition state depends on the reactivity in agreement with RSP. In particular, stabilization of the intermediate as a result of conjugation, such as that in the reaction of enol ethers, makes the transition state very early. The few available KSIEs also suggest that the transition states for aromatic series are earlier than those for alkenes. 

Neutral sulphur and oxygen nucleophiles of similar structure react with carbonyl groups at similar rates (Jensen and Jencks, 1979) the position of the transition state for thiolactonization is therefore expected to be similar. The comparisons of EM possible for three compounds in Table 4 show that the EMk/EMeq ratios are somewhat smaller for thiolactonization, by factors of 3 and 9 for the two compounds where all four EM s can be estimated. 

As already noted, in the Born-Oppenheimer approximation, the nuclear motion of the system is subject to a potential which expresses the isotope independent electronic energy as a function of the distortion of the coordinates from the position of the transition state. An analysis of the motions of the N-atom transition state leads to three translations, three rotations (two for a linear molecule), and 3N - 6 (3N- 5 for a linear transition state) vibrations, one which is an imaginary frequency (e.g. v = 400icm 1 where i = V—T), and the others are real vibrational frequencies. The imaginary frequency corresponds to motion along the so-called reaction... 

This expression was derived by Bell (1978), who used Kramers theory to show that bond lifetime ean be shortened by an applied force in processes such as cell adhesion. Although Eq. (3.2) is quite useful, it is in practice limited, most notably by the fact that it assumes that xp is constant. Typically, measurements of force dependency are made under conditions in which force changes with time, and it is likely that the position of the transition state will move as the shape of the potential surface is perturbed by an applied force (Evans and Ritchie 1997 Hummer and Szabo 2003). Theoretical and empirical treatments of various cases have been put forth in the hterature, but they are outside the scope of this chapter and will not be reviewed here. 

Figure 2 The coupling Junction g (s) defined in Eq. (36). The deviation from a straight line is the deviation from bilinear coupling. The positions of the transition state, the reactant and product wells are also shown by the dashed vertical lines.

The most sophisticated and computationally demanding of the variational models is microcanonical VTST. In this approach one allows the optimum location of the transition state to be energy dependent. So for each k(E) one finds the position of the transition state that makes dk(E)/dq = 0. Then one Boltzmann weights each of these microcanonical rate constants and sums the result to find fc ni- There is general agreement that this is the most reliable of the statistical kinetic models, but it is also the one that is most computationally intensive. It is most frequently necessary for calculations on reactions with small barriers occurring at very high temperatures, for example, in combustion reactions. 

Fig. 23 Energy diagram that illustrates (a) the generation of a simplified SN2 reaction profile from reactant, N R- -X, and product, N- -R X , configurations. Dotted lines denote avoided crossing (i.e. the reaction profile after configuration mixing). (b) The effect of stabilization of N- -R X (e.g. by a substituent effect) is indicated by dotted lines. Arrows indicate the positions of the transition states with and without the stabilization...

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