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The octahedral splitting ${\Delta }_o$ separates the metal $t_{2g}$ and $e_g$ orbital sets. The Racah parameter $B$ characterizes interelectronic repulsion and hence the spacing of many-electron d-shell terms; it is not another name for ${\Delta }_o$. A Tanabe-Sugano diagram plots term excitation energies $E/B$ against ${\Delta }_o/B$, for specified values of the other repulsion-parameter ratios. Each ordinate is measured relative to whichever term is the ground state at that field strength. The original many-electron treatment diagonalizes the relevant d-shell energy matrices rather than identifying every absorption with a one-electron $t_{2g}\to e_g$ gap.^[ref]

A theoretical physicist who, with Yukito Tanabe, calculated electronic energy levels of transition-metal complex ions using crystal field theory. Their treatment considered different populations of the d shell in a cubic field. It supplied a framework for interpreting absorption bands and lines, connecting the local environment of an ion with the spectrum used to identify its electronic states.^[ref]

A theoretical physicist who coauthored the electronic-level calculations underlying Tanabe-Sugano diagrams with Satoru Sugano. The work applied crystal field theory to complex ions, balancing the effect of the surrounding ligands with interactions within the d shell. This made optical absorption a way to investigate electronic states in a particular chemical environment.^[ref]