## Crystal Field Theory Preparation and Properties

Crystal Field Theory :

• CFT was proposed by Bethe (1929) and Van vleck (1932).
• This theory accounts for more satisfactory explanation for the properties of complexes especially colour and magnetic properties.

→ The main points of the theory are:

• The bonding in complex ion is purely electrostatic ie, this theory does not consider any orbital overlap.
• The complex is regarded as a combination of a central metal cation surrounded by ligands which act as negative point charges or point dipoles.
• The arrangement of the ligands around the central metal ion is such that the repulsion between these negative points or dipoles is minimum.
• Interactions between positively charged nucleus of the central metal ion and the negatively charged ligands are of two types :

→ The attractive forces arise due to the positive metal ion and negatively charged ligands or the negative end of a polar neutral molecules. These attraction forces bind the ligands to the metal ion i.e.,the bond between metal and the surrounding ligands are purely ionic.

→ The repulsive forces between the lone pair and electrons in the d-orbitals of the metal ion or atom. The crystal field theory mainly focused on these repulsive forces. These forces are responsible for causing a considerable effect on the relative energies of the d-orbitals of the central metal ion or atom.

→ In a free transition metal atom or ion, there are five d-orbitals which are divided into two sets depending on the nature of their orientation in space. The three d-orbitals (dxy, dxyz, dzx) which orient in the regions between the co-ordinate axes are designated as t2g orbitals. The other two d-orbitals ($$d_{x^{2}-y^{2}}$$, $$d_{z^{2}}$$) which orient along the axes are called eg orbitals.

→ In a free transition metal ion, all the five d-orbitals are degenerated. However, when the ligands approach the central metal ion, the electrons of the d-orbitals of the central metal ion are repelled by lone pairs of the ligands. As a result of these interactions, the degeneracy of d-orbitals of the metal ion is lost depending on the orientation of ligands in space. The d-orbitals split into two set of orbitals having different energies.

→ This is called crystal field splitting. It is the basis of CFT. The extent of splitting depends on the number of ligands, nature of ligands. The splitting is different in different structures with different coordination numbers.

## Splitting of d-orbitals in Octahedral Complexes

→ In an octahedral complex, central metal ion is placed at the centre of the octahedron and is surrounded by six ligands which reside at the six corners of the octahedron.

→ Since the lobes of two eg orbitals lie in the path of approaching ligand, the electron in these orbitals experience greater force of repulsion than those in t2g orbitals whose lobes are directed in space between the path of the ligands i.e., energy of t2g and eg orbitals is increased by different magnitude.

→ Thus, an energy difference exists between two sets of orbitals. This energy difference is called crystal field splitting energy (CFSE = ∆0).

→ For any given metal ion, the magnitude of CFSE depend on the nature of the ligands. The ligands which affect only a small degree of CFSE are termed weak field liganda while those which affect a large splitting are called strong field ligand.

→ When the ligands are arranged in order of magnitude of crystal field splitting, energy the arrangement thus obtained is called spectrochemical series :

→ Distribution of d-electrons in t2g and eg orbitals in octahedral complexes : Distribution takes place on the basis of nature of ligands. Two cases may arise :

→ When the ligands are weak: Under the influence of weak ligand, CFSE is relatively small than P (pairing energy which is energy required to pair two electron in the same orbital) and hence all the five d-orbitals may be supposed to be degenerate and the distribution of electrons in tax and eg sets according to Hund’s rule. This can be shown as:

→ When the ligands are strong: Under the influence of strong ligand, CFSE is relatively higher than P and thus the distribution of d-electrons in lze and eg sets does not obey Hund’s rule. This can be shown as:

The above points are summerized in following table :

## Splitting of d-orbitals in Tetrahedral Complex

→ During the formation of tetrahedral complexes, t2g orbitals are closed to the approaching ligands. As a result of this, the t2g orbitals suffer more repulsion than eg orbitals thus splitting occur in following way:

It is observed that ∆t (CFSE in tetrahedral complex) is considerably less than ∆0. It has been found that

$$\Delta_{t}=\frac{4}{9} \Delta_{o}$$

→ Under the influence of strong or weak ligand, CFSE is relatively small than P and hence all the five d-orbitals may be supposed to be degenerate and the distribution of electrons in t2g and eg sets according to Hund’s rule. This can be shown as:

## Cause of Colour According to CFT

→ A complex shows colour because it absorbs light at a specific wavelength in the visible part of the electromagnetic spectrum and transmits the rest of the wavelength which representa a particular colour. The absorption of light is arises from the excitation of electrons from the d-orbitals of lower energy to the d-orbital of higher energy i.e. d-d-transition of electron is main cause of colour which is based on the splitting of d-orbitals.

 Colour of absorbed light Colour/complementary colour of coordinate group Yellow Violet Blue-green Red Blue Yellow orange Violet Pale Yellow Red Blue

→ In coordinate compounds colour occurs due to d-d transitions. During these transitions, when electron falls to t2g from eg orbital energy released in form of coloured photon.