How do ligands accelerate catalytic reactions?

How do ligands accelerate catalytic reactions?
1.Preface:
More than a decade has passed since the discovery of the titanium-catalyzed asymmetric allylic alcohol epoxidation (AE) reaction. The mechanism of this reaction has been investigated in order to understand the reaction process as well as to further expand the application of this reaction. Some of these findings have been applied in chemical synthesis. The discovery of titanium-catalyzed asymmetric allyl alcohol epoxidation (AE) demonstrated that abiotic catalysts can overcome the problem of high substrate selectivity of enzymes (lock-and-key phenomenon) and at the same time achieve enzyme-like catalytic activity in the reaction. At the same time, the osmium tetroxide-catalyzed asymmetric double hydroxylation (AD) of olefins also caught our attention. At first glance, osmium tetroxide-catalyzed olefin asymmetric double hydroxylation (AD) and titanium-catalyzed asymmetric allylic alcohol epoxidation (AE) do not seem to have anything in common except for the fact that they both introduce heteroatoms enantioselectively on the prechiral olefin. However, there is one particular phenomenon that makes these two reactions irreversibly linked. This phenomenon is that they are both ligand-accelerated catalyzed reactions (LAC). At the same time, the success of these two reactions owes a great deal to the existence of this phenomenon.

The aim of this article is to show, by means of these and other important examples, how the ligand-accelerated effect can achieve a fast and highly enantioselective access to the corresponding products in a catalytic reaction. A brief description of the ligand-accelerated catalytic reaction (LAC) will be given in Section II.
2.Basic concepts:
In ligand-accelerated catalytic reactions (LAC), the addition of a specific ligand accelerates the reaction rate of an existing catalyzed reaction. In this reaction process, the ligand-accelerated catalytic reaction (LAC) process as well as the underlying catalytic conversion process are co-existing and the two catalytic reaction processes show competition with each other. This reaction process can be represented by the following diagram

For catalytic reactions, the nature of the ligand bound to the metal center or complex always affects the rate and selectivity of the organic transformation process catalyzed by this species. When a ligand is bound to a catalytically active metal or complex, the reaction rate of the catalyzed reaction in which this species is involved can be reduced, the same, or accelerated compared to the reaction rate of the catalyzed reaction before the addition of the ligand. One of the ligand-accelerated catalytic processes can dramatically increase the efficiency of the reaction.
The simplest definition for the ligand acceleration effect can be given by the following equation. When the ligand is added, the reaction rate vML of the reaction catalyzed by the species bound to the ligand is compared to the reaction rate vM of the reaction catalyzed by the metal or complex not bound to the ligand, and this ratio should be greater than 1. For the ligand-accelerating effect a definition can be given in a similar manner, i.e., when the reaction rate vML of the reaction catalyzed by the species complexed with the ligand is compared to the reaction rate vM of the reaction catalyzed by the metal or complex not bound to the ligand. reaction catalyzed by the species complexed with the ligand compared to the reaction rate vM
The binding of the ligand to the metal or complex is often accompanied by this rapid ligand exchange process. Therefore, the microscopic rate constants (k0 and k1) of the reaction catalyzed by the catalytically active species, as well as the equilibrium complexation constants of the catalyst with the ligand (Keq), have an impact on the macroscopic ligand-accelerating effect (LAE) exhibited by the reaction as a whole.

The ligand acceleration effect (LAE) offers the most attractive possibilities when the added ligand can affect the stereoselectivity of the reaction end product. This is because if the rate enhancement of a catalyzed reaction is caused by a chiral species generated by binding to a chiral ligand, the amount of a single enantioselective product catalyzed by this chiral species will far exceed the amount of a product catalyzed by a catalytic species that is not bound to a ligand in an abasic manner, thus achieving control over the enantioselectivity of the reaction product. The presence of multiple catalytically active species in the reaction system, which include single enantioselective catalysts as well as catalysts that are not enantioselective, does not affect our enantioselective control of the end product. Even in the case where the ligand acceleration effect (LAE) is less influential, we still have good control over the enantioselectivity of the reaction. In general, we consider this asymmetric catalytic reaction to be potentially applicable when the value obtained using Equation 2 is greater than or equal to 20 after the addition of chiral ligands. This is because for a catalytic reaction that meets this requirement, the products from the ligand-driven catalytic process should account for more than 95% of the total products. Therefore, ideally, the ee value of the final product obtained from this asymmetric catalytic reaction would be greater than or equal to 95%.
However, for most of the current asymmetric catalytic reactions, there is no