Chemists have developed models to explain how electrons are arranged in metal complexes and how they interact with surrounding ligands. Crystal Field Theory (CFT) provides a useful explanation of how d orbitals split into different energy levels when ligands approach a metal ion. This helps explain the color and magnetic properties of many metal complexes. ^[1-4]

However, CFT has some limitations. It treats the metal-ligand bond as purely ionic and does not account for any electron sharing between the metal and the ligands. In reality, many metal-ligand bonds have covalent character. To understand this better, we need a more advanced model.

This is where Ligand Field Theory (LFT) comes in. LFT builds upon both CFT and Molecular Orbital Theory to provide a deeper understanding of bonding in transition metal complexes. It explains not only why complexes have certain colors or magnetic properties but also how ligands affect the stability and reactivity of these compounds.

Core Concepts of Ligand Field Theory

1. Metal-Ligand Bonding as Orbital Interactions

In a transition metal complex, the central metal ion is surrounded by ligands – molecules or ions that donate a pair of electrons. These electrons, which typically come from lone pairs, interact with the orbitals of the metal atom. To describe this interaction properly, LFT considers not only the d orbitals of the metal but also its s and p orbitals. Together, these orbitals participate in bonding with the ligands.  ^[1-4]

The key idea is orbital overlap. For bonding to occur, the ligand’s orbitals (containing lone pairs) must overlap with the metal’s empty or partially filled orbitals. If the overlapping orbitals are aligned along the same axis (e.g., p_x with p_x), the bond formed is called a sigma (σ) bond. If the overlap is lateral or involves orbitals that do not directly face each other, such as d_xy orbitals with ligand orbitals, the bond is referred to as a pi (π) bond. The strength and type of bonding depend on the degree of orbital overlap and the symmetry of the complex.

b. Molecular Orbital Approach

Instead of merely splitting the d orbitals into two sets (as in CFT), LFT constructs a molecular orbital (MO) diagram for the entire complex. This diagram shows how the atomic orbitals of the metal and ligands combine to form new molecular orbitals – some lower in energy (bonding), some higher (antibonding), and some unchanged (non-bonding).  ^[1-4]

In an octahedral complex (where six ligands surround the metal), the symmetry of the system results in two main sets of metal d orbitals: t_2g and e_g. The t_2g orbitals (d_xy, d_yz, d_xz) do not point directly at the ligands and, therefore, interact weakly. The e_g orbitals (d_z² and d_x²_{– y}²), however, point directly at the ligands and interact strongly. This difference in interaction results in an energy gap, which helps explain various properties of the complex, such as its color and magnetic behavior.

In some cases, ligands can also participate in π bonding – either by donating electrons through their filled π orbitals or by π backbonding, where the metal donates electron density into the ligand’s empty π* orbitals. These interactions can further influence the energy levels of the molecular orbitals.

Ligand Field Splitting

When ligands approach a transition metal ion and form a complex, the five d orbitals of the metal ion no longer remain degenerate (equal in energy). Instead, they split into two sets with different energies. This happens because the ligands create an electric field that affects each d orbital differently, depending on its spatial orientation. The energy difference between these two sets is called the ligand field splitting energy, usually denoted by Δ. ^[1-4]

In an octahedral complex, the d orbitals split into:

• t_2g orbitals (d_xy, d_yz, d_xz) – lower in energy
• e_g orbitals (d_z² and d_x²_{– y}²) – higher in energy

In a tetrahedral complex, the d orbitals split into:

• t₂ orbitals (d_xy, d_yz, d_xz) – lower in energy
• e orbitals (d_z² and d_x²_{– y}²) – higher in energy

The energy gap between them is denoted Δ_oct (for octahedral geometry) and Δ_tet (for tetrahedral geometry). This splitting strongly influences how electrons are arranged in the d orbitals, affecting the color, magnetism, and stability of the complex.

Applications of Ligand Field Theory  ^[1-4]

• Explaining Colors: Explains the colors of metal complexes based on d–d electron transitions induced by visible light
• UV-Visible Spectroscopy: Interprets UV-Vis spectra by linking absorption peaks to the energy splitting of d orbitals
• Catalyst Design: Chemists use LFT to design metal-based catalysts with ligands that influence reactivity and stability.
• Biological Molecules: Provides insight into how metal ions in biomolecules like hemoglobin and vitamin B₁₂ function
• Magnetic Properties: Predicts the magnetic behavior of complexes by showing how electrons fill the split d orbitals.