Lecture 25: Ligand Field Stabilization

Read sections 20.4 and 20.5 from your textbook.

Ligand Field Stabilization

The average energy of the d orbitals in a complex is the same as the equivalent d orbitals in a spherical "field" of the same ligand. Treating metals and their ligands as point charges allows us to set up an energy order of the d orbitals. When electrons are added to orbitals lower than the average energy, the complex is stabilized. When electrons are added to orbitals above the average energy, the complex is destabilized.

Let's look at an octahedral complex.

The energy gap between the upper d orbitals and the lower ones is the ligand-field splitting parameter for the octahedral field. This quantity is sometimes called 10 Dq. The two high energy orbitals are: 0.6 x 10 Dq or 6 Dq above the average and the lower ones are -0.4 x 10 Dq or 4 Dq below average. If you know the value of 10 Dq from spectroscopic studies, it is possible to calculate the amount of stabilization or destabilization energy from adding electrons to the d orbitals.

There are other values associated with the stabilization/destabilization energy for different geometries.

Calculate the ligand field stabilization for [PdCl₄]^2- in a tetrahedral field and in a square planar filed. Which is better with regard to energy? Which is better with regard to steric factors?

The magnitude of the ligand field splitting parameter depends on the type of ligand (see the spectrochemical series in Lecture 24) and on the metal. The splitting increase as we go down a group in the transition elements and it increases with increasing oxidation number.

If the energy between sets of d orbitals is less than the pairing energy, or the energy required to put two electrons of opposite spins in the same orbital, then electrons can occupy the higher orbitals. The complex is high spin. In low spin complexes, the energy difference between the d orbitals is greater than the pairing energy.

There are 5 unpaired electrons in [Fe(H₂O)₆]⁺³ but only 1 in [Fe(CN)₆]^-3. What would you predict for [Fe(H₂O)₄]⁺³? What about [Os(H₂O)₆]⁺⁴?

Pi Bonding

Pi bonding between metal and ligands has a dramatic effect on the magnitude of the ligand field splitting parameter. There are two types of pi bonding between metals and ligands:

Pi donor ligands
- Ligands like I^- with available lone pairs of electrons
- The ligand orbitals that are below the d orbitals in energy
- Interaction of metal d orbitals and ligand orbitals increases (destabilizes) the energy of the metal orbitals
Pi acceptor ligands
- Ligands like CO with empty pi symmetry orbitals
- The ligand orbitals that are above the d orbitals in energy
- Interaction of metal d orbitals and ligand orbitals decreases (stabilizes) the energy of the metal orbitals

Unpaired electrons and the magnetic moment

Many transition metal complexes are paramagnetic because they have unpaired electrons in d orbitals. We can calculate the spin-only magnetic moment of a molecule when we know the number of unpaired electrons, n.

Using the crystal field splitting diagram and what you know about strong field/weak field ligands and the way the magnitude of the ligand field splitting parameter changes with the nature and oxidation state of a transition element, you should be able to determine how many unpaired electrons are in any transition metal complex.

For example, [Mn(H₂O)₆]²⁺:

Total electron count = -7 (Mn) - 12 (water ligands) + 2 (charge) = -17, 17 e^-
Oxidation state, +2 = Mn + (0), Mn = +2, Mn(II)
d electrons, +2 (oxidation state) - 7 (valence electrons) = -5, d⁵
Because Mn is a first row transition metal, relatively low oxidation state, with a weak field ligand, the complex will be high spin with 5 unpaired electrons.

The molar magnetic susceptibility of complexes is measured experimentally by several techniques including the Gouy balance, the Faraday balance, and a SQUID. There is also an NMR spectroscopy method, the Evan's method, to determine the molar magnetic susceptibility. Orbital angular momentum changes the molar magnetic susceptibility from what we would expect from the spin-only value but this is most pronounced for the heavier transition elements.

Trans Effect

A ligand can affect the bonding of the ligand trans to it in a square planar or octahedral metal complex because the same d orbital is involved in the interaction. A change in the bond distance is called the trans influence and a change in reactivity is called the trans effect.

Ligand ordering:

₂

₃

₂

₃

₂

₄

₃