**Explanation:**

The E2 (elimination 2) reaction is a type of elimination reaction in organic chemistry. In an E2 reaction, a leaving group (often a halogen) is eliminated from a molecule along with a proton from a neighboring carbon atom to form a double bond. E2 reactions typically occur in one step and follow second-order kinetics. The rate of the reaction is proportional to the concentration of both the substrate and the base.

Let's analyze each statement to see which one does not fit the criteria of E2 reactions:

a) **Follow second order kinetics:**
This statement is true for E2 reactions. The rate of the reaction depends on the concentrations of both the substrate and the base, making it a second-order reaction.

b) **Are accompanied by rearrangement:**
This statement is not true for E2 reactions. E2 reactions do not involve any rearrangement of atoms within the molecule. The reaction simply involves the elimination of a leaving group and a proton to form a double bond.

c) **Show a large deuterium isotope effect:**
This statement is true for E2 reactions. E2 reactions often exhibit a large deuterium isotope effect. This means that when a deuterium (D) is substituted for a hydrogen (H) in the molecule, the rate of the reaction is significantly affected. This is because the breaking of the C-H bond is the rate-determining step in the reaction, and the C-D bond is typically stronger than the C-H bond.

d) **Do not undergo hydrogen deuterium exchange:**
This statement is true for E2 reactions. E2 reactions do not undergo hydrogen deuterium exchange. This means that the hydrogen atoms involved in the reaction are not exchanged with deuterium atoms. Instead, the hydrogen atoms are simply eliminated along with the leaving group.

Therefore, the statement that does not fit the criteria of E2 reactions is option **'B' (Are accompanied by rearrangement)**. E2 reactions do not involve any rearrangement of atoms within the molecule.