Reaction Path Energy Profiles

The MP2//HF reaction path energy profile calculated with the procedures described above is shown in Fig.2. The barrier height is 6.4 kcal/mol (including... 

The changes in the extent of electronic reorganisation for different reactions are reflected in the way in which the electronic potential changes along the reaction path. These profiles of potential energy are depicted in the third column of Table 1. For most four-centre molecule-molecule reactions there is a high barrier to reaction. Indeed, for, it is not clear that reaction occurs... 

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.

Initially, we have applied the modified NEB method to the calculation of both steps of the 40T catalyzed reaction. The free energy profiles and relative free energies obtained with this method were compared to our previously determined profiles [33], As we had previously shown, the calculated MEPs for Ref. [33] determined with the reaction coordinate driving method, and the MEPs for Ref. [25] calculated with the parallel path optimizer method, agree in the overall shape and relative potential energies. This provides a good starting point for our comparison. 

Figure 3-6. Free energy profiles for both steps of the reaction catalyzed by 40T (path B)...

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])...

Free energy profiles can also be evaluated within the partial path transition interface sampling method (PPTIS), a path sampling technique designed for the calculation of reaction rate constant in systems with diffusive barrier-crossing events [31,32], In this approach, the reaction rate is expressed in terms of transitions probabilities between a series of nonintersecting interfaces located between regions. c/ and... 

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

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. 

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. 

---