Tanabe-Sugano diagram

An Orgel diagram is a fine qualitative guide, but the moment you want to pull real numbers out of a spectrum — the actual size of delta-o and the strength of electron-electron repulsion — you need a more careful chart drawn to a clever scale. A Tanabe-Sugano diagram (named for the two Japanese physicists who computed them in the 1950s) is that quantitative tool: a plot that lets you read electronic structure straight off a measured spectrum.

It is drawn cleverly to make it usable for measurement. The ground state is laid flat along the bottom as a horizontal baseline, and every excited state's energy is plotted above it. Both axes are scaled by the Racah parameter B (a measure of electron-electron repulsion), so the horizontal axis reads delta-o/B and the vertical axis reads energy/B. This dimensionless scaling means one diagram works for any complex of a given dn configuration. Crucially, it includes states of all spin multiplicities, so it shows the vertical line where the ground state changes spin: to the left of that line the complex is high-spin, to the right it is low-spin, and the abrupt kinks in the lines there are the spin crossover.

Using one is a real piece of detective work. You measure the d-d band energies, take ratios of them (to cancel B), slide along the horizontal axis until the predicted ratios match what you measured, and read off delta-o/B at that point; then the absolute band energies give you B itself. Out comes both the ligand-field splitting and a measure of how covalent the bonding is (a reduced B signals the nephelauxetic effect). The honest caveat: it is a model fit, sensitive to which bands you assign and to overlapping or hidden bands, and the simplest diagrams ignore spin-orbit coupling — for the heavier metals and lanthanides that approximation gets shaky.