The correct answer is option 'D' - Hydrogen bond.

Explanation:
Hydrogen bonding is an intermolecular interaction that occurs when a hydrogen atom is bonded to a highly electronegative atom (such as oxygen, nitrogen, or fluorine) and is attracted to another electronegative atom in a different molecule. It is a type of dipole-dipole interaction that is responsible for many important chemical and biological phenomena.

Hydrogen bonding is dependent on the inverse cube of the distance between the molecules involved. This means that as the distance between the molecules decreases, the strength of the hydrogen bond increases. The inverse cube relationship is a result of the electrostatic nature of the hydrogen bond.

Here is a detailed explanation of why hydrogen bonding is dependent on the inverse cube of the distance:

1. Definition of Hydrogen Bonding:
A hydrogen bond is a strong dipole-dipole interaction that occurs between a hydrogen atom and an electronegative atom, such as oxygen, nitrogen, or fluorine. The hydrogen atom is covalently bonded to one molecule but is attracted to the electronegative atom of another molecule.

2. Electrostatic Nature of Hydrogen Bonding:
The hydrogen bond is primarily an electrostatic interaction between the positively charged hydrogen atom and the negatively charged electronegative atom. This electrostatic interaction is due to the difference in electronegativity between the hydrogen and electronegative atoms.

3. Inverse Cube Relationship:
The strength of an electrostatic interaction is inversely proportional to the cube of the distance between the charged particles. This means that as the distance between the hydrogen and electronegative atoms decreases, the strength of the hydrogen bond increases.

4. Role of Interatomic Distance:
The interatomic distance between the hydrogen and electronegative atoms determines the strength of the hydrogen bond. As the distance decreases, the attractive forces between the atoms become stronger, leading to a stronger hydrogen bond.

5. Importance of Inverse Cube Relationship:
The inverse cube relationship is important because it allows the strength of the hydrogen bond to be determined by the distance between the hydrogen and electronegative atoms. This relationship helps explain why hydrogen bonds are generally weaker than covalent or ionic bonds but stronger than other intermolecular forces such as London dispersion forces or dipole-dipole interactions.

In conclusion, the intermolecular interaction that is dependent on the inverse cube of the distance between the molecules is the hydrogen bond. This type of interaction plays a crucial role in many biological and chemical processes, including protein folding, DNA structure, and the properties of water.