Ligand Field Theory: Definition, Examples, Diagrams & Application


Ligand field theory, in chemistry, one of several theories that describe the electronic structure of coordination or complex compounds, notably transition metal complexes, which consist of a central metal atom surrounded by a group of electron-rich atoms or molecules called ligands. The ligand field theory deals with the origins and consequences of metal– ligand interactions as a means of elucidating the magnetic, optical, and chemical properties of these compounds.

Attributed mainly to the works of the U.S. physicist J.H. Van Vleck, the ligand field theory evolved from the earlier crystal field theory, developed for crystalline solids by the U.S. physicist Hans Albrecht Bethe. Bethe’s theory considers the metal–ligand linkage as a purely ionic bond; i.e., the bond between two particles of opposite electrical charges.

It further assumes that the electronic structure of the metal atom is altered by the electrical field generated by the surrounding negative charges (the ligand field). In particular, the effects of the ligand field on the five d orbitals of an inner electron shell of the central atom are considered. (The d orbitals are regions within an electron shell with certain preferred orientations in space; in transition metals these orbitals are only partly occupied by electrons.)

In the isolated metal atom, the d orbitals are of the same energy state and have equal probabilities of being occupied by electrons. In the presence of the ligand field these orbitals may be split into two or more groups that differ slightly in energy; the manner and the extent of orbital splitting depend on the geometric arrangement of the ligands with respect to the orbitals and on the strength of the ligand field.

What You Need To Know About Ligand Field Theory


Coordination complexes are often colored and display unique magnetic properties, indicating that the electronic structure of these compounds differs from that of free metal atoms or ions. LFT was developed as an extension of crystal field theory (CFT) to better account for these properties.

Main Assumptions

  • LFT acknowledges that ligands are not just point charges but possess distinct molecular orbitals that interact with the metal’s d orbitals.
  • The d orbitals of the metal ion are affected by the ligand’s electron density and geometry.

Splitting of d Orbitals

In a free metal atom, the five d orbitals (dxy, dxz, dyz, dx²-y², dz²) are degenerate, meaning they have the same energy. When ligands approach the metal ion, electrostatic interactions cause the d orbitals to split into two energy levels: a set of lower energy orbitals and a set of higher energy orbitals.

  • Octahedral Complexes: In octahedral complexes, where six ligands surround the metal, the d orbitals split into a lower energy set of three (t2g) and a higher energy set of two (eg) orbitals due to the ligand’s repulsion along the axes and attraction along the axes.
  • Tetrahedral Complexes: In tetrahedral complexes, where four ligands surround the metal, the splitting is different. The eg orbitals have lower energy than the t2g orbitals due to the different geometry.

Crystal Field vs. Ligand Field Theory

  • Crystal Field Theory (CFT) considers only the electrostatic interactions between ligands and metal ions, leading to a qualitative understanding of color and magnetism.
  • Ligand Field Theory (LFT) expands on CFT by considering the molecular orbitals of the ligands, providing a more accurate description of complex properties like magnetic behavior and spectral features.

Spectrochemical Series

LFT explains the ordering of ligands based on their ability to cause higher or lower splitting of the d orbitals. This ordering is known as the spectrochemical series. Ligands that cause greater splitting are called strong-field ligands (e.g., CN-, CO), while those causing less splitting are called weak-field ligands (e.g., Cl-, H2O).

Color and Spectra

The color of coordination complexes arises from the absorption of light corresponding to energy differences between the split d orbitals. Strong-field ligands cause larger energy gaps and absorption in the visible region, leading to intense coloration.

Magnetic Properties

LFT explains magnetic behavior by considering the distribution of electrons in the split d orbitals. Unpaired electrons in the lower-energy set (t2g) give rise to paramagnetism, while paired electrons in the eg set result in diamagnetism.

Limitations and Extensions

While LFT improves upon CFT by including ligand molecular orbital effects, it still simplifies certain aspects of bonding and ignores more advanced concepts like covalency and electron correlation. More advanced models like Molecular Orbital Theory (MO) and Density Functional Theory (DFT) provide a more comprehensive understanding.

Ligand Field Theory: Key Takeaways

  • Ligand field theory is a modification or an extension of crystal field theory and molecular obital theory. It describes bonding in transition metal complexes and how the orbitals arrange to a more energetically favored geometry based on a ligands electron donating.
  • Ligand field theory represents an application of molecular orbital theory to transition metal complexes. A transition metal ion has nine valence atomic orbitals-consisting of five nd, one (n+1)s, and three (n+1)p orbitals.
  • In Ligand field theory, the various d orbitals are affected differently when surrounded by a field of neighboring ligands and are raised or lowered in energy based on the strength of their interaction with the ligands.
  • The Ligand Field Theory analysis is highly dependent on the geometry of the complex, but most explanations begin by describing octahedral complexes, where six ligands coordinate to the metal.
  • The ligand field theory was developed by John Hasbrouck Van Vleck and Hans Albrecht Bethe.
  • Ligand field theory describes both electrostatic interactions and covalent bonding between metal ions and ligands.
  • Ligand field theory is more realistic than crystal field theory. It delivers insights into the process of chemical bonding in transition metal complexes.