free-ion term symbol

An electron configuration like d2 looks like a single tidy answer, but it actually hides several distinct energy states, because two electrons can arrange their orbital motions and their spins relative to each other in more than one way. A free-ion term symbol is a compact label for each of those states of an isolated ion — a shorthand that packages how the electrons' angular momenta add up before any ligands are around to disturb them.

The symbol is written as a letter with a superscript and (in full form) a subscript, like 3F. The capital letter encodes the total orbital angular momentum L using the code S, P, D, F, G for L = 0, 1, 2, 3, 4; it tells you how the electrons' orbital motions combine. The superscript on the left is the spin multiplicity 2S+1, where S is the total spin — it counts the unpaired-electron pattern (a superscript of 3 means a triplet, two unpaired electrons). The optional right subscript is J, the total angular momentum from coupling spin and orbital together. For a given configuration, Hund's rules pick out which term is the ground state: highest spin first, then highest L.

These terms matter because they are the true starting points for understanding a complex's spectrum. The faint d-d bands of a complex are transitions between states that descend from these free-ion terms once a ligand field splits them apart, and the analysis is done with Orgel and Tanabe-Sugano diagrams, which plot exactly how each free-ion term spreads out as the field grows. So before you can read a spectrum, you list the ion's terms, find the ground term by Hund's rules, and follow them into the field. The honest caveat: term symbols describe the free, gas-phase ion; the moment you put it in a complex the picture changes, which is the whole point of the field-splitting diagrams that come next.