Reaction path Profile

Quantum-chemical calculations show that the reaction path profiles Urp(qr) (where qr is a reaction coordinate) for exothermic reactions of a gas molecule B with a surface center A/s/ via a surface precursor AB/s/ with the formation of a gas molecule D and a new surface center C/s/ have... 

The following set of macroscopic reactions corresponds to the reaction path profiles presented in Figures 9.1 and 9.2 ... 

Fig. 9.1. Reaction path profile of an exothermic gas-surface reaction without activation energy via a precursor.

Figure 6-6. Reaction path profile (potential energy curve) for the elementary process of NO synthesis O + N2 — NO + N, showing adiabatic and non-adiabatic reaction channels.

Fig. 6. Reaction path profile for the reaction of A with diatomic molecule BC.

The situation with dissociation reactions is most favorable in this respect because, as a rule, it may be assumed that Ea for these reactions coincides with the reaction heat Q. For exchange reactions, the reaction path profile displays a potential barrier. Therefore, Q obtained from thermochemical data is not directly related here to the activation energy value. Nevertheless, it can be expected on the ground of qualitative theoretical arguments [230] that for similar reactions... 

For direct reactions, the reaction path profile has one potential barrier. In the frameworic of the theory of activated complex, the deviations of the temperature dependence of the rate constant from the Arrhenius equation for direct reactions can be explained by the temperature dependence of statistical sums of the reactants and activated complex. After inserting rotation, vibration, and translational statistical sums into expression (4.76), the temperature dependence of the rate constant is presented by the expression... 

Figure 8 An accurate estimate of the barrier height can be found by adding a sufficient number of intermediate points in the discretized transition pathways. The solid line in the graph represents the energy profile for a reaction path described by 11 intermediate configurations of the system. The dashed line shows a coarse pathway described by only two intermediate configurations. The latter path underestimates the true energy ban ier.

Figure 11-9. CASSCF potential-energy profiles of the ground-state So (circles), the lnjr state (triangles), the Lb state (squares), and the La state (filled squares) of the 9H-adenine along the linear interpolation reaction path from the equilibrium geometry of the nit state to the CI32 (a) and CI16 (b) conical intersections. The diabatic correlation of the states is shown in (a). (From Ref. [138])...

Fig. 18. Energy profiles for the most favourable reaction paths for the reactions in Fig. 17 c.

To obtain Vmin for a PFR, the T profile is chosen so that the reaction path follows the locus of maximum rates as fA increases that is, the rate is ( —rA)mflJ[ at each value of fA in the design equation (from equation 15.2-2) ... 

Fig. 16 (a) Comparison of potential energy profile for the formal Cope rearrangement of 3,4-difluorohexa-l,5-diyne-3-ene with that of (Z)-hexa-l,5-diyne-3-ene, (b) Rehybridization in the C(F) bond along the reaction path. EDI = 3,4-difluoro-hex- 3-ene-l,5-diyne ED2 = 1,6-di-fluoro-hex-3-ene-l,5-diyne BZY = difluoro-l,4-didehydrobenzezne TSBC = the transition state for the Bergman cyclization TSRBC = the transition state for the retro Bergman cyclization. 

We looked briefly at reaction profiles in Section 8.2. Before we look at the reaction profile for the concurrent reactions of hydrolysing a secondary alkyl halide, we will look briefly at the simpler reaction of a primary alkyl halide, which proceeds via a single reaction path. And for additional simplicity, we also assume that the reaction goes to completion. We will look not only at the rate of change of the reactants concentration but also at the rate at which product forms. 

FIGURE 5.6 (See color insert following page 302.) Momentum and coordinate space charge density profiles for the reaction path from HNC to HCN. 

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 ... 

The top of the profile is maximum (saddle point) and is referred as the transition state in the conventional transition state theory. It is called a saddle point because it is maximum along the orthogonal direction (MEP) while it is minimum along diagonal direction of Fig. 9.12. The minimum energy path can be located by starting at the saddle point and mapping out the path of the deepest descent towards the reactants and products. This is called the reaction path or intrinsic reaction coordinate. 

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