The Diels-Alder reaction is classified as a:

A. polar reaction
B. radical reaction
C. substitution reaction
D. pericyclic reaction
E. rearrangement reaction

The Diels-Alder reaction is classified as a D. pericyclic reaction.

In the Diels-Alder reaction, a conjugated diene (a molecule with two double bonds) reacts with a dienophile (a molecule with a double bond) to form a cyclic compound. It is a concerted reaction, meaning that it occurs in a single step without any intermediates. The reaction proceeds through a cyclic transition state and follows the Woodward-Hoffmann rules, which describe the stereochemical outcomes of pericyclic reactions.

To determine the classification of the Diels-Alder reaction, we need to understand the reaction mechanism and properties involved. Here's how you can arrive at the answer by considering the key features of the Diels-Alder reaction.

The Diels-Alder reaction is a chemical reaction between a diene (a molecule containing two double bonds) and a dienophile (a molecule containing a double bond). The reaction proceeds through a concerted mechanism, which means all the bond-making and bond-breaking steps occur simultaneously.

One important characteristic of the Diels-Alder reaction is the formation of a new ring system. By combining the diene and dienophile, a cyclic compound, known as the Diels-Alder adduct, is formed. This ring-forming process is achieved by the participation of π electrons from both the diene and dienophile.

Now, let's consider the options provided:

A. Polar reaction: The Diels-Alder reaction is not classified as a polar reaction because it does not involve significant changes in electron density or charges on atoms during the reaction.

B. Radical reaction: The Diels-Alder reaction does not rely on a chain-initiating step involving radicals nor does it proceed via radical intermediates. Therefore, it is not categorized as a radical reaction.

C. Substitution reaction: The Diels-Alder reaction does not involve the displacement of one atom or group by another. Therefore, it is not a substitution reaction.

D. Pericyclic reaction: The Diels-Alder reaction is indeed classified as a pericyclic reaction. Pericyclic reactions are characterized by the involvement of cyclic transition states or intermediates. The formation of a cyclic product in the Diels-Alder reaction aligns with this characteristic, making it a pericyclic reaction.

E. Rearrangement reaction: Rearrangement reactions typically involve the movement of atoms or groups within a molecule to yield isomers. Since the Diels-Alder reaction does not involve rearrangement of atoms or groups, it is not categorized as a rearrangement reaction.

Therefore, the correct answer is D. pericyclic reaction.