The magnetic behavior of a molecule provides insight into its fundamental electronic structure. Predicting a molecule’s magnetic nature requires accurately mapping the location and spin of every electron within the bonded structure. This analysis is particularly important for diatomic molecules. This article applies Molecular Orbital Theory (MOT) to determine whether the lithium dimer, \(\text{Li}_2\), is paramagnetic or diamagnetic.
Defining Molecular Magnetism
The magnetic behavior of any substance is determined by the spin of its electrons. When electrons occupy an orbital, they possess spin, which generates a tiny magnetic field.
Paramagnetism is the magnetic state where molecules are weakly attracted to an external magnetic field. This attraction occurs only when the molecule contains one or more unpaired electrons whose magnetic moments can align with the external field.
Diamagnetism, by contrast, is the property of being weakly repelled by an external magnetic field. This is characteristic of molecules where all electrons are paired, meaning every electron shares an orbital with another electron of opposite spin. In a fully occupied orbital, the opposing spins cancel out their magnetic moments, resulting in a net magnetic moment of zero. The distinction between paramagnetic and diamagnetic rests solely on whether the molecule possesses any unpaired electrons.
The Tool of Molecular Orbital Theory
Determining the pairing status of electrons in a molecule requires a theory more advanced than traditional concepts like Lewis structures. Simple models that depict bonds as shared electron pairs localized between two atoms fail to explain the magnetic behavior of several common molecules, such as oxygen gas. Molecular Orbital Theory (MOT) addresses this limitation by treating electrons as delocalized across the entire molecule, occupying molecular orbitals (MOs) rather than just atomic ones.
The process begins by mathematically combining the atomic orbitals (AOs) from the individual atoms to form an equal number of new MOs. These MOs are divided into bonding orbitals, which are lower in energy and stabilize the bond, and antibonding orbitals, which are higher in energy and destabilize the bond. Bonding orbitals are denoted by \(\sigma\) or \(\pi\), while antibonding orbitals are indicated by an asterisk (e.g., \(\sigma^\) or \(\pi^\)).
Once the MOs are established, electrons are systematically filled into them following established rules:
- Electrons first populate the lowest energy MOs, adhering to the Aufbau principle.
- The Pauli Exclusion Principle dictates that each MO can hold a maximum of two electrons with opposing spins.
- Hund’s Rule specifies that if multiple MOs have the same energy, electrons will occupy them singly before any pairing occurs.
Applying MOT to the Lithium Dimer (\(\text{Li}_2\))
The lithium dimer, \(\text{Li}_2\), is a homonuclear diatomic molecule composed of two identical lithium atoms. A single lithium atom (Li) has an electronic configuration of \(1s^2 2s^1\). Consequently, the \(\text{Li}_2\) molecule contains a total of six electrons.
The molecular orbitals are formed by combining the corresponding atomic orbitals. The two \(1s\) orbitals combine to form the \(\sigma_{1s}\) bonding orbital and the \(\sigma_{1s}^\) antibonding orbital. Similarly, the two \(2s\) orbitals combine to yield the \(\sigma_{2s}\) bonding orbital and the \(\sigma_{2s}^\) antibonding orbital. The six electrons must now be placed into these four available MOs, starting from the lowest energy level.
The first two electrons enter the lowest energy \(\sigma_{1s}\) orbital, where they are paired. The next two electrons occupy the \(\sigma_{1s}^\) antibonding orbital, where they also become a paired set. The final two electrons are placed into the \(\sigma_{2s}\) bonding orbital, resulting in a third, paired set of electrons.
The resulting molecular orbital configuration for the lithium dimer is written as \((\sigma_{1s})^2 (\sigma_{1s}^)^2 (\sigma_{2s})^2\). This configuration confirms that all six electrons are contained within completely filled molecular orbitals. Since every electron in its structure is paired, the lithium dimer (\(\text{Li}_2\)) is diamagnetic.