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Crystal Field Theory


Crystal field theory was developed originally by the physicista Hans Bethe and John Hasbrouck van Vleck in the 1930s to explain the absorption spectra of the transition metals such as Ni, Co, Fe, Ti etc.
At its present state of development, the theory can be applied to account for some magnatic properties, colors, hydration enthalpies and spinal structures of transition metal complexes. 

Crystal field theory describes the effects of electrostatic fields on the energy levels of the valence electrons (electrons in the outermost orbitals) of a transition metal when it is surrounded by negatively charged ligands in a crystal structure. 
The ligands are assumed to be point negative charge sited on the Cartesian axes, and the bonding entirely ionic. The more comprehensive ligand-field theory which is too complicated to be discussed here, treats the metal-ligand interaction as a covalent bonding interaction involving overlap between the d-orbitals of the metals and the ligand donor orbitals.

Crystal Field Splitting

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In crystal field theory, the ligands to be the point charges and there is interaction between the electrons of the ligands and the electrons of the central metal atom or ion. The five d-orbitals in an isolated gaseous metal atom or ion are degenerate.

The degeneracy is maintained if an spherically  symmetrical negative field surrounds the metal atom or ions. The five d-orbitals in an isolated gaseous metal atom or ion are degenerate. The degeneracy is maintained if an spherically symmetrical negative field surrounds the metal atom.

The five d-orbitals can be classified in two sets as follows:
1) The d-orbitals oriented in between the co-ordinate axes are called t2g orbitals.
2) The d-orbitals oriented along the axes are called eg orbitals.

In the case of free metal ion, all the five d-orbitals are degerate, they have equal energy. But their degeneracy is removed in the presence of ligands. The two sets of d-orbitals experience different repulsive interactions from the lone pairs of ligands and their energies also become different. The splitting of five d-orbitals of central metal ion under the influenece of approaching ligands is called crystal field splitting.
The energy difference between two sets of d-orbitals (eg and t2g) is designated by $\Delta$ and is called crystal field splitting energy or crystal field stabilization energy (CFSE). The ligands which cause greater crystal field splitting are termed as strong ligands while those which cause lesser crystal field splitting are weak ligands.
On the basis of spectroscopic data for a number of co-ordinate compounds having same metal ion but different ligands the crystal field splitting for each ligand has been calculated.

The arrangement of ligands in decreasing order of field strength is referred to as spectrochemical series as given below:

CO > CN- > NO2 > en > NH3 > py > NCS- > H2O > O2- > C2O42- > OH- > F- > Cl- > SCN- > Br- > I
The crystal field splitting of tetrahedral complex is shown below:

Crystal Field Splitting of Tetrahedral

The crystal field splitting of octahedral complex is shown below:

Crystal Field Splitting of Octahedral

Crystal Field Theory Color

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The color of a macroscopic mineral specimen is the result of a complex interplay among the reflection, absorption, transmission, refraction, scattering and dispersion of light as it interacts with the minerals chemical and structural components. This interplay is strongly influenced by chemical impurities and structural irregularities called defects that are common in all naturally occurring solids. Minerals characterized by a relatively constant shade of color are said to be idiochromatic, which means they are "self-colored". 
Idiochromatic minerals possess essentially the same color independent of any impurities and defects that occur. Color is a diagnostic property of idiochromatic minerals and can be used as a criterion for their identification. Excellent examples of idiochromatic minerals include azurite, which is always blue, sulfur which is always yellow and galena which is always grey.
The small amounts of chemical impurities and crystal defects permissible in the definition of a mineral are insufficient to affect its color significantly. If a mineral is colorless in its pure state, small amounts of impurities will transmit or reflect selected wavelength that give color.