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

Assumptions

• 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

Bonding

• 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