Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: The potential energy curve for the ${\text{H}}_2$ molecule as a function of internuclear distance is

The formation of a chemical bond is one of the most elegant phenomena in nature. It is a delicate dance between attractive and repulsive forces, perfectly captured by the potential energy curve. Let's embark on a journey to understand how two isolated hydrogen atoms come together to form a stable ${\text{H}}_2$ molecule.

At this vast separation, they are completely oblivious to each other's existence. There are no electrostatic interactions—no attraction, no repulsion. Because there is no interaction, we define the potential energy of this system as zero. This is our starting point, the baseline of our energy landscape.

The positively charged nucleus of one atom starts to attract the negatively charged electron cloud of the other. Simultaneously, their nuclei repel each other, and their electrons repel each other.

However, at these relatively large distances, the attractive forces dominate. Because the system is moving under the influence of an attractive force, it releases energy, becoming more stable. This is why the potential energy curve dips below zero, becoming increasingly negative.

They continue to approach until they reach a magical distance called the bond length ($r_0$). At this exact point, the attractive forces perfectly balance the repulsive forces ($F_{\text{net}}=0$). The system has reached its absolute minimum potential energy ($-E_0$). This deep well in the energy curve represents the formation of a stable chemical bond. The depth of this well is the bond dissociation energy—the exact amount of energy you would need to pump back into the system to tear the atoms apart.

What happens if we try to force the atoms even closer than their equilibrium bond length ($r<r_0$)?

As the internuclear distance becomes very small, the electron clouds overlap excessively, and the two positively charged nuclei are forced into close proximity. The internuclear repulsion suddenly becomes overwhelmingly strong, completely overpowering any attractive forces.

To push the atoms this close requires a massive input of energy. Consequently, the potential energy curve shoots up drastically, crossing the zero line and heading towards positive infinity. The atoms strongly resist being squashed together.

Start near zero at large distances. 2. Dip to a minimum negative value at the bond length. 3. Rise steeply towards positive infinity at very short distances.

Looking at the given options, only the curve in option (c) perfectly illustrates this beautiful balance of forces, making it the correct representation of the ${\text{H}}_2$ molecule's potential energy.