Orgel diagram
/ OR-gel /
Once you accept that a free ion's terms split apart inside a ligand field, the natural next question is: in what pattern, and which way do the levels go as the field gets stronger? An Orgel diagram is a simple picture that answers this. It is a graph with the strength of the ligand field along the bottom axis and energy up the side, and on it you trace how each free-ion term fans out into a set of states as the field grows.
Reading one is straightforward. The free ion sits at the far left where the field is zero; moving right, each term splits into the states allowed by the field, drawn as lines that slope up or down. The spacing between the ground state and the upper states tells you the energies of the allowed d-d transitions — exactly the bands you would measure in a spectrum. An elegant economy built into Orgel diagrams is that one diagram serves several ions at once: by a hole formalism, a dn configuration and its complement behave as mirror images, and octahedral and tetrahedral cases are related by flipping the diagram, so a single chart covers a whole family.
Orgel diagrams are the friendly, qualitative tool for interpreting spectra: count the bands, match them to the sloping lines, and you can assign the transitions and estimate delta-o. Their deliberate limitation is the honest point — they show only the spin-allowed terms of the same multiplicity as the ground state, and they assume a weak-to-moderate field where high-spin behavior is kept throughout. They cannot describe what happens when a strong field forces a switch to low-spin, because that involves crossing to a term of different spin. For that you need the more complete Tanabe-Sugano diagram, which Orgel diagrams are the gentle introduction to.
For octahedral nickel(II), a d8 ion, the Orgel diagram shows the ground 3F term splitting into three spin-allowed states, predicting three d-d bands — and a real [Ni(H2O)6]2+ spectrum does show three bands, whose positions can be read off the diagram to extract delta-o.
Octahedral Ni(II) (d8): the Orgel diagram predicts three spin-allowed d-d bands.
An Orgel diagram only shows terms of the same spin multiplicity as the ground state and assumes high-spin throughout, so it cannot handle the high-spin to low-spin switch in a strong field — that is precisely what the Tanabe-Sugano diagram adds.