Understanding the Paramagnetic Nature of Oxygen Molecule

The oxygen molecule ($\text{O}_2$) exhibits a unique property: it is paramagnetic. This means it is weakly attracted to a magnetic field. Explaining this behavior requires understanding the electronic structure and bonding within the molecule. Let's examine how different chemical bonding theories address this.

Limitations of Valence Bond Theory

Valence bond theory (VBT) describes covalent bonding as the overlap of atomic orbitals. According to simple VBT, the oxygen molecule is formed by sharing electrons between two oxygen atoms. Each oxygen atom has an electron configuration of $1s^2 2s^2 2p^4$. In forming a double bond, two pairs of electrons are shared, and the remaining electrons on each oxygen atom are paired as lone pairs. A Lewis structure and simple VBT picture for $\text{O}_2$ would show all electrons paired.

According to VBT, if all electrons are paired, the molecule should be diamagnetic (repelled by a magnetic field). However, experimental evidence clearly shows that the oxygen molecule is paramagnetic. Therefore, valence bond theory fails to accurately predict or explain the paramagnetic nature of $\text{O}_2$. Hybridisation, often used alongside VBT to explain geometry, also does not account for paramagnetism.

Explaining Paramagnetism with Molecular Orbital Theory

The paramagnetic nature of the oxygen molecule is successfully explained by Molecular orbital theory (MOT). Molecular orbital theory considers the molecule as a whole, where atomic orbitals combine to form new molecular orbitals that extend over the entire molecule. These molecular orbitals are of two types: bonding molecular orbitals (lower energy, favor bonding) and antibonding molecular orbitals (higher energy, oppose bonding).

Electrons from the atoms are filled into these molecular orbitals according to the Aufbau principle, Hund's rule of maximum multiplicity, and the Pauli exclusion principle. For diatomic molecules like oxygen ($\text{O}_2$), the relative energy levels of the molecular orbitals formed from $2s$ and $2p$ atomic orbitals are important.

For $\text{O}_2$, which has a total of 16 electrons (8 from each oxygen atom), the filling of molecular orbitals is as follows:

• Electrons from $1s$ orbitals form $\sigma_{1s}$ and $\sigma^*_{1s}$. (Usually not shown in MO diagrams for valence electrons).
• Electrons from $2s$ orbitals form $\sigma_{2s}$ and $\sigma^*_{2s}$.
• Electrons from $2p$ orbitals form $\sigma_{2p}$, $\pi_{2p}$ (two degenerate orbitals), $\pi^*_{2p}$ (two degenerate orbitals), and $\sigma^*_{2p}$.

For $\text{O}_2$, the energy order of molecular orbitals derived from $2p$ atomic orbitals is $\sigma_{2p} < \pi_{2p} < \pi^*_{2p} < \sigma^*_{2p}$.

Filling the 16 electrons (8 valence electrons from each O, total 16):

Configuration up to $1s$ orbitals: $(\sigma_{1s})^2 (\sigma^*_{1s})^2$ (4 electrons)

Configuration for $2s$ and $2p$ orbitals (12 electrons): $(\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p})^2 (\pi_{2p})^4 (\pi^*_{2p})^2$

Let's write the full Molecular orbital theory configuration:

$\sigma_{1s}^2 \sigma_{1s}^{*2} \sigma_{2s}^2 \sigma_{2s}^{*2} \sigma_{2p}^2 \pi_{2p}^4 \pi_{2p}^{*2}$

The last two electrons go into the degenerate $\pi^*_{2p}$ antibonding orbitals. According to Hund's rule, these two electrons will occupy the two separate $\pi^*_{2p}$ orbitals with parallel spins to minimize repulsion and maximize multiplicity. This results in two unpaired electrons in the $\pi^*_{2p}$ molecular orbitals.

Why Molecular Orbital Theory is Key

The presence of two unpaired electrons, as predicted by Molecular orbital theory, is the reason for the observed paramagnetism of the oxygen molecule. Molecules with unpaired electrons are paramagnetic. This successful prediction is a major triumph of Molecular orbital theory over simpler theories like Valence Bond Theory when it comes to explaining the magnetic properties of molecules. Neither Resonance nor Hybridisation theories directly address or predict magnetic properties based on unpaired electrons in this manner.

In summary, while Valence bond theory provides a useful picture for many molecules, it fails for $\text{O}_2$'s paramagnetism. Molecular orbital theory, by providing a more complete picture of electron distribution in molecular orbitals, correctly accounts for the unpaired electrons and hence the paramagnetic property of the oxygen molecule.