Describe the bonding in the \(\mathrm{O}_{3}\) molecule and the \(\mathrm{NO}_{2}^{-}\) ion using the localized electron model. How would the molecular orbital model describe the \(\pi\) bonding in these two species?

In the localized electron model, the bonding in O₃ consists of single bonds between the central oxygen atom and each of the peripheral oxygen atoms, as well as resonance that leads to a 1.5 bond nature. Similarly, in NO₂⁻, the bonding involves single bonds between the nitrogen atom and each oxygen atom as well as resonance that results in a 1.5 bond nature. In both cases, the π bonding is described using resonance structures. In contrast, the molecular orbital model considers bonding on a molecular level, treating electrons as they occupy delocalized molecular orbitals that extend over the entire molecule. In both O₃ and NO₂⁻, the π orbitals combine to form a continuous set of molecular orbitals distributed over the whole molecule, resulting in a delocalized distribution of electron density in the π system across all bonds.