28.3 Colour of complexes

Degenerate orbitals have the same energy. In an isolated transition-metal ion the five d orbitals are degenerate; surrounding ligands create an electric field that splits them into non-degenerate energy levels.

The splitting pattern depends on geometry: octahedral ligands approach along axes, while tetrahedral approaches lie between axes. The energy gap affects colour and magnetic behaviour.

In an octahedral complex, dxy, dxz and dyz form one set and dz², dx²−y² another, with different energies.

Degenerate does not mean identical shapes, and ligand-field splitting is not caused by changing the principal quantum number.

Ligand-field splitting removes the equality of the five d-orbital energies. In an octahedral complex, two orbitals point towards ligands and rise in energy while three lie between axes and are lower; in a tetrahedral complex the pattern is reversed, with three higher and two lower.

The separation is ΔE. It is not a new electron shell: it is an energy difference within the same d subshell, created by the ligand arrangement around the metal.

For an octahedral ion, the dxy, dxz and dyz orbitals form the lower set, while dz² and dx²−y² form the upper set. A tetrahedral diagram must show the opposite 3:2 ordering.

Do not copy the octahedral diagram for a tetrahedral complex, or treat “higher” and “lower” as absolute energies independent of the complex.

A transition-metal complex can absorb visible light when a d electron is promoted from a lower split d level to a higher one. The absorbed photon has energy ΔE = hf, so its frequency is set by the size of the splitting.

The colour seen is not the colour absorbed: it is the complementary mixture of wavelengths that pass through or are reflected. A transition is possible only when the metal has an appropriate partially filled d set.

If a complex absorbs mainly orange-red light, the transmitted or observed colour is toward the blue-green complement. Changing ligands can change ΔE and therefore shift the observed colour.

“The d orbitals emit the colour” is the wrong model for the syllabus explanation; the key event is selective absorption during promotion between non-degenerate levels.

Different ligands create different electric fields around the same metal ion. That changes ΔE; because ΔE = hf, it changes the frequency and wavelength of light absorbed, so the complementary colour observed can change.

Compare complexes only after holding the metal oxidation state and geometry in view. A stronger ligand-field effect gives a larger splitting and absorption at higher frequency (shorter wavelength).

Replacing water ligands around a metal with ammonia can alter the splitting and shift the absorption band. The solution may therefore change colour even though the central metal and its oxidation state are unchanged.

Do not say a ligand “has a colour that it transfers” to the complex. The observed colour comes from the new energy gap and selective absorption.

When a ligand is replaced at a transition-metal centre, the geometry and ligand field can change. The new ΔE changes which visible wavelength is absorbed, so ligand exchange can produce a different solution colour.

Use the ligand, stoichiometry and medium to identify the complex actually present. Water, ammonia, hydroxide and chloride provide contrasting examples for Cu(II) and Co(II).

Adding excess ammonia to a hydrated Cu(II) solution produces a deep-blue ammine complex; hydroxide can instead precipitate Cu(OH)₂. These are different chemical outcomes, not simply “more blue” of the same species.

A colour change does not by itself prove redox. Ligand exchange can leave the oxidation state at +2 while changing coordination, geometry and absorption.