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Crystal Field Splitting

An ionic theory which is an offshoot of electrostatic theory. It ignores all covalent bonding effects. It was developed by Hans Bethe in 1929 by applying group theory and quantum mechanics to electrostatic theory. It was further developed by physicists during the 1930s and 1940s. It can be used to predict chemical properties, kinetic properties, reaction mechanisms, magnetic and spectral properties, and thermodynamic data. It cannot, however, be applied to sulfides, since sulfide forms mainly covalent bonds.

A splitting of energy levels ("crystal field splitting") occurs because the orientation of the d orbital wavefunctions will increase an electron's energy when the orbital is located in a region of high electron density, and lower it when the reverse is true. In crystals, the , , , , and  orbitals split up as depicted below, depending on their cation's coordination. The total energy splitting  is termed the crystal field stabilization energy.  may be estimated from

where r is the radius of the d orbital and R is the metal-ligand internuclear distance. A large crystal field splitting energy is provided by ligands with high negative charge and small radius, and by metal cations with a large oxidation number.
Let  denote the cubic splitting,  the tetrahedral splitting, and  the octahedral splitting. Then







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