Energy profiles along the reaction

The corresponding free-energy profile along the reaction path is thus as sketched in Figure 1.13a, leading to the following linear free-energy relationship ... 

How does the present model account for the wide difference in the tunneUing corrections between steps (a) and (d) The most readily recognizable factors responsible for that difference can be deduced from an examination of the potential sur-faces The energy profiles along the reaction coordinates are given in Fig. 8,... 

FIGURE 2. Potential energy profile along the reaction surface for Mg + C2H3CI -> C2H3MgCl at the RHF/3-21G level. The zero point on the abscissa along the IRC is the TS and the product is toward the positive direction. Reprinted with permission from Reference 19. Copyright 1991 American Chemical Society... 

Figure 7 Qualitative depiction of the energy profile along the reaction co-ordinate for the Sn2 reaction Cl ICII3CI >CICn3 I Cl, which involves nucleophilic substitution of the chloride of methylchloride by a chloride ion. The potential energy curves drop as the two reactants approach until a loose complex is formed. Then the energy rises rapidly to the transition state, which has two equal C-Cl interatomic distances (zero on the abscissa). The energy profile looks quite different in the gas and solution phases. Compared to the reactants (or products), the loose complex and the TS are poorly solvated, so the energies for these are much higher in solution than in a vacuum.

Figure 4 Comparison of energy profiles along the reaction path for linear H3. (-...

The basic principles describing the efFects of CT complexes on the energy profile along the reaction coordinate stem from the theory of electron transfer. Redox processes may occur (i) as ground-state thermal reactions, (ii) by direct irradiation of the CT band, and (iii) upon photoexcitation of one of the redox partners followed by diffusional complex formation [4, 24], as depicted in Chart 3. 

If a free radical mechanism is not involved in the reaction, and it takes place by an E mechanism, it is a one-step reaction, with the energy profile along the reaction coordinate illustrated in Figure 2.4.1. The energy of activation AE is the result of... 

FIGURE 18.11 The energy profile along the reaction coordinate for the reaction NO2 + CO —> NO + CO2. This direct reaction dominates the kinetics at high temperatures (above about 500 K). 

Figure 4.10 Free energy profiles along the reaction coordinate for (a) a reaction of zero -AG° (b) the normal region where 0 s -AG° s A, (c) the condition for maximum rate constant where -AG° = A (d) the inverted region where -AG° > A.

Fig. 6.2 Free energy profile along the reaction coordinate q for a non adiabatic process AC + 0...

Fig. 31a and b. Potential energy profiles along the reaction coordinate a) exothermic b) endothermic processes... 

Suppose also that the standard free energy profiles along the reaction coordinate have the parabolic shapes shown in Figure 3.3.2. The upper frame of that figure depicts the full path from reactants to products, while the lower frame is an enlargement of the region near the transition state. It is not important for this discussion that we know the shapes of these profiles in detail. 

Here is the energy profile along the reaction path, viewed as a... 

Inference from the trapped intermediates Several enzymes, particularly hydrolases, form covalent enzyme intermediates such as acyl enzyme intermediates (Bell and Koshland, 1971), which are proximal to the transition states in the energy profile along the reaction coordinate. Since the reaction intermediates, in some cases, can be trapped/isolated for characterization, they represent informative models for the transition states of enzymatic reactions. 

We will use the energy profile along the reaction coordinates to decide which mechanism would be the most favorable one. For complicated systems, the calculation of the energy of a molecule or radical in terms of the mutual distances of the atoms is a tedious procedure and therefore it seems that this approach is often dismissed, when... 

The non-equilibrium free energy profile along the reaction coordinate can be realized by the XRISM theory as follows. To calculate AE in Eq. (1.124), we use the following equation,... 

The potential and free-energy profiles along the reaction coordinate calculated both by the standard ab initio MO and the RISM-SCF in the Hartree-Fock level are shown in Fig. 2.8. Although this reaction is endothermic in the gas phase by 106.3 kcal/mol with the HF method, it becomes exothermic in aqueous solution by 27.8 kcal/mol at the RISM-HF level. The barrier height was calculated to be 17.7 kcal/mol. As seen in Fig. 2.8, there is a very shallow potential well around 1.9 A, which corresponds to a contact ion pair of NH3CH3+ and Cl formed in aqueous solution. The Cl-H RDF depicted in Fig. 2.9 clearly demon-... 

Fig. II.1.17 Schematic drawing of the energy profile along the reaction coordinate for a heterogeneous electron transfer with the electrode poised at three different potentials...

Figure 1 Free energy profiles along the reaction coordinate (77) for the initial and final diabatic states, indicating the reorganization energy if), activation free energy (G ), and reaction driving force (—...

These conclusions follow directly from the simulation of a time-dependent proton energy profile along the reaction coordinate. Figure 4.4 demonstrates how random thermal fluctuations cause a temporary lowering of the potential barrier on the line between two extreme positions for a proton. Due to structural fluctuation, at a certain moment of time (t 16.5 ps) there appears the transient configuration for which an oxonium state becomes more stable... 

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