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Transition metal complexes absorb specific wavelengths of visible light when photons have enough energy to excite electrons between d orbitals. The absorbed light depends on crystal field splitting energy (delta), which determines which colors are absorbed and thus which colors appear to the human eye. For example, hexafluorocobaltate(III) absorbs red light and appears green, while hexaamminecobalt(III) absorbs blue light and appears yellow.

Strong-field ligands create large crystal field splitting (large delta), causing complexes to absorb high-energy violet or blue light and appear yellow, orange, or red. Weak-field ligands produce small delta values, causing complexes to absorb lower-energy yellow, orange, or red light and appear blue-green, blue, or indigo. The spectrochemical series ranks ligands by their ability to split d orbital energies.

When delta is smaller than the spin-pairing energy, electrons occupy higher-energy orbitals singly before pairing, creating high-spin complexes with unpaired electrons. When delta exceeds spin-pairing energy, electrons pair in lower-energy orbitals first, forming low-spin complexes with fewer unpaired electrons. Hexafluorocobaltate(III) is high-spin with four unpaired electrons, while hexaamminecobalt(III) is low-spin with zero unpaired electrons.

Complexes with unpaired electrons are paramagnetic and attracted to magnetic fields. High-spin complexes like hexafluorocobaltate(III) are paramagnetic due to their unpaired electrons. Complexes with no unpaired electrons are diamagnetic and repelled by magnetic fields. Low-spin hexaamminecobalt(III) is diamagnetic because all electrons are paired in lower-energy orbitals.

Different oxidation states alter the number of d electrons available for excitation and change the crystal field splitting energy. For example, Cu+ complexes with d10 configuration require ultraviolet photons to excite electrons, appearing colorless. Cu2+ complexes have vacancies in d orbitals that allow visible light absorption, appearing blue, blue-green, violet, or yellow depending on the ligands present.

The magnetic moment of a complex is directly proportional to the number of unpaired electrons present. Complexes with more unpaired electrons exhibit larger magnetic moments. Measuring the magnetic moment experimentally confirms the spin state: high-spin d6 [Fe(H2O)6]2+ shows four unpaired electrons with a corresponding magnetic moment, while low-spin d6 [Fe(CN)6]4− is diamagnetic with zero unpaired electrons.

The energy gap between d orbitals determines the wavelength of absorbed light. When all d orbitals are filled (like Cu+ with d10 configuration), electrons must be excited to much higher orbitals, requiring ultraviolet photons and producing colorless complexes. When d orbital vacancies exist, visible light photons can excite electrons, producing colored complexes. The specific ligands coordinated to the metal center influence this energy gap.