d-d transition

Why is a copper sulfate solution blue, a chromium alum violet, a nickel salt green? The everyday answer is that these transition-metal ions soak up part of the visible light that falls on them and let the rest through, and the part they keep is set by a small energy gap inside the metal's d orbitals. A d-d transition is the event that does the soaking up: a photon of just the right energy bumps one of the metal's d electrons from a lower-energy d orbital into a higher-energy one.

Here is the picture. In a free metal ion the five d orbitals all sit at the same energy, but the moment ligands cluster around the metal they no longer do. In an octahedral complex the two d orbitals pointing straight at the ligands (dz2 and dx2-y2, called the eg set) are pushed up, while the three pointing between the ligands (dxy, dxz, dyz, the t2g set) are pushed down; the energy gap between them is called delta-o (the octahedral ligand-field splitting). A d-d transition is an electron jumping across that gap — say from t2g up to eg — and it absorbs a photon whose energy exactly matches delta-o. Because delta-o for typical complexes happens to land in the visible range, the absorbed photon is a visible color, and we see what is left over.

The size of delta-o, and hence the color absorbed, depends on the metal, its oxidation state, and above all the ligands (the spectrochemical series ranks ligands by how large a delta they produce). So a d-d band is a direct readout of the ligand field: stronger-field ligands give a larger gap, shift absorption to shorter wavelengths, and change the observed color. One honest caveat: d-d transitions are usually weak (the Laporte and spin rules forbid them in an idealized centrosymmetric complex), which is why many transition-metal solutions are only pale, not vivid — the truly intense colors usually come from charge-transfer bands instead.