Reaction energy profiles

Although there is no simple quantitative relationship between the stability of a carbocation intermediate and the rate of its formation, there is an intuitive relationship. It s generally true when comparing two similar reactions that the more stable intermediate forms faster than the less stable one. The situation is shown graphically in Figure 6.13, where the reaction energy profile in part (a) represents the typical situation rather than the profile in part (b). That is, the curves for two similar reactions don t cross one another. 

When this correction is included, the reaction energy profile diagram results for the cationation and the first three propagation steps in the gas phase and in solution (Fig. 16). 

Figure 2.P25 shows the calculated [B3LYP/6-31G(4,/f)] reaction energy profile for the aldol addition of benzaldehyde and cyclohexanone catalyzed by alanine. The best TSs leading to (S,R) (R,S) (S,S) and (R,R) products are given. What factors favor the observed (R,S) product ... 

Fig. 2.P25. Top Reaction energy profile for alanine-catalyzed aldol reaction of benzaldehyde and cyclohexanone. Bottom Diastereomeric transition structures. Reproduced from Angew. Chem. Int. Ed. Engl., 44, 7028 (2005), by permission of Wiley-VCH...

On page 313, the effect of methyl substitution on the stereoselectivity of a,a-diallylcarboxylic acids under iodolactonization conditions was discussed. Consider the two compounds shown and construct a reaction energy profile for... 

Figure 5.52 A schematic reaction energy profile for the bimolecular elementary reaction (5.82).

Figure 5.55 A comparison of the reaction energy profiles for the full calculation (circles) and the CT-deleted calculation (crosses), with the np—ocf NBO interaction deleted in the latter case.

Fig. 19 The reaction energy profiles for thermal (on the left) and radical-anionic (on the right) C1-C6 and C1-C5 cyclizations of the parent enediyne computed at the B3LYP/ 6-31G level.

Fig. 6 Reaction energy profile for reactions 34a/34b (A), 35a/35b (B), and 36a/36b (C). (A) and (B) Aromatic stabilization of the transition state is greater than that of benzene or cyclopentadienyl anion, respectively. (C) Anti-aromatic destabilization (positive ASE) of the transition state is less than that of cyclobutadiene the high barrier results from the additional contribution by angular and torsional strain at the transition state.

V). As illustrated in Fig. 1, without knowledge of Q, even the most accurate gas-phase reaction energy profiles are useless for projecting activation barriers AE for adsorbate transformations. 

The rebound mechanism, though in a modified version, has been recently supported by theoretical calculations of KIF using the density functional theory (Yoshizawa et al., 2000). The calculations demonstrate that the transition state for the H-atom abstraction from ethane involves a linear [FeO.H...C] array a resultant radical species with a spin density of nearly one is bound to an iron-hydroxy complex, followed by recombination and release of product ethanol. According to the calculation of the reaction energy profile, the carbon radical species is not a stable reaction intermediate with a finite lifetime. The calculated KIF at 300 K is in the range of 7-13 in accord with experimental data and is predicted to be significantly dependent on temperature and substituents. It was also shown from femtosecond dynamic calculations in the FeOVCH4 system that the direct abstraction mechanism can occur in 100-200 fs. 

While several studies have also pointed out that nitroaromatic products are more characteristic of laboratory studies where high NOx mixing ratios are employed rather than the ambient environments where lower NOx mixing ratios exist, understanding the formation mechanisms of these nitroaromatic compounds is critical to properly defining the reaction mechanisms for aromatic compounds. The only computational study to date that probed the NO2 reaction with the aromatic-OH adducts is that of Andino et al. [27], and their work considered only the reactions of the most likely aromatic-OH adduct, as predicted from the computational results. However, theoretical work involving NOx tends to be complicated by symmetry problems, so that reaction energy profiles are difficult to obtain. 

Figure 7 Calculated reaction energy profile for methanol synthesis over ZnO...

They have compared the reaction energy profiles of five different reaction paths, including oxidative insertion, nucleophilic substitution, and single-electron transfer mechanisms involving radical species, both in the gas phase as well as using an electrostatic continuum model to include the effect of a solvent in an approximate fashion (Structures 3-5). 

Bulk solvent alone is not able to describe these effects which are to be ascribed to the quantum behaviour of a single water molecule. Bulk solvent, in its continuum representation, indeed modifies the picture of the reaction mechanism we have resumed here. Its effect on the reaction energy profile... 

Here and represent the single H-transfer rate constants of the formation of the individual intermediates in Fig. 6.21(a). Equations (6.31) and (6.48) had already been discussed by Limbach et al. [58] but used only after independent confirmation in the cases of azophenine and oxalamidines [21, 22[, discussed below. Equation (6.48) was visualized in Fig. 6.12 and 6.14(b). The reaction energy profile of the HH-transfer involves two transition states of equal height. Thus, the product side is reached only with probability V2 as the internal return to the initial state also exhibits the same probability. The same is true for the DD reaction, only the effective barriers are larger. However, the symmetry is destroyed in the HD reaction. The rate-limiting step is the D-transfer which involves the same barrier as the corresponding process of the DD reaction. But as there is only a single barrier of this type in contrast to the DD reaction the HD reaction is about 2 times faster than the DD reaction. 

Figure 12.2. A reaction energy profile for enzyme catalyzed A + B Q + P reaction. The chemical step is marked and the rate-limiting step is product Q release. The portions of this...

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