Why does the molecular orbital model do a better job in explaining the bonding in \(\mathrm{NO}^{-}\) and \(\mathrm{NO}\) the hybrid orbital model?

Molecular orbital (MO) theory is a method for describing the electronic structure of molecules using quantum mechanics. In MO theory, atomic orbitals from all the atoms in a molecule are combined to form molecular orbitals, which are distributed over the entire molecule. On the other hand, hybrid orbital theory (or hybridization) is a simplified approach to understanding chemical bonding. In hybridization, atomic orbitals of an atom are mixed or "hybridized" to form new orbitals suitable for bonding in a molecule. The newly formed hybrid orbitals overlap with atomic orbitals of other atoms, forming sigma or pi bonds.

Molecular orbital model provides a more accurate description of electron distribution in a molecule. It also allows us to describe the bonding and antibonding orbitals and can explain delocalized electron systems like aromatic compounds. In molecular orbital model, electrons in bonding molecular orbitals are attracted to both nuclei involved in the bond, while electrons in antibonding molecular orbitals are mainly positioned in areas with less electron density and are not associated directly with any one atom. Furthermore, molecular orbital model allows us to understand the behavior of molecules with odd numbers of electrons, like \(\mathrm{NO}^{-}\) and \(\mathrm{NO}\), where an odd number of valence electrons could result in unpaired electrons.

In hybrid orbital model, atomic orbitals of an atom are mixed or "hybridized" to form new orbitals suitable for bonding in a molecule. This model is useful for understanding localized bonding, for example, in simpler molecules like methane or ethane. However, it fails to account for unpaired electrons and electron delocalization, which are crucial for understanding the bonding in molecules like \(\mathrm{NO}^{-}\) and \(\mathrm{NO}\).

The molecular orbital model is better suited for explaining the bonding in \(\mathrm{NO}^{-}\) and \(\mathrm{NO}\) as compared to the hybrid orbital model, because it can account for unpaired electrons and delocalization of electrons in molecular orbitals. This property allows the molecular orbital model to provide a more accurate description of the electron distribution and bonding in these molecules, whereas the hybrid orbital model falls short in these aspects.