Reaction coordinate-diagram

A transition structure is the molecular species that corresponds to the top of the potential energy curve in a simple, one-dimensional, reaction coordinate diagram. The energy of this species is needed in order to determine the energy barrier to reaction and thus the reaction rate. A general rule of thumb is that reactions with a barrier of 21 kcal/mol or less will proceed readily at room temperature. The geometry of a transition structure is also an important piece of information for describing the reaction mechanism. 

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 is the reaction coordinate diagram for Fig. 5-2. Note the region of the maximum potential energy on the reaction coordinate this region assumes great importance in kinetic theory. At this point the reacting system is unstable with respect to motion along the reaction coordinate. However, at this same point the system possesses minimum energy with respect to motion along dashed line cd. This portion of the reaction coordinate is called the transition state of the reaction. (This concept was introduced in Fig. 1-1.)...

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

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. 

Figure 5-5. Reaction coordinate diagram corresponding to Fig. 5-4, showing that the initial state is more stable than the final state and the transition state is productlike.

Thus far we have drawn reaction coordinate diagrams with potential energy as the ordinate. However, the free energy is a much more accessible quantity (actually... 

With these relationships and the appropriate experimental data we can plot reaction coordinate diagrams that are quantitatively useful in displaying the free energy differences between states. Figure 5-9 is an example, the data being drawn from Table 4-3, System 2. For this reversible reaction. 

Figure 5-9. Free energy reaction coordinate diagram for System 2 of Table 4-3, the formation of a cyclodextrin inclusion complex.

Let us now sketch the reaction coordinate diagram for the complex reaction of Scheme U, where R represents the reactant state, P the products, and I an intermediate. 

Figure S-10. Hypothetical free energy reaction coordinate diagram for Scheme 11 (TS = transition state).

Strictly speaking, the flow analogy is valid only for consecutive irreversible reactions, and it can be misleading if reverse reactions are significant. Even for irreversible reactions the rds concept has meaning only if one of the reactions is much slower than the others. For reversible reactions the free energy reaction coordinate diagram is a useful aid. In Fig. 5-10, for example, the intermediate 1 is unstable with respect to R and P, and its formation (the kf step) is the rds of the overall reaction. 

Let us apply this method to the hypothetical reaction coordinate diagram of Fig. 5-11, which consists of two sections. The requisite energy differences are for the vertical distances (T2 — R) and (T3 — I2). Because (T3 — I2) > (T2 — R), the second section contains the rds, which must be the I2 —> T3 step. Note that T3 actually has a lower free energy than do Ti and T2 it is the change in free energy from the valley at the beginning of the section that determines the rate. 

This is an interesting exercise, but we should not become excessively concerned with formal schemes for the identification of the rds. We want to know the rds because it is a piece of information about the reaction mechanism. If we have already acquired so much information about the system that we can construct a reaction coordinate diagram displaying ail intermediates and transition states, we probably have no need to specify the rds. As an example of the experimental detection of the rds we will describe Jencks study of the reaction of hydroxyiamine with acetone. The overall reaction is... 

Figure S-IS. Representation of a reaction coordinate diagram by straight line trajectories determined by the condition of minimum time or distance. The reaction coordinate is specibed as the bond order of a bond formed in the reaction.

We will follow Murdoch s development. Figure 5-16 shows schematic reaction coordinate diagrams for a reaction series of varying product stability. It is evident that a at the transition state varies with AG for the reaction. We will assume a linear relationship. 

Figure S-16. Schematic reaction coordinate diagrams of a reaction series, showing ACj, the intrinsic barrier, and ACma, the maximum standard free energy difference.

Figure 5-20. Reaction coordinate diagram generated from a valence bond description of initial and final state configurations.

For the oximation of a ketone (see Fig. 5-12 and aeeompanying text), sketeh the free energy reaction coordinate diagram at pH 7 and pH 2. 

Sketch qualitative reaction coordinate diagrams corresponding to the several areas and lines in Fig. 8-5. 

Recent evidence supports the view that at least in some cases structure 1 corresponds to an intermediate of finite stability and that the potential-energy vs. reaction-coordinate diagram in such cases consists of two maxima (transition states) separated by a minimum (intermediate). 

Click Coached Problems for a self-study module on reaction coordinate diagrams. 

The low efficiency of exchange in water can be explained by postulating that the ion-molecule pair (8.13 in Scheme 8-10) is almost completely trapped by water molecules, i.e., the first intermediate reacts so easily with this more strongly nucleophilic species that the reaction of the second intermediate (8.14) with N2 is not detectable. Therefore, the reaction coordinate diagrams for the dediazoniation in TFE and in water may be visualized as shown in Figure 8-4. 

One traditional depiction of a reaction coordinate diagram for the scheme A s= I - P. The peaks are meant to represent the transition states, and the minimum the intermediate I. This useful presentation. however, cannot be taken too literally since the abscissa is not defined (see text). 

Reactant flux. 85-86 Reaction coordinate diagram, 84 Reaction intermediates (see Intermediates)... 

Fig. 5. Potential energy-reaction coordinate diagram for an electron transfer reaction leading to a product adsorbed on the electrode surface.

Fig. 12. Energy-reaction coordinate diagram for electron transfer in solution when there is only weak interaction between the initial and final energy states.

Fig. 8. Reaction coordinate diagram for the bromination of tra/iM-methylstilbene (a) and trans-4,4 -bis(trifluoromethyl)stilbene (b).

Figure 1. Energy-reaction coordinate diagram for the acid-catalyzed hydration of phenylacetylene. The ordinate is not to scale (20).

Quantum tunnelling in chemical reactions can be visualised in terms of a reaction coordinate diagram (Figure 2.4). As we have seen, classical transitions are achieved by thermal activation - nuclear (i.e. atomic position) displacement along the R curve distorts the geometry so that the... 

Figure 2.4. Reaction coordinate diagram for a simple chemical reaction. The reactant A is converted to product B. The R curve represents the potential energy surface of the reactant and the P curve the potential energy surface of the product. Thermal activation leads to an over-the-barrier process at transition state X. The vibrational states have been shown for the reactant A. As temperature increases, the higher energy vibrational states are occupied leading to increased penetration of the P curve below the classical transition state, and therefore increased tunnelling probability.

Scheme 7-19 Predicted qualitative reaction coordinate diagrams (free PPh3S omitted)...

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