Crystal field theory is used to describe the electronic structure of transition metal complexes. It is successful in describing the magnetic properties, colors, hydration enthalpies and spinel structures of transition metal complexes, but it cannot provide an adequate description of bonding. Crystal field theory was developed by the physicists Hans Bethe and John Hasbrouck van Vleck. It was combined with molecular orbital theory to form ligand field theory, which delivers insight into the process of chemical bonding in transition metal complexes. This article is in need of attention. ... A complex in chemistry and biochemistry is a reversible association of molecules, atoms, or ions through weak non-covalent chemical bonds. ... Spinel is one of a group of minerals which crystallize in the isometric system with an octahedral habit, and whose chemical compositions are analogous. ... Hans Albrecht Bethe (born July 2, 1906), is a German-American physicist from Strassburg (then part of Germany, now Strasbourg, France). ... John Hasbrouck van Vleck (March 13, 1899 – October 27, 1980) was an American physicist. ... In quantum chemistry, molecular orbitals are the statistical states electrons can have within molecules. ... Ligand field theory was developed during the thirties and fourties of the twentieth century as an expansion of the electrostatic crystal field theory, which offered a good description of the electronic structure of metal ions in coordination complexes but was not able to provide a proper explanation for their bonding. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ...

In crystal field theory the metal ion is assumed to be free in gas form, the ligands are assumed to behave like point charges and it is assumed that the orbitals of the metal and the ligands do not interact. A refined form of crystal field theory called ligand field theory takes an empirical constant called the Racah parameter in the calculations to make up for covalent effects. Covalent bonding is a form of chemical bonding characterized by the sharing of one or more pairs of electrons between atoms, in order to produce a mutual attraction, which holds the resultant molecule together. ...

The bonding between a transition metal and the ligands is due to the attraction between the positively charged metal ion and the electrons of the ligand. Crystal field theory describes how the ligands pull on some of the 3d electrons and split them in to higher and lower (in terms of energy) groups. This crystal field splitting depends on several factors:

• the nature of the metal ion, specifically the number of electrons in the d orbitals
• the metal's oxidation state. A high oxidations state leads to high energy splitting.
• the arrangement of the ligands around the metal ion.
• the nature of the ligands surrounding the metal ion. The stronger the ligands then the greater the energy difference between the split high and low 3d groups, this is called spectrochemical series.

The most common type of complex are octahedral complexes, here six ligands form a octahedral field around the metal ion, the ligands point directly into the d-orbitals and cause high-energy splitting. Tetrahedral complexes are the second most common type, here four ligands form a tetrahedral field around the metal ion, since in this case the ligands electrons aren't oriented directly against the d-orbitals the energy splitting will be lower than in the octahedral case. Square planar complexes are mostly by transition metals in period 5 and 6 and nickel in period 4. Crystal field theory works best for period 4 transition metals. General Name, Symbol, Number nickel, Ni, 28 Chemical series transition metals Group, Period, Block 10 , 4, d Density, Hardness 8908 kg/m³, 4. ...

Transition metals have ions with party filled d-orbitals. There are 5 d-orbitals which each can have two electrons. These five d-orbitals are degenerate, i.e. they have the same energy. When a ligand approaches the metal ion, the electrons from the ligand will be closer to some of the d-orbitals and farther away from others, the electrons in the d-orbitals and the electrons in the ligand repulse each other, since the different d-orbitals are repulsed unequally by the ligand electrons they ones closest to the ligands will have higher energy than the ones not so close to the ligands because it takes more energy for an electron to go into an orbital with more repulsive negative charge nearby so the d-orbitals will split in energy. What determines the energy split, Δ is the orientation of the ligands with respect to the metal d orbitals. If there are six ligands there will most likely be one at each axis so the complex will have octahedral geometry, the orbitals d_xy, d_xz and d_yz will be in lower energy and the orbitals d_z² and d_x²-y² will have higher energy. This is called octahedral crystal field splitting, it will be split as Δ_oct=3/5Δ + 2/5Δ, this means the energy of the lower orbitals is −2/5Δ while the energy in the higher orbitals is +3/5Δ. In tetrahedral crystal field splitting Δ_tet the low energy orbitals will be d_z² and d_x²-y² while the high energy orbitals will be d_xy, d_xz and d_yz so its just the opposite of octahedral. Since its most stable to put electrons in the low energy orbitals this is a determining factor in transition metal complex bonding.