Diatomic boron (\(B_2\)) is a molecule whose magnetic behavior has puzzled chemists because it does not follow the straightforward rules taught in introductory chemistry. \(B_2\) is known to be attracted to a magnetic field, a property called paramagnetism. Simple bonding theories fail to predict this experimental fact. To understand why \(B_2\) exhibits this unusual property, it is necessary to employ the more sophisticated framework of Molecular Orbital Theory (MOT). MOT reveals a specific arrangement of electrons that explains the molecule’s magnetic character.
Defining Paramagnetism and Diamagnetism
The magnetic behavior of a substance is determined by how its electrons are arranged within their orbitals. Paramagnetism is the property of being weakly attracted to an externally applied magnetic field. This attraction occurs only when a molecule or atom contains one or more unpaired electrons, which occupy an orbital alone. The spin of each unpaired electron creates a tiny magnetic moment that aligns with the external field, resulting in a net attractive force.
Diamagnetism, in contrast, is the property of being slightly repelled by a magnetic field. This repulsion is noticeable when a substance has all of its electrons paired. When two electrons occupy the same orbital, they must have opposite spins (spin-pairing), which cancels out their individual magnetic moments. A purely diamagnetic substance thus has no intrinsic magnetic moment.
Why Simple Bonding Models Fail
Traditional methods like Lewis structures and Valence Bond Theory rely on electron pairing to form bonds. Boron has three valence electrons, giving the \(B_2\) molecule a total of six valence electrons. A Lewis structure for \(B_2\) would typically predict a double bond between the two boron atoms, with all six valence electrons forming three pairs.
This paired arrangement would lead to the prediction that \(B_2\) should be diamagnetic. Valence Bond Theory also struggles to account for the magnetic properties without complex modifications. Since experimental measurements show that \(B_2\) is paramagnetic, these simple models demonstrate a clear limitation. Their inability to reconcile the observed paramagnetism necessitates the use of a more comprehensive theory, as a localized view of electrons is insufficient.
Understanding Molecular Orbital Theory
Molecular Orbital (MO) Theory describes bonding where electrons are delocalized over the entire molecule, not confined to bonds between two atoms. When atomic orbitals combine, they form new molecular orbitals, which are either bonding (lower energy) or antibonding (higher energy). An equal number of atomic orbitals combine to form an equal number of molecular orbitals. These molecular orbitals have distinct shapes and energy levels, which are filled by the molecule’s electrons using the same rules as atomic orbitals.
The Role of S-P Mixing
A phenomenon known as s-p mixing is crucial for understanding the electronic structure of \(B_2\) and other light diatomic molecules. S-p mixing occurs when the \(2s\) and \(2p\) atomic orbitals are close enough in energy to interact significantly. This interaction changes the normal energy order of the molecular orbitals by pushing the \(\sigma_{2s}\) and \(\sigma_{2p}\) orbitals further apart.
The most important consequence of s-p mixing for \(B_2\) is the reversal in the energy order of the \(2p\)-derived molecular orbitals. In heavier diatomic molecules, the \(\sigma_{2p}\) orbital is lower in energy than the \(\pi_{2p}\) orbitals. For \(B_2\), however, the strong s-p mixing pushes the \(\sigma_{2p}\) orbital above the two \(\pi_{2p}\) orbitals. Consequently, the two \(\pi_{2p}\) orbitals become the lowest-energy molecular orbitals derived from the \(2p\) atomic orbitals. This orbital reordering is the theoretical reason for \(B_2\)‘s observed magnetic properties.
Applying the Molecular Orbital Diagram to Boron
The \(B_2\) molecule possesses a total of ten electrons, but we focus on the six valence electrons (three from each boron atom). The four core electrons fill the \(\sigma_{1s}\) and \(\sigma_{1s}^\) molecular orbitals, which do not contribute to bonding or magnetic properties. The six valence electrons are placed into the molecular orbitals derived from the \(2s\) and \(2p\) atomic orbitals.
The first two valence electrons fill the lowest energy \(\sigma_{2s}\) bonding orbital, and the next two fill the \(\sigma_{2s}^\) antibonding orbital. The remaining two valence electrons must be placed into the molecular orbitals derived from the \(2p\) atomic orbitals. Due to the s-p mixing, the next available orbitals are the two degenerate \(\pi_{2p}\) bonding orbitals, which are lower in energy than the \(\sigma_{2p}\) orbital.
Following Hund’s rule, electrons occupy degenerate orbitals singly before pairing up. Therefore, the fifth and sixth valence electrons enter the two separate \(\pi_{2p}\) orbitals, each with parallel spin. This configuration, written as \((\pi_{2p})^1 (\pi_{2p})^1\), results in two unpaired electrons. The presence of these two unpaired electrons is the definitive molecular orbital explanation for why \(B_2\) is paramagnetic, as they create a net magnetic moment attracted to an external magnetic field.