Briefly describe the valence bond theory of covalent bond formation by taking an example of hydrogen.

(N/A) Valence bond theory $(VBT)$ was introduced by Heitler and London $(1927)$ and developed further by Pauling and others. $VBT$ is based on the knowledge of atomic orbitals, electronic configurations of elements, the overlap criteria of atomic orbitals, the hybridization of atomic orbitals, and the principles of variation and superposition.
Consider two hydrogen atoms $A$ and $B$ approaching each other, having nuclei $N_{A}$ and $N_{B}$, and electrons represented by $e_{A}$ and $e_{B}$. When the two atoms are at a large distance from each other, there is no interaction between them.
As these two atoms approach each other, new attractive and repulsive forces begin to operate.
- Attractive forces arise between:
$(i)$ Nucleus of one atom and its own electron: i.e., $N_{A}-e_{A}$ and $N_{B}-e_{B}$
$(ii)$ Nucleus of one atom and the electron of the other atom: i.e., $N_{A}-e_{B}$ and $N_{B}-e_{A}$
- Similarly, repulsive forces arise between:
$(i)$ Electrons of the two atoms: $e_{A}-e_{B}$
$(ii)$ Nuclei of the two atoms: $N_{A}-N_{B}$
Experimentally, it is found that the magnitude of the new attractive forces is greater than the new repulsive forces. As a result, the two atoms approach each other and the potential energy decreases. A stage is reached where the net force of attraction balances the force of repulsion, and the system attains minimum energy. At this stage, the two $H$ atoms are bonded together to form a stable molecule having a bond length of $74 \text{ pm}$.
Energy is released when the bond is formed between two hydrogen atoms, making the hydrogen molecule more stable than isolated hydrogen atoms.