Free energy surfaces and transition state theory

Abstract

Free Energy Surfaces and Transition State TheoryMany major chemistry textbooks contain diagrams exhibiting a function referred to vaguely as the "free energy" plotted against a quantity referred to by a phrase such as the "reaction co-ordinate." The diagrams usually have the general form indicated in Figure 1. The "free energy" curve goes through a maximum and this feature is interpreted as representing a "harrier" which the system must cross when reactants are converted to products.There are numerous variations-The term "free energy," (G), may sometimes be replaced by "free energy change," (AG); in some, rather rare, cases an attempt at qualifying the expression further to "standard free energy," (G°), or "standard free energy change," AG°is made and in some cases the same type of figure appears with the abscissa labelled "extent of reaction."As we shall see, the correct definition of such a free energy curve, or surface, requires highly sophisticated concepts (1-3) and involves the finest points of the definition of a transition state1 (4). It is the purpose of the present letter to try to establish that unless such diagrams are very precisely labelled and explained they are seriously misleading and often incorporate a major error of principle. Discussion of the points at issue can be found in some textbooks but rarely in those at undergraduate level (1,5,6). Extent of Reaction and Reaction Co-Ordinate The confusion probably begins with a tendency to regard the terms "extent of reaction" and "reaction co-ordinate" as interchangeable. A sharp distinction must be made between the two concepts involved in the definition of these terms. The usage in the present note is as follows.

Thermodynamically and kinetically controlled products

“…where J is the reaction quotient (of the same form as the equilibrium constant, but with general values of the concentrations) which will be very small at low product concentrations, giving a large and negative, initial AG value, decreasing to zero as the product concentration builds up to its equilibrium value, that is as the thermodynamic extent of reaction approaches 1. In discussing "thermodynamic and kinetic control," the situation has been made more confusing, through misuse of diagrams of potential energy against reaction coordinate (6,7). Such diagrams do not give information concerning AGe, and hence K, for a reaction.…”

What is the rate-limiting step of a multistep reaction?

“…A generalization which has often been used in current textbooks is that, the RLS will be determined by the transition state of highest energy. Like the flow analogies, this approach has also been widely used to illustrate the idea of the RLS through energy (or more properly, free energy) diagrams such as Figure 2. Unfortunately, the use of transition states also has its pitfalls (17), and one of the most serious is that this generalization does not always work for irreversible reactions where the flow analogies are appropriate. An example is the diagram in Figure 1 where the step associated with &2 is rate limiting but the corresponding transition state is lower in energy (or free energy) than the first transition state.…”

“…Since the transition state approach is valid for situations such as Figure 2 where the steady state approximation is applicable to all intermediates, the simplest solution might be to tell students to use the flow analogies for irreversible reactions and transition states for steady state reversible mechanisms. While there are a number of points which must be carefully handled when using transition states for developing the idea of the RLS (17), it is also true that the transition state concept (18) is the foundation on which most treatments of substituent effects are based. Consequently, it might be preferable to develop a generalization for the RLS in terms of transition state energies as well as rates and rate constants.…”

An intuitive approach to steady state kinetics

“…Applying Free-Energy Profiles A free-energy profile is a simple way to illustrate complex kinetic and thermodynamic relationships, such as those discussed above (14). Notional free-energy profiles depicting the six possible relationships between the rate constants of eq 1 are shown in Figure 1.…”