Electronic spectra of complexes and Tanabe-Sugano diagrams
A complex often shows more than one absorption band, which a single splitting energy cannot explain. Labelling the electronic states of the whole ion, not the orbitals, gives a diagram that accounts for every band.
What a learner can do afterwards
- Explains why several bands appear for one configuration and what each transition connects
- Reads a Tanabe-Sugano diagram to extract the splitting energy from band positions
- Distinguishes a weak d to d band from an intense charge transfer band and gives the selection-rule reason
- Explains why manganate(VII) is intensely coloured although the metal has no d electrons
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Ligand field theory gives one gap, Δ, between the t2g and eg sets. A single gap predicts a single band, yet real complexes show two or three. The fix is to label states of the whole d shell instead of single orbitals: electron repulsion splits each configuration into several states with different energies. Every observed band is a jump between two of these many electron states.
Spin allowed d to d transitions keep total spin S unchanged (ΔS = 0). In centrosymmetric complexes they give the main weak bands; spin forbidden ones are much weaker or missing. S includes spin coupling. A Tanabe-Sugano diagram plots E/B against Δ/B, where B measures electron repulsion. Match band-energy ratios to read Δ/B. Divide a measured band energy by its E/B to find B, then multiply Δ/B by B to get the gap.
In a centrosymmetric complex, d to d transitions are Laporte forbidden and weak. Charge transfer moves an electron between ligand and metal and is often allowed and intense. Intense ligand-centred bands can also occur, so intensity alone cannot prove charge transfer. Manganate(VII) is d0 and purple from oxygen to metal charge transfer. Octahedral nickel(II) is d8: its three main weak bands are spin allowed transitions from the ground state.
State labels such as A and T describe the symmetry of the whole ion's electronic state, not single orbitals. Centrosymmetric means having a centre of symmetry. The d orbitals have the same parity; the Laporte rule forbids d to d transitions between states of the same parity in such complexes. Count bands and compare their positions and intensities with the state diagram. Intensity alone cannot distinguish charge transfer from ligand-centred absorption.
Count the bands, compare their heights, and use the diagram to identify jumps between whole ion states.
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One rewritten reading was written for this dataset; three readings written for this project. Videos by Khan Academy.
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