Ligand Field Theory Concepts

Ligand field theory is used to calculate the influence of local environment on the energy levels of transition-metal and rare-earth ions. In the ligand field theory, the ligand atoms are represented as point charges, and the electrostatic field of environment is calculated at the location of the ion of interest. The ligand field is treated by summing all the neighboring ions and calculating a multipole expansion of the electric potential at the location of the central ion using a known expansion in spherical harmonics. The calculation is simplified by letting the charge density of the ligands to have same symmetry as the coordination shells. This leads to a simplified expression for the potential.