Reaction barriers, calculation

The overall a//3-selectivity of the thermal decomposition of PPE is determined by the relative constants for the hydrogen abstraction reactions by phenoxy and benzyl only. This is an important result because rate constants are extremely sensitive to errors in the reaction barriers and significant errors can occur due to the anharmonicity in the vibrations. Generally, errors in reaction barriers calculated with ab initio or density functional methods are systematic and the anharmonic correction introduced in Section 7.3.1.3 reduces the nonsystematic errors in the prefactors. When calculating relative rate constants, errors cancel, particularly for the ratios of rate constants in Eq. (7.42), because k2a and k2b are rate constants for reactions with the same reactants and very similar transition states (analogously, for k a and k b). 

Consequently, any association must decrease chain tendency to degradation. However, the existence of such intermediate particles at association, which possess lower height of the reaction barrier, may be probable. In this case, kinetic probabilities of the process performance increase. A sufficiently sharp increase of kinetic probabilities of the reaction must be observed in the case, if a low-molecular compound (oxygen, for example) participating in the reaction is highly stressed. But it is necessary to remember that even if kinetic probabilities of the process are increased, the reaction will also proceed in the case of its thermodynamic benefit. As association depends on macromolecule concentration, it should be taken into account at the calculation of kinetic and thermodynamic parameters of the process according to thermodynamics. 

The crucial ingredient in a reaction rate calculation is the identification of reactive trajectories. To this end, initial conditions sampled from Eq. (49) are propagated forward and backward to a time 7)nt. Those trajectories that begin on the reactant side of the barrier at t = — 7jnt and end on the product side at t = +T-mt are then regarded as (forward) reactive. The identification of reactive... 

Figure 5. Reaction probabilities for a given instance of the noise as a function of the total integration time Tint for different values of the anharmonic coupling constant k. The solid lines represent the forward and backward reaction probabilities calculated using the moving dividing surface and the dashed lines correspond to the results obtained from the standard fixed dividing surface. In the top panel the dotted lines display the analytic estimates provided by Eq. (52). The results were obtained from 15,000 barrier ensemble trajectories subject to the same noise sequence evolved on the reactive potential (48) with barrier frequency to, = 0.75, transverse frequency co-y = 1.5, a damping constant y = 0.2, and temperature k%T = 1. (From Ref. 39.)...

Figure 2-9. Reaction scheme for the complete catalytic cycle in glutathione peroxidase (left). Numbers represent calculated reaction barriers using the active-site model. The detailed potential energy diagram for the first elementary reaction, (E-SeH) + H2O2 - (E-SeOH) + H2O, calculated using both the active-site (dashed line) and ONIOM model (grey line) is shown to the right (Adapted from Prabhakar et al. [28, 65], Reprinted with permission. Copyright 2005, 2006 American Chemical Society.)...

Surprisingly, the aromatic product is not obtained in the reaction with fumaroni-trile (47) - the Diels-Alder cycloadduct is the only product. The activation barriers calculated for this aromatization were the highest reported in this work [52],... 

The CASPT2/6-311G(2d,p) barrier for the process 2b — 3b is only ca. 3 kcal/mol, and this reaction is calculated to be exothermic by about 6 kcal/mol. These computational results are consistent with the failure of Schuster s time-resolved IR experiments to detect 2b.38b,c A barrier of 3 kcal/mol implies rapid conversion of 2b to 3b at room temperature, and a 6 kcal/mol difference in energy between 2b and 3b means that at 25°C the equilibrium would overwhelmingly favor 3b. In addition, azirine 2b probably absorbs less strongly than cyclic ketenimine 3b in the infrared, thus rendering detection of the azirine even more difficult. 

In addition to the electronic difference between PR3 and PH3, bulkier ligands on the phosphine can change the reaction through their steric effect. Using the R = Bu on the anthraphos system, Haenel et al. calculated the available molecular surface (AMS) around the metal center as a measure of the space available to the alkane (13b). They correlated the AMS to the relative reactivities of the catalysts and the results show that two bulky tert-butyl groups on each P certainly limit the access to the metal center, and thus, may reduce the reactivity. Other theoretical studies on the pincer complexes showed that this steric contribution/ limitation plays a less important role than the activation barriers introduced by the catalyst itself (22), where the increase in energy barrier induced by the bulky 4Bu is smaller than the original barriers calculated... 

Instead of having the olefin insertion reactions, the calculations indicate that M2b and M2c can only proceed uphill with the reductive elimination of HB(OH)2, leading to the formation of M3, an olefin complex which could be in principle obtained directly from the addition of olefin to the catalyst Rh (PH3)2C1. The olefin complex M3 then could undergo a-bond metathesis processes with HB(OH)2, giving two isomeric products M4 and M5 depending on the orientation of the HB(OH)2 borane. The a-bond metathesis processes are however found to be unfavorable because of the very high reaction barriers (Figure 4). 

Furthermore, a brief review of dyotropic rearrangements starting with the hypothetical transformations of 1,2-disubstituted cyclobutenes was published98 in which two types of these processes were described and a general theory covering such rearrangements was outlined. Quantum chemical calculations of the reaction barrier for the dihydrogen... 

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