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How does the crystal field theory explain the color properties of transition metal complexes? Provide an example of a transition metal complex and its corresponding color that can be explained by this theory.

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Crystal field theory  CFT  is a model used to describe the electronic structure and color properties of transition metal complexes. The theory is based on the interaction between the central metal ion and the ligands surrounding it. The ligands are considered as point charges that create an electric field around the metal ion, which in turn affects the energy levels of the metal's d-orbitals.In a transition metal complex, the central metal ion has partially filled d-orbitals. When the ligands approach the metal ion, they cause the degeneracy of the d-orbitals to be lifted, meaning that the energy levels of the d-orbitals are no longer equal. The d-orbitals are split into two groups with different energy levels: the lower energy group  usually t2g  and the higher energy group  usually eg . The energy difference between these two groups is called the crystal field splitting energy   .The color properties of transition metal complexes arise from the absorption of light, which promotes an electron from the lower energy d-orbitals to the higher energy d-orbitals. The energy of the absorbed light corresponds to the energy difference between the two sets of d-orbitals   . Since the energy of light is inversely proportional to its wavelength, the color of the complex is determined by the wavelength of the light that is not absorbed, i.e., the complementary color of the absorbed light.For example, consider the hexaaquachromium III  ion, [Cr H2O 6]. In this complex, the central chromium ion  Cr  is surrounded by six water molecules as ligands in an octahedral geometry. The d-orbitals of the Cr ion are split into two groups: t2g  lower energy  and eg  higher energy . The Cr ion has three d-electrons, which occupy the t2g orbitals.When light is absorbed by the complex, an electron from the t2g orbitals is promoted to the eg orbitals. The energy difference between these orbitals corresponds to the energy of the absorbed light. In the case of [Cr H2O 6], the absorbed light has a wavelength in the yellow-orange region of the spectrum. Consequently, the complex appears violet, which is the complementary color of yellow-orange. This color property of the hexaaquachromium III  ion can be explained by the crystal field theory.

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