for the reactant molecules to collide effectively giving the products, they must overcome an energy barrier, which is called activation energy (Ea) (Fig. 1.4). This is true for both exergonic (ΔG < 0, Fig. 1.4a) and endergonic (ΔG > 0, Fig. 1.4b) reactions. The activation energy (Ea) is a free energy term, which includes contributions from both enthalpy and entropy. The state in which the reaction system reaches a maximum energy level in the energy profile (Fig. 1.4a or b) is called transition state. It is also referred to as activated complex in which reorganization of the atoms in the reactant molecules are taking place such that some old bonds are being partially broken, coincident with the partial formation of some new bonds. The transition state (activated complex) is highly energetic and therefore, it is in general very unstable and short‐lived [with the half‐life being in the order of picosecond (10−12 s) for many reactions]. Once formed, it rapidly collapses (dissociates) spontaneously. As a result, the old bonds in the reactants are fully broken, and simultaneously, the new bonds are completely formed, giving the final stable products in the end of the reaction.
FIGURE 1.4 Early transition state (a) and late transition state (b).
In a concerted reaction (Fig. 1.4), the activation energy (Ea) is equal to the free energy of the transition state (Ea = ΔG‡ = ΔΗ‡ – TΔS‡). ΔG‡, ΔΗ‡, and ΔS‡ are the difference in free energy, enthalpy, and entropy values, respectively, between the transition state and the reactants (ΔG‡ = GTS − Greactants, etc.), and they are referred to as free energy, enthalpy, and entropy of the transition state. In the case that the entropy (ΔS‡) effect is small and can be neglected, the activation energy is then approximately equal to the activation enthalpy (Ea = ΔΗ‡). In the individual chapters, we will see that this approximation is very often valid and works well for many reactions. The energy level (in the free energy term) that the transition state possesses is the quantitative measure for the stability of the transition state. A fast reaction requires a relatively stable transition state (with a relatively low energy level). A reaction is getting slower as the stability of the transition state decreases (with an increase in its energy level). The quantitative relationship between the rate constant (k) of a reaction (concerted) and the activation energy (Ea) is described by the well‐known Arrehnius equation (Eq. 1.54):
1.6.2 The Hammond Postulate
The exact structure of a transition state is in general not measurable due to its instability. It is in‐between the structures of reactants and products, which can be qualitatively predicted and described by the Hammond postulate [3]. It states that the structure of the transition state for a concerted reaction resembles (closer to) the species (reactant or product) to which it is most similar in energy. According to the Hammond postulate, if a concerted reaction is exergonic (or exothermic if entropy of the reaction ΔS is small and negligible) (Fig. 1.4a), the energy of the transition state is most similar to that of the reactant. Therefore, the structure of the transition state resembles the reactant. Such a transition state is called early transition state. If a concerted reaction is endergonic (or endothermic if entropy of the reaction ΔS is small and negligible) (Fig. 1.4b), the energy of the transition state is most similar to that of the product. Therefore, the structure of the transition state resembles the product. Such a transition state is called late transition state.
Figure 1.5 shows examples of exothermic (ΔH < 0) and endothermic (ΔH > 0) SN2 reactions (concerted). Usually, the entropies of simple SN2 reactions are small relative to the reaction enthalpies, and they are negligible. According to the Hammond postulate, the exothermic SN2 reaction has an early transition state whose structure resembles the reactants (Fig. 1.5a), while the endothermic SN2 reaction has a late transition state whose structure resembles the products (Fig. 1.5b). Although a simple SN2 reaction has a small entropy, the entropy of its transition state (ΔS‡) possesses a relatively large negative value. This is because in the transition state two reactant molecules combine loosely resulting in decrease in entropy. For the exothermic SN2 reaction (Fig. 1.5a), since the reaction has an early transition state which resembles the reactants, both breaking of the old C─I bond and formation of the new C─C bond in the transition state have only proceeded to a small extent. This gives rise to a small ΔΗ‡ value. Therefore, the major contributor to the activation energy is the entropy effect (Ea ≈ −TΔS‡). On the other hand, the endothermic SN2 reaction (Fig. 1.5b) has a late transition state which resembles the products. Breaking of the old C─Cl bond and formation of the new C─I bond in the transition state are close to completion (ΔΗ‡ ≈ ΔH). As a result, both enthalpy (ΔΗ‡) and entropy (ΔS‡) have substantial contributions to the activation energy (Ea = ΔΗ‡ − TΔS‡). Their combination makes the Ea value greater than the reaction enthalpy (ΔH).
FIGURE 1.5 The SN2 reactions that proceed via (a) an early transition state and (b) a late transition state.
1.6.3 The Bell–Evans–Polanyi Principle
For similar concerted reactions that take place at a certain given temperature, the activation energy (Ea) can be directly correlated to the reaction enthalpy (ΔH) as follows (the Bell–Evans–Polanyi principle):
where c1 and c2 are positive
