Concerted transition

Do we expect this model to be accurate for a dynamics dictated by Tsallis statistics A jump diffusion process that randomly samples the equilibrium canonical Tsallis distribution has been shown to lead to anomalous diffusion and Levy flights in the 5/3 < q < 3 regime. [3] Due to the delocalized nature of the equilibrium distributions, we might find that the microstates of our master equation are not well defined. Even at low temperatures, it may be difficult to identify distinct microstates of the system. The same delocalization can lead to large transition probabilities for states that are not adjacent ill configuration space. This would be a violation of the assumptions of the transition state theory - that once the system crosses the transition state from the reactant microstate it will be deactivated and equilibrated in the product state. Concerted transitions between spatially far-separated states may be common. This would lead to a highly connected master equation where each state is connected to a significant fraction of all other microstates of the system. [9, 10]... 

TABLE 8. Values of the length (A) of the forming C—C bonds (.R) and of the energy barrier (AE) (in kcal mol-1) for the concerted transition state of the butadiene + ethylene reaction computed at several levels of calculation ... 

On the basis of theoretical data and experimental observations it was concluded that TMSCN reacts via a concerted transition state. Et2AlCN initially forms a... 

DFT calculations have been used to study the mechanistic pathway of the intramolecular Diels-Alder cycloaddition involved in the biosynthesis of natural products paraherquamide A and VM55599. The cycloaddition involves a dihydropyrolo[l,2- ]pyrazine as the azadiene and a standard alkene as the dienophile (Scheme 1). Analysis of the results reveals that these cycloadditions take place through concerted transition structures associated with [4+2]... 

Fig. 2 Computed concerted transition states for rearrangement and substitution reactions...

The SB-GA mechanism consists of a rapid equilibrium deprotonation of the ZH intermediate, followed by rate-limiting, general acid-catalysed leaving-group departure from the anionic cr-complex Z via the concerted transition state, 2. The derived expression for this mechanism is equation 4, where fctBH is the rate coefficient for acid-catalyzed expulsion of L from Z and K3 is the equilibrium constant for the reaction ZH Z- + BH. 

In the context of the Monod-Wyman-Changeux concerted-transition model for allosteric effects, one usually considers the effects of specific site occupancy on the behavior of other binding sites. Thus, a more correct... 

In 2002, Musaev and coworkers performed the first theoretical investigation of the mechanism with the aid of density functional theory calculations [26]. They first studied the mechanism of cycloisomerization in the absence of a tungsten catalyst, as shown in Scheme 4.14. The D FT calculations showed that the exo-cycloisomerization of 4-pentyn-l-ol via a concerted transition state leading to a five-membered-ring exo product had a high barrier (52.0 kcalmol ) (path a of Scheme 4.14). The pathways leading to a six-membered-ring endo product have also been calculated (paths b and c... 

A novel approach to achieve high regioselectivity was recently developed by Yang and coworkers, in which the in-situ-generated dioxirane functionality, contained within the substrate, oxidizes the secondary 5c-h bond rather than the more reactive tertiary yc-H bond, due to a favorable concerted transition state (equation 31). A limitation of this method, however, is that the ketone unit has to be incorporated into the substrate molecule at the appropriate position, normally a rather unpractical and cumbersome task. Moreover, such a process is necessarily stoichiometric in practice and, thereby, it lacks appeal since nowadays catalytic enantioselective oxyfunctionalizations are in vogue ... 

For isotope effect evidence regarding the nature of the concerted transition state, see McMichael Korver J. Am. Chem. Soc. 1979, 101, 2746 Gajewski Conrad J. Am. Ckem. Soc. 1979, 101, 2747 Kupczyk-Subotkowska Saunders Shine /. Am. Chem. Soc. 1988,110, 7153. 

The kinetics of concerted thermal elimination reactions of a series of ethyl (hetero) arylcarboxylate esters (2-thienyl-, 3-thienyl-, 2-furyl, 3-furyl, 4-pyridyl-, 3-pyridyl-, and 2 -pyridylcarbo x y I ate) in the gas phase seem to indicate that there is tittle charge separation in the transition state (83) this is in contrast with the behaviour of the corresponding /-butyl and isopropyl esters for which a semi-concerted transition state (82) was proposed previously.49 Results of a kinetic study of the gas-phase elimination reactions of methylbenzoyl fonnate (84) and 3-hydroxy-3-methylbutan-2-one (85) have been compared with those for pyruvic acid (87) and benzoylformic acid (86).50 The relative rates of reaction [(86)/(87) 46, (87)/(85) = 1.1 x 105 and (86)/(82) = 1 x 106] reveal that the acidity of the hydrogen atom involved in the elimination process, rather than the initial polarization of the C—C bond which undergoes cleavage, is the important rate-controlling factor. 

DFT calculations were performed for the double proton transfer in bicyclic 2,2 -bis(4,5,6,7-tetrahydro-l,3-diazepine) (Figure 8) <2001CPL591>. Both a concerted and a stepwise mechanism for proton transfer are considered. Though the concerted transition state has two imaginary eigenfrequencies, dynamical calculations have demonstrated that it has to be taken into account in the mechanism of the proton transfer even if it is not a true reaction path. 

Theoretical studies on 12 4-substituted phenyl acetates concluded that, in contrast to the proposed interpretation based on 13C NMR chemical shifts and ground-state destabilization calculations, the electrophilicity of the C=0 group increases due to the effect promoted by the electron-withdrawing groups in these systems.11 A DFT investigation of the alkaline hydrolysis of 4-nitrophenyl acetate has shown that a model including seven water molecules proceeds via a concerted transition state.12... 

Calculations on the experimental system and a model reaction were unable to locate a transition structure for formation of the diradical intermediate of a stepwise mechanism. The stepwise mechanism and the asynchronous concerted mechanism start out geometrically similar, and the two pathways appear to have merged at a highly asynchronous concerted transition structure. 

Because the 3-4 bond is less weakened and the 1-6 bond formation is facilitated, 2-substituted transition states are more symmetrical than 1- or 3-substituted transition states. This conclusion can also be reached using another argument. If, following Hrovat et al.,57 we assume that the concerted transition state is a resonance between the limiting forms A in which the 3-4 and 1-6 bonds are completely made, and B in which these bonds are completely broken ... 

The reaction of butadiene and ethylene has been studied at many computational levels and serves as a prototype for pericyclic reactions [6,7], The concerted transition structure with Cs symmetry, shown in Fig. 5, is found to be lowest in energy. The calculated activation energy varies widely, from over 45 kcal/mol at the Hartree-Fock limit to 17.6 kcal/mol, with MP2/6-31G calculations. Inclusion of dynamic correlation energy, such as provided by QCISD(T) calculations [35], is necessary to give accurate activation energies near the experimental values of 24 kcal/mol [6, 36]. 

Fig. 5. Concerted transition structure of the Diels-Alder reaction of butadiene and ethylene...

Concerted transition states of the E2 reaction. The orbitals of the hydrogen atom and the halide must be aligned so they can begin to form a pi bond in the transition state. 

---