Crystal field theory

 Crystal field theory-

Developed by Hans Bethe (1929) and John Van Vleck (1932).The main postulates of this theory are as follows -

·       This theory considers that the bonding between metal ion and ligand is purely electrostatic or ionic.

·       Ligands are treated as point charges in case of anions but are treated as dipole in case of neutral molecules.

·       The five d-orbitals in an isolated gaseous metal atom/ion have same energies, i.e, they are degenerate.

·       This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the central metal/ion.

·       This degeneracy of d-orbitals get disturbance when the negative fields due to ligands which may be anions or polar molecules with their negative ends toward the central atom/ion, the field no longer remains symmetrical. it results in splitting of the d-orbitals.

·       The pattern of splitting depends upon the nature of the crystal field.

·       In octahedral complexes, the d_x²_-y² and d_z² orbital have lobes along the axes. Hence they point toward the ligands, will experience more repulsion and will be raised in energy whereas the lobes of  d_xy, d_yz, and d_xz orbitals which are directed between the axes, will lowered in energy as compared to average energy in the spherical crystal field. Thus in octahedral complex five d-orbital looses their degeneracy and split up into two sets as t_2g (three lower energies d_xy, d_yz, d_xz orbitals) and e_g (two higher energies orbitals d_x²_-y² , d_z²).

·       The splitting of the degenerate orbitals due to the presence of ligands in a definite geometry is known as crystal field splitting and the difference between two sets of degenerate orbitals as a result of crystal field splitting is known as crystal field stabilisation energy.

           It is denoted by Δ_o(the subscript o stands for octahedral)

         It is found that e_g orbitals are 3/5 Δ_o above the average energy level and t_2g orbitals 2/5 Δ_o below the average energy level.

    ·       The magnitude of  Δ_o depends upon the field produced by ligand and metal ion.

     ·       Spectrochemical series- the arrangement of ligands in order of their CFSE values/in the order of increasing field strength is known as spectrochemical series

      I^- < Br ^- < SCN^- < S^2- < F^- <OH^- <C2O4^2- <H₂O <NCS^- <edta^4- <NH₃ < en < CN^- <CO

     ·       In d² and d³ coordination entities, the d-electrons occupy singly in accordance with Hund’s rule.

        For d⁴ ions the electronic configuration depends upon CFSE(Δ_o) and pairing energy(P represents the energy required for electron pairing in a single orbital). the two options are –

Option-I	Option-I
a.  If Δo< P then fourth electron enters in one of the eg orbitals without pairing. It will be in presence of weak ligand and form high spin complexes.   b.  with electronic configuration    t2g3 eg1	a. If Δo>P then fourth electron enters in the t2g orbitals with pairing. It will be in presence of strong ligand and form low spin complexes.  b. with electronic configuration    t2g4 eg0

In tetrahedral complexes, the d-orbitals splitting is inverted and is smaller as compared to the octahedral field splitting. 

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