Orgel and Tanabe–Sugano Diagrams: Interpreting d–d Spectra

What the diagrams show

A free ion's electronic states are described by term symbols. Placing that ion in a ligand field splits those terms, and how much they split depends on the field strength. Both diagram types plot term energies against field strength so that observed transitions can be matched to calculated ones.

Orgel diagrams

Simple, and limited on purpose. They cover only weak-field high-spin complexes, and show only terms of the same spin multiplicity as the ground state — which is all that is needed, since spin-forbidden transitions are too weak to matter in most spectra.

A useful economy is that one Orgel diagram serves several configurations, because of the hole formalism: a dⁿ configuration in an octahedral field behaves like a d¹⁰⁻ⁿ configuration in a tetrahedral field, and vice versa. That symmetry halves the number of diagrams needed.

Tanabe–Sugano diagrams

More general and more useful. Their distinguishing features are worth stating explicitly:

• The ground state is drawn along the horizontal axis, so the vertical distance to any excited term is the transition energy. No subtraction is needed.
• Energies are plotted in units of the Racah parameter B, making them applicable to any metal ion of that configuration.
• They include spin-forbidden terms, so weak bands can also be assigned.
• They show the high-spin to low-spin crossover as a vertical discontinuity, where the ground state changes.

The selection rules, and why bands are weak

Both rules are relaxed rather than absolute. Vibrations momentarily destroy the centre of symmetry, allowing Laporte-forbidden transitions to gain intensity — vibronic coupling. Spin–orbit coupling similarly mixes states of different multiplicity, giving spin-forbidden bands a little intensity.

Two consequences follow that are frequently examined. Tetrahedral complexes are more intensely coloured than octahedral ones, because a tetrahedron has no centre of symmetry so the Laporte rule does not apply. And charge transfer bands are far more intense than d–d bands, because they are not forbidden by either rule — which is why intensely coloured compounds usually owe their colour to charge transfer rather than to d–d transitions.

Extracting parameters from a spectrum

Given the observed transition energies, take their ratios — the ratios are independent of B. Find the position on the diagram where the calculated ratios match, read off the corresponding field strength in units of B, and then use one absolute energy to obtain B itself and the ligand field splitting.

The nephelauxetic effect is worth noting alongside: B in a complex is smaller than in the free ion, indicating that the d electrons are spread over a larger region because of covalency. The extent of reduction measures how covalent the bonding is, which is a genuinely useful piece of information.

Frequently asked questions

Why is the ground state drawn along the axis?

So that the vertical distance to any excited term is directly the transition energy. It removes a subtraction step and makes reading the diagram much faster.

Why are octahedral complexes usually pale?

Because d–d transitions are Laporte-forbidden in a centrosymmetric environment and gain intensity only through vibronic coupling. Tetrahedral complexes, lacking a centre of symmetry, are considerably more intense.

What does the Racah parameter measure?

Interelectronic repulsion between d electrons. Its reduction from the free-ion value in a complex measures covalency in the metal–ligand bonding.

Which diagram should I use?

Orgel for a straightforward weak-field high-spin complex where only spin-allowed bands are of interest. Tanabe–Sugano whenever the field may be strong, the spin state is in question, or spin-forbidden bands must be assigned.