Reaction coordinate, potential energy surfaces

Figure 8.53 Schematic illustrations of potential energy surface, reaction coordinate and transition state, (a) 3D depiction of potential energy surface-left and contour depiction-right, (b) Conversion of species A and B to P, illustrating the transition state C+and free energy of activation A6 +(illustrations a) and b) Reproduced from Atkins, 1995, Figs. 27.15 27.16 respectively).

Figure 6.3 Potential energy surface for colinear reaction AB + C —> A + BC (a) 2-D topographical representation (b) 3-D representation (c) potential energy along reaction coordinate (d) atomic configurations along reaction coordinate...

Fig. 7. Energetics of a bimolecular rate process. Top Representation of the potential energy surface along coordinate axes corresponding to the interatomic distance of B-to-C and A-to-B, where incremental displacements along the potential energy axis are shown as a series of isoenergetic lines (each marked by arbitrarily chosen numbers to indicate increased energy of the transition-state (TS) intermediate relative to the reactants). Bottom Typical reaction coordinate diagram for a bimolecular group transfer reaction.

Despite its complexity. Fig. 14.7 begs one important question. Consider either the reaction intermediate in that figure or, when no such intermediate is formed, the corresponding transition state (shown dotted in Fig. 14.7). Compared to the coordination number of the metal in the reactant complex, at this point in the potential energy surface the coordination number of the metal could have increased by one, decreased by one or stayed the same. The rate-determining step in the reaction mechanism involves association, dissociation or an interchange, respectively, and these labels. A, D and I, are used to describe the reaction type. The job of classifying a particular... 

The reaction coordinate is one specific path along the complete potential energy surface associated with the nuclear positions. It is possible to do a series of calculations representing a grid of points on the potential energy surface. The saddle point can then be found by inspection or more accurately by using mathematical techniques to interpolate between the grid points. 

If the complete potential energy surface has already been computed, a reaction coordinate can be determined using an adaptation of the IRC algorithm. The IRC computation requires very little computer time, but obtaining the potential energy surface is far more computation-intensive than an ah initio IRC calculation. Thus, this is only done when the potential energy surface is being computed for another reason. 

As a last resort, compute the entire potential energy surface and then obtain a reaction coordinate from it. 

MEP (IRC, intrinsic reaction coordinate, minimum-energy path) the lowest-energy route from reactants to products in a chemical process MIM (molecules-in-molecules) a semiempirical method used for representing potential energy surfaces... 

HyperChem can calculate transition structures with either semi-empirical quantum mechanics methods or the ab initio quantum mechanics method. A transition state search finds the maximum energy along a reaction coordinate on a potential energy surface. It locates the first-order saddle point that is, the structure with only one imaginary frequency, having one negative eigenvalue. 

The potential energy surface consists of two valleys separated by a col or saddle. The reacting system will tend to follow a path of minimum potential energy in its progress from the initial state of reactants (A + BC) to the final state of products (AB -F C). This path is indicated by the dashed line from reactants to products in Fig. 5-2. This path is called the reaction coordinate, and a plot of potential energy as a function of the reaction coordinate is called a reaction coordinate diagram. 

Figure 5-3. Reaction coordinate diagram for the potential energy surface of Fig. 5-2.

Potential energy surfaces calculated by means of the London equation (5-15) cannot be highly accurate, but the results have been very useful in disclosing the general shape of the surface and the reaction coordinate. The London equation also forms the basis of some semiempirical methods. 

Let us now turn to the surfaces themselves to learn the kinds of kinetic information they contain. First observe that the potential energy surface of Fig. 5-2 is drawn to be symmetrical about the 45° diagonal. This is the type of surface to be expected for a symmetrical reaction like H -I- H2 = H2 -h H, in which the reactants and products are identical. The corresponding reaction coordinate diagram in Fig. 5-3, therefore, shows the reactants and products having the same stability (energy) and the transition state appearing at precisely the midpoint of the reaction coordinate. 

The entries in the table are arranged in order of increasing reaction coordinate or distance along the reaction path (the reaction coordinate is a composite variable spanning all of the degrees of freedom of the potential energy surface). The energy and optimized variable values are listed for each point (in this case, as Cartesian coordinates). The first and last entries correspond to the final points on each side of the reaction path. 

Transition State Geometry. The geometry corresponding to a Stationary Point on the Potential Energy Surface which is an energy minimum in all directions except one (the Reaction Coordinate), for which it is an energy maximum. 

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