A coordination compound forms when surrounding molecules or ions, called ligands, arrange themselves around a central metal atom and donate an electron pair to it, forming a genuinely distinct type of chemical bond from an ordinary shared covalent pair. Ligand field theory explains a striking consequence of that specific arrangement: the surrounding ligands' electric field splits the central metal's set of d-orbitals, normally all equal in energy, apart into groups of different energy, a splitting directly responsible for the vivid, often quite specific colours many transition metal compounds actually display.
Ligands surround a metal atom and donate electrons rather than sharing them equally
Unlike an ordinary covalent bond, where two atoms each contribute one electron to a shared pair, a coordination bond forms when a ligand alone donates both electrons of the bonding pair to the metal atom, which contributes none of its own to that particular bond. Several ligands typically surround a single central metal atom simultaneously, often six of them arranged symmetrically, gripping the metal from multiple directions at once, and the specific number and geometric arrangement of those ligands is itself a defining feature of the resulting coordination compound's structure.
That surrounding arrangement splits the metal's d-orbitals and produces colour
In an isolated metal atom or ion, its five d-orbitals all sit at exactly the same energy, but once ligands arrange themselves around the metal in a coordination compound, their electric field pushes some of those d-orbitals to higher energy and others to lower energy depending on each orbital's specific spatial orientation relative to where the ligands actually sit. Electrons can then absorb a specific amount of light energy to jump between these newly split energy levels, and because that energy gap corresponds to a specific wavelength of visible light, the compound absorbs that particular wavelength and displays the complementary colour, which is exactly why so many transition metal coordination compounds show such vivid, chemically diagnostic colours.
What we're still unsure about
That ligand field theory correctly explains d-orbital splitting and its connection to coordination compound colour is well established, extensively confirmed inorganic chemistry, verified through decades of matching predicted absorption against measured spectra. What's more genuinely a matter of ongoing theoretical refinement is exactly how well ligand field theory's relatively simple electrostatic picture holds up against more computationally demanding quantum mechanical treatments for genuinely complex coordination compounds, since the simpler theory works remarkably well for many common cases but requires real correction for others, and chemists continue to develop and apply more sophisticated models for exactly the coordination compounds where the simpler ligand field picture proves insufficient on its own.
This sits inside Coordination Compounds & Ligand Field Theory, one of seven topics in Inorganic Chemistry, one of six domains in Chemistry, one of seventeen subjects the app can quiz you on.