Position and Height of the Energy Barrier

The Hammond postulate is a valuable criterion of mechanism, because it allows a reasonable transition state structure to be drawn on the basis of knowledge of the reactants and products and of energy differences between the states (i.e., AG and AG°). Throughout this chapter we have located transition states in accordance with the Hammond postulate. 

It would be desirable to achieve a quantitative version of the Hammond postulate. For this purpose we need a measure of progress along the reaction coordinate. Several authors have used the bond order for this measure.The chemical significance of bond order is that it is the number of covalent bonds between two atoms thus the bond orders of the C—C, C==C, bonds are 1, 2, and 3, 

The simplest argument is that of Agmon based on Fig. 5-15. Because of the reflection symmetry at point T, the triangles ATR and BTP are similar, so we can write AT/AR = TB/PB, or, if we express the ordinate in free energies. 

According to this very simple derivation and result, the position of the transition state along the reaction coordinate is determined solely by AG° (a thermodynamic quantity) and AG (a kinetic quantity). Of course, the potential energy profile of Fig. 5-15, upon which Eq. (5-60) is based, is very unrealistic, but, quite remarkably, it is found that the precise nature of the profile is not important to the result provided certain criteria are met, and Miller obtained Eq. (5-60) using an arc length minimization criterion. Murdoch has analyzed Eq. (5-60) in detail. Equation (5-60) can be considered a quantitative formulation of the Hammond postulate. The transition state in Fig. 5-9 was located with the aid of Eq. (5-60). 

We will explore further the idea that there may be a relationship between rates and equilibria. Although such a relationship is not required by thermodynamics, neither is it forbidden, and much empirical evidence supports the frequent occurrence of such relationships. Chapter 7 is devoted to this topic here we restrict attention to correlations of AG (or log k) with AG° (or log K) of the same reaction. Such correlations are usually sought within a reaction series in which a set of reactants having a common reaction site but different substituent sites are subjected to the same reaction. 

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The reader may now recall the discussion in Section 5.3, Position and Height of the Energy Barrier, on correlations of rates and equilibria of the same reactions and the interpretation of the slope a from such LEER as a measure of the position of the transition state along the reaction coordinate. It will now be apparent why the term Breasted coefficient is applied both to this quantity and also to the slope of LEER according to Eqs. (7-58) and (7-59). The interpretation of a and P from Eqs. (7-58) and (7-59) as measures of fractional progress along a reaction coordinate may be misleading when the reaction is complex, and caution is appropriate. - pp- 38-41... 

Reaction Coordinate Diagrams 209 The Rate-Determining Step 213 Composition of the Transition State 216 Position and Height of the Energy Barrier 220 Concerted and Stepwise Reactions 230... 

Fig. 20.15 Cathodic reduction of M" (aq.) to metal in which the activation energy (height of the energy barrier) for the cathodic reaction is lowered to E + 0FE whilst that for the anodic reaction is raised to — (1 — /3) FE (note that E is positive and E negative). (After...

Fig. 20.16 Potential energy against distance curves Morse curves), (a) No potential dilTerence (p.z.c.), (b) at the equilibrium potential when / = / and the heights of the energy barrier are the same for both reactions, but p.z.c W potential made more negative than E q and (d) potential made more positive than E. The p.z.c. has been taken as zero potential, and A, and h,. are the heights of the potential barriersj or the anodic and cathodic reactions, respectively / is the rate of the cathodic reaction and / the rate of the anodic reaction (after Bockris...

Fig. 15.51 Energy and position of the hydrogen atom in (a) the symmetric HF7 system and (b) an unsymmeiric 0-H --0 system. In (a) the average position of the hydrogen atom is midway between the fluoride ions. In (b) the positional sketch on the left represents the average position of the hydrogen in the left potential well and the dotted sketch represents the average position for the other potential well. The height of the energy barrier is qualitative and not meant to represent any particular system.

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