TanabeSugano

Tanabe–Sugano diagrams are graphical tools used in inorganic and solid-state chemistry to analyze the electronic spectra of transition-metal ions in crystals. They were introduced by Y. Tanabe and S. Sugano in 1954 to describe how the energies of d-electron configurations change as the crystal-field splitting increases, taking into account electron–electron repulsion via Racah parameters.

The diagrams plot the energy of electronic states (in units of the Racah parameter B) as a function of the ratio Δ/B, where Δ represents the crystal-field splitting (often expressed as 10Dq in octahedral fields). They cover d^n configurations for n = 1–9 and are provided for common coordination geometries, notably octahedral (Oh) and tetrahedral (Td). Each curve corresponds to a term arising from a given electron configuration; as Δ/B increases, the ordering of states can change, revealing which transitions are likely as ligand strength varies.

Applications of Tanabe–Sugano diagrams include helping to interpret UV–visible spectra of transition-metal complexes. By matching observed absorption bands to positions on the diagrams, one can estimate the Racah parameter B and the crystal-field splitting Δ (and thus 10Dq), aiding in the assignment of electronic transitions and the assessment of spin-allowed versus spin-forbidden processes.

Limitations and notes: the diagrams are based on a free-ion–plus-crystal-field framework and assume relatively simple electrostatic interactions. In real systems, covalency, spin–orbit coupling, and vibronic effects can modify energies and intensities. Despite these caveats, Tanabe–Sugano diagrams remain a standard heuristic for interpreting the electronic structure of transition-metal ions in crystals.