Energy transition state

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). 

Under the usual conditions their ratio is kinetically controlled. Alder and Stein already discerned that there usually exists a preference for formation of the endo isomer (formulated as a tendency of maximum accumulation of unsaturation, the Alder-Stein rule). Indeed, there are only very few examples of Diels-Alder reactions where the exo isomer is the major product. The interactions underlying this behaviour have been subject of intensive research. Since the reactions leadirig to endo and exo product share the same initial state, the differences between the respective transition-state energies fully account for the observed selectivity. These differences are typically in the range of 10-15 kJ per mole. ... 

In summary, it seems that for most Diels-Alder reactions secondary orbital interactions afford a satisfactory rationalisation of the endo-exo selectivity. However, since the endo-exo ratio is determined by small differences in transition state energies, the influence of other interactions, most often steric in origin and different for each particular reaction, is likely to be felt. The compact character of the Diels-Alder activated complex (the activation volume of the retro Diels-Alder reaction is negative) will attenuate these eflfects. The ideas of Sustmann" and Mattay ° provide an attractive alternative explanation, but, at the moment, lack the proper experimental foundation. 

In the stable trans-form the H atoms lie along the diagonal of the square. The energy of the cis-form, in which the atoms are positioned on one of the edges, is 3-5 kcal/mol higher than that of the trans-form [Smedarchina et al. 1989]. The transition state energies for trans-cis and... 

Another means of resolution depends on the difference in rates of reaction of two enantiomers with a chiral reagent. The transition-state energies for reaction of each enantiomer with one enantiomer of a chiral reagent will be different. This is because the transition states and intermediates (f -substrate... f -reactant) and (5-substrate... R-reactant) are diastereomeric. Kinetic resolution is the term used to describe the separation of enantiomers based on different reaction rates with an enantiomerically pure reagent. 

Preparation of enantiomerically enriched materials by use of chiral catalysts is also based on differences in transition-state energies. While the reactant is part of a complex or intermediate containing a chiral catalyst, it is in a chiral environment. The intermediates and complexes containing each enantiomeric reactant and a homochiral catalyst are diastereomeric and differ in energy. This energy difference can then control selection between the stereoisomeric products of the reaction. If the reaction creates a new stereogenic center in the reactant molecule, there can be a preference for formation of one enantiomer over the other. 

To account for the course of this reaction theoretical calculations of the coordination of ketomalonate 37 to copper(II) and zinc(II) have revealed that the six-membered ring system is slightly more stable than the five-membered ring system (Scheme 4.30). The coordination of 37 to catalyst (l )-39 shows that the six-membered intermediate is C2-symmetric with no obvious face-shielding of the carbonyl functionality (top), while for the five-membered intermediate (bottom) the carbonyl is shielded by the phenyl substituent. Calculations of the transition-state energy for the reaction of the two intermediates with 1,3-cyclohexadiene leads to the lowest energy for the five-membered intermediate this approach is in agreement with the experimental results [45]. 

In an investigation by Yamabe et al. [9] of the fine tuning of the [4-1-2] and [2-1-4] cycloaddition reaction of acrolein with butadiene catalyzed by BF3 and AICI3 using a larger basis set and more sophisticated calculations, the different reaction paths were also studied. The activation energy for the uncatalyzed reaction were calculated to be 17.52 and 16.80 kcal mol for the exo and endo transition states, respectively, and is close to the experimental values for s-trans-acrolein. For the BF3-catalyzed reaction the transition-state energies were calculated to be 10.87 and 6.09 kcal mol , for the exo- and endo-reaction paths, respectively [9]. The calculated transition-state structures for this reaction are very asynchronous and similar to those obtained by Houk et al. The endo-reaction path for the BF3-catalyzed reaction indicates that an inverse electron-demand C3-0 bond formation (2.635 A... 

Further studies by Garcia, Mayoral et al. [10b] also included DFT calculations for the BF3-catalyzed reaction of acrolein with butadiene and it was found that the B3LYP transition state also gave the [4+2] cycloadduct, as happens for the MP2 calculations. The calculated activation energy for lowest transition-state energy was between 7.3 and 11.2 kcal mol depending on the basis set used. These values compare well with the activation enthalpies experimentally determined for the reaction of butadiene with methyl acrylate catalyzed by AIGI3 [4 a, 10]. 

In a combined experimental and theoretical investigation it was found that the / -alkyl group in the dienophile gave a steric interaction in the transition-state structure which supported the asynchronous transition-state structure for the Lewis acid-catalyzed carbo- and hetero-Diels-Alder reactions. The calculated transition-state energies were of similar magnitude as obtained in other studies of these BF3-catalyzed carbo-Diels-Alder reactions. 

The four different transition states in Fig. 8.10 were considered with BF3 as a model for the BLA catalyst in the theoretical calculations. It was found that the lowest transition-state energy for the BF3-catalyzed reactions was calculated to be 21.3 kcal mol for anti-exo transition state, while only 1.5 kcal mol higher in energy the syn-exo transition state, was found. The uncatalyzed reaction was calculation to proceed via an exo transition state having an energy of 37.0 kcal mol . The calculations indicated that the reaction proceeds predominantly by an exo transition-state structure and that it is enhanced by the coordination of the Lewis acid. 

The theoretical investigations of Lewis acid-catalyzed 1,3-dipolar cycloaddition reactions are also very limited and only papers dealing with cycloaddition reactions of nitrones with alkenes have been investigated. The Influence of the Lewis acid catalyst on these reactions are very similar to what has been calculated for the carbo- and hetero-Diels-Alder reactions. The FMOs are perturbed by the coordination of the substrate to the Lewis acid giving a more favorable reaction with a lower transition-state energy. Furthermore, a more asynchronous transition-structure for the cycloaddition step, compared to the uncatalyzed reaction, has also been found for this class of reactions. 

Figure 11.5 The effects of changes in reactant and transition-state energy levels on reaction rate, (a) A higher reactant energy level (red curve) corresponds to a faster reaction (smaller AG ), (bl A higher transition-state energy level (red curve) corresponds to a slower reaction (larger AG ).

It should be emphasized again that both the SN1 and the 5 2 reaction show solvent effects but that they do so for different reasons. SN2 reactions are disfavored in protic solvents because the ground-state energy oi the nucleophile is lowered by solvation. S l reactions are favored in protic solvents because the transition-state energy leading to carbocation intermediate is lowered by solvation. 

The transition-state energy is defined as the saddle point of the energy of the system when plotted as a function of the reaction coordinates illustrated in Figure 1.1. 

A Gst is the difference in free energy due to steric constants in reactant and transition state, k is the rate constant of the nonsterically constrained reaction. The contribution of the steric component to the transition-state energy cannot be deduced accurately from DFT calculations because van der Waals energies are poorly computed. Force field methods have to be used to properly account for such interactions. 

As long as there are no important steric contributions to the transition-state energies, the elementary rate constant of Eq. (1.22) does not sensitively depend on the detailed shape of the zeolite cavity. Then the dominant contribution is due to the coverage dependent term 9. 

Eigure 1 shows the plots for the relation between A AG and E at three different temperatures 50, 0, and —50°C. At the lower temperature (—50°C), the curve flattens quickly, and E value of 100 requires AAG = 2047calmoU, less than those of 2506 (at 0°C) and 2965 cal moF (at 50°C), and thus a small difference in transition-state energy (AAG ) between the enantiomers gives a large effect on the enantioselectivity. Thus, lowering the temperature increases the... 

Here the thermodynamics still favor stepwise reaction by way of pentacoordinate intermediate, 25, but the preference is weaker than in the triester case above. A concerted path might be barely possible here but would be expected to be close in structure and transition state energy to the pentacoordinate intermediate. 

---