Valence Bond (VB) theory and Molecular Orbital (MO) theory offer different insights into molecular stability and bonding. VB theory can explain the stability of molecules like F2, which Hartree-Fock calculations fail to stabilize. However, VB theory struggles with complex systems like metallic or semi-metallic compounds, requiring numerous resonance structures that can complicate calculations. While VB calculations are generally more accurate than Hartree-Fock, they demand more computational resources. MO theory is essential for understanding phenomena such as back-bonding in carbonyl metal complexes and the mechanisms behind cycloadditions, where the interaction of molecular orbitals plays a crucial role. The discussion also highlights that the Woodward-Hoffmann rules can be interpreted through VB theory, demonstrating the versatility of both theories in explaining various chemical behaviors.