text: According to crystal field theory, the interaction between a transition metal and ligands arises from the attraction between the positively charged metal cation and the negative charge on the non-bonding electrons of the ligand. The theory is developed by considering energy changes of the five degenerate d-orbitals upon being surrounded by an array of point charges consisting of the ligands. As 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, causing a loss of degeneracy. The electrons in the d-orbitals and those in the ligand repel each other due to repulsion between like charges. Thus the d-electrons closer to the ligands will have a higher energy than those further away which results in the d-orbitals splitting in energy. This splitting is affected by the following factors:
  * the nature of the metal ion.
  * the metal's oxidation state. A higher oxidation state leads to a larger splitting relative to the spherical field.
  * the arrangement of the ligands around the metal ion.
  * the coordination number of the metal (i.e. tetrahedral, octahedral...)
  * the nature of the ligands surrounding the metal ion. The stronger the effect of the ligands then the greater the difference between the high and low energy d groups.
  The most common type of complex is octahedral, in which six ligands form the vertices of an octahedron around the metal ion. In octahedral symmetry the d-orbitals split into two sets with an energy difference, Δ (the crystal-field splitting parameter, also commonly denoted by 10Dq for ten times the "differential of quanta") where the d, d and d orbitals will be lower in energy than the d-y, and the two higher-energy orbitals as e. These labels are based on the theory of molecular symmetry: they are the names of irreducible representations of the octahedral point group, O.(see the O character table) Typical orbital energy diagrams are given below in the section High-spin and low-spin.
  Tetrahedral complexes are the second most common type; here four ligands form a tetrahedron around the metal ion. In a tetrahedral crystal field splitting, the d-orbitals again split into two groups, with an energy difference of Δ. The lower energy orbitals will be d-y, d and d - opposite to the octahedral case. Furthermore, since the ligand electrons in tetrahedral symmetry are not oriented directly towards the d-orbitals, the energy splitting will be lower than in the octahedral case. Square planar and other complex geometries can also be described by CFT.
  The size of the gap Δ between the two or more sets of orbitals depends on several factors, including the ligands and geometry of the complex. Some ligands always produce a small value of Δ, while others always give a large splitting. The reasons behind this can be explained by ligand field theory. The spectrochemical series is an empirically-derived list of ligands ordered by the size of the splitting Δ that they produce (small Δ to large Δ; see also this table):
  I    (S–bonded)      O O  (N–bonded) CN     < CO.
  It is useful to note that the ligands producing the most splitting are those that can engage in metal to ligand back-bonding.
  The oxidation state of the metal also contributes to the size of Δ between the high and low energy levels. As the oxidation state increases for a given metal, the magnitude of Δ increases. A V complex will have a larger Δ than a V complex for a given set of ligands, as the difference in charge density allows the ligands to be closer to a V ion than to a V ion. The smaller distance between the ligand and the metal ion results in a larger Δ, because the ligand and metal electrons are closer together and therefore repel more.