What modification to the molecular orbital model was made from the experimental evidence that \(\mathrm{B}_{2}\) is paramagnetic?

Molecular orbital theory is a model that describes the behavior of electrons in molecules by combining the atomic orbitals of the atoms involved in the molecule. In the molecular orbital model, electrons are considered to be delocalized and distributed over all the atomic nuclei in a molecule. These delocalized molecular orbitals can either be bonding (lower in energy) or antibonding (higher in energy) in nature.

To understand the molecular orbital model for B2, we first need to know the electron configuration of a boron atom. The electron configuration for boron (Z = 5) is: 1s² 2s² 2p¹. In the case of B₂, it will have a total of 10 valence electrons (5 from each boron atom). The molecular orbitals of B₂ are formed by the linear combination of the atomic orbitals (2s and 2p) of the two boron atoms. The molecular orbitals formed are: 1. σ(2s) - bonding orbital formed by the in-phase combination of the 2s orbitals 2. σ*(2s) - antibonding orbital formed by the out-of-phase combination of the 2s orbitals 3. σ(2p) - bonding orbital formed by the in-phase combination of the 2p_z orbitals 4. π(2p) - bonding orbitals formed by the in-phase combination of the 2p_x and 2p_y orbitals 5. σ*(2p) - antibonding orbital formed by the out-of-phase combination of the 2p_z orbitals 6. π*(2p) - antibonding orbitals formed by the out-of-phase combination of the 2p_x and 2p_y orbitals

Now, we will fill in the 10 valence electrons into the molecular orbitals in the order of their increasing energy levels, following the aufbau principle, Hund's rule, and the Pauli exclusion principle. The resulting electron configuration for B₂ would be σ(2s)² σ*(2s)² σ(2p)² π(2p)⁴.

As per the electron configuration of B₂, there are 2 unpaired electrons in the π(2p) orbitals. These unpaired electrons are responsible for the paramagnetic properties of B₂.

Initially, the molecular orbital model predicted that σ(2p) would have higher energy than π(2p) and would be filled before the π(2p) orbitals. This would have resulted in all the electrons being paired up, and B₂ would be diamagnetic. However, the experimental evidence that B₂ is paramagnetic led to a modification in the molecular orbital model. The energies of the σ(2p) and π(2p) orbitals were swapped, such that π(2p) has lower energy and gets filled before σ(2p). This change in the model accounts for the unpaired electrons in the π(2p) orbitals, explaining the paramagnetic behavior of B₂.