What determines the color observed in a transition metal complex?

The color observed in a transition metal complex is primarily determined by d-d electron transitions. Transition metals have partially filled d-orbitals, and when light hits the complex, certain wavelengths are absorbed to promote an electron from a lower energy d-orbital to a higher energy d-orbital. The specific wavelengths of light absorbed correspond to specific colors, and the complementary color of the absorbed light is what is observed.

The energy difference between the d-orbitals in a transition metal complex can be influenced by various factors such as the nature of the metal, the oxidation state of the metal, and the type and arrangement of ligands surrounding the metal ion. Different ligands can cause varying degrees of splitting of the d-orbitals (due to ligand field theory), which in turn affects the specific wavelengths of light absorbed. This is why the arrangement of ligands is also relevant, but the direct cause of color in such complexes comes from the d-d transitions themselves.

Other factors like the ionic radius of the metal may affect the general electronic structure and properties of the complex, but they do not directly determine the observed color in the same way that d-d transitions do.