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Ligand/Crystal Field Theory

  • LFT can be summed up as the effect that the “field” of ligand has on the orbital energy of the coordinated metal ion


  • Ligands are negative point charges
  • Metal-Ligand bonding is entirely ionic

The concept

  • The best way to think about LFT is that ligands coordinate in specific configurations that will interact with the orbitals in specific ways
    • The orbitals in which the ligand overlaps are distorted, causing them to take on a higher energy and the non interacting ones relax, causing them to lower
  • An implication of this is that the splitting of the d-orbitals is entirely dependent on the geometry of the complex, with each geometry splitting the orbitals in a different manner


The maths

  • The energy distance between the split orbitals is \(\Delta_O\) (change in ocrtahedral)
    • \(\Delta_O=10 Dq\)


  • This can be split into stabilisation and destabilisation energy
    • \(−4\Delta_O\) and \(+6\Delta_O\)
    • In the below example, there is one electron occupying the d-orbitals, so there is a total of \(0.4\Delta_O\) of crystal field stabilisation energy (CFSE)


  • As we increase the occupation of the stabilising orbitals, the CFSE increases
    • CFSE\(=3(0.4\Delta_O )=1.2\Delta_O\)


Low Spin and High Spin

  • Since the splitting of d-orbitals can be quite small, the energy required to pair electrons can be overcome, causing both high and low spin modes
  • High spin is paramagnetic and low spin is diamagnetic
    • High spin CFSE\(=3(0.4\Delta_O )−3(0.6\Delta_O )=0\Delta_O\)
    • Low spin CFSE\(=5(0.4\Delta_O )=2\Delta_O\)
High Low
  • Since high spin happens when the d orbitals aren’t split too far, it’s a property of weak field ligands


  • Ligands-metal bonds aren’t entirely ionic and need to be though of in terms of \(\sigma\), \(\pi\) and \(\Delta\) bonds
  • The strength of the ligand field and the resulting energy associated with \(\Delta_O\) is completely based on the ligand and it’s relative field strenght
  • The general rule :
    • \(\ce{I− < S^{2}− < SCN− < Cl− < NO3− < N3− < F− < OH− < C2O4^{2−} < H2O < … < CN− < CO}\)
  • The magnitude of the ligand’s charge is only half the story. We also need to consider the types of bond formed


Spectrochemical series

  • The spectrochemical series directly links the strength of the ligand field and the resulting \(\Delta_O\) to the colour of the light produced through HOMO-LUMO excitation


  • Going down a periodic group also results in a larger \(\Delta\)

Limitations of CFT

  • CFT is very powerful, however it only considers species to be of point charges and calculates a resulting dipole
  • It neglects to consider the shape of orbitals and thus can’t explain the properties of all the ligands