Correction: Diversified polyoxovanadate derivatives obtained by copper(i)-catalysed azide-alkyne cycloaddition...

Cycloadditions are one of the most valuable and effective synthesis routes to form cyclic compounds. These are concerted pericyclic reactions between two unsaturated compounds resulting in a cyclic product with two new σ bonds formed at the expense of π bonds. The [4 + 2] cycloaddition, known as the Diels–Alder reaction, is the most common. The other example is a [2 + 2] cycloaddition.

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. 

Direct alkylation of ammonia produces polyalkylated amines, along with a quaternary ammonium salt. To exclusively prepare primary amines, the azide synthesis method can be used.
Azide ions act as good nucleophiles and react with unhindered alkyl halides to form alkyl azides. Alkyl azides do not participate in further nucleophilic substitution reactions, thereby eliminating the chances of polyalkylated products. Alkyl azides are reduced by hydride-based reducing agents, like lithium aluminum...

Thermal cycloadditions are reactions where the source of activation energy needed to initiate the reaction is provided in the form of heat. A typical example of a thermally-allowed cycloaddition is the Diels–Alder reaction, which is a [4 + 2] cycloaddition. In contrast, a [2 + 2] cycloaddition is thermally forbidden.

Some cycloaddition reactions are activated by heat, while others are initiated by light. For example, a [2 + 2] cycloaddition between two ethylene molecules occurs only in the presence of light. It is photochemically allowed but thermally forbidden.

Introduction
Alkylation of terminal alkynes with primary alkyl halides in the presence of a strong base like sodium amide is one of the common methods for the synthesis of longer carbon-chain alkynes. For example, treatment of 1-propyne with sodium amide followed by reaction with ethyl bromide yields 2-pentyne.