N-Heterocyclic Carbene Catalyzed Quadruple Domino Reactions: Asymmetric Synthesis of Cyclopenta[c]chromenones

Synthesis and decomposition are two types of redox reactions. Synthesis means to make something, whereas decomposition means to break something. The reactions are accompanied by chemical and energy changes. 

As depicted in Figure 1, base-catalyzed aldol addition involves adding two carbonyl compounds in aqueous sodium hydroxide to form a β-hydroxy carbonyl compound.

The aldol reaction of a ketone under acidic conditions successfully forms an unsaturated carbonyl as the final product instead of an aldol. The acid-catalyzed aldol reaction is depicted in Figure 1.

Rate laws describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In a rate law, the rate constant k and the reaction orders are determined experimentally by observing how the rate of reaction changes as the concentrations of the reactants are changed. A common experimental approach to the determination of rate laws is the method of initial rates. This method involves measuring reaction rates for multiple experimental trials carried out using...

Heterocyclic amines, where the N atom is a part of an alicyclic system, are similar in basicity to alkylamines. Interestingly, the heterocyclic amine having a nitrogen atom as part of an aromatic ring has much less basicity than its corresponding alicyclic counterpart. For this reason, as presented in Figure 1, piperidine (pKb = 2.8) is significantly more basic than pyridine (pKb = 8.8).

By definition, a spherically symmetric body has the same moment of inertia about any axis passing through its center of mass. This situation changes if there is no spherical symmetry. Since most rigid bodies are not spherically symmetric, these require special treatment.
The relationship between the angular momentum of any rigid body and its angular velocity, both of which are vectors, involves the moment of inertia. The moment of inertia is a scalar quantity only for spherically symmetric...