Crystal Field Theory (CFT)

Crystal field theory differs from valence bond theory in viewing the complex as held together by purely electrostatic attractions. That is, it ignores covalent bonding.

The most significant aspects of the theory is its concern with the effect that the ligands have on the energies of the d-orbitals of the metal. The ligands are viewed as pointing their negative end in the direction of the metal cation.

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:

a) The nature of the metal ion.

b) The metal's oxidation state. A higher oxidation state leads to a larger splitting.

c) The arrangement of the ligands around the metal ion.

d) 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; here six ligands form an octahedron around the metal ion. In octahedral symmetry the d-orbitals split into two sets with an energy difference, Δ_oct (the crystal-field splitting parameter) where the d_xy, d_xz and d_yz orbitals will be lower in energy than the d_z² and d_x²_-y², which will have higher energy, because the former group is farther from the ligands than the latter and therefore experience less repulsion.

The three lower-energy orbitals are collectively referred to as t_2g, and the two higher-energy orbitals as e_g

 

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:

I ⁻ < Br⁻ < S²⁻ < SCN⁻ < Cl⁻ < NO₃⁻ < N₃⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < CH₃CN < py < NH₃ < en < 2, 2’ - bipyridine < phen < NO₂⁻ < PPh₃ < 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. For d⁴ ions 2 possibilities are there:

1. The fourth electron could enter t_2g level and pair with an electron

2. It can enter e_g level and avoid pairing

The selection of one of these possibilities depends on magnitude of splitting, ∆₀ and pairing energy, P

1. If ∆₀ < P, electron enters eg orbitals.

Ligands with ∆₀ < P are weak field ligands and form high spin complexes

2. If ∆₀ > P, electron enters t2g orbital.

Ligands with ∆₀ > P are strong field ligands and form low spin complexes

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_tet where the lower energy orbitals will be d_z² and d_x²_-y², and the higher energy orbitals will be d_xy, d_xz and d_yz - 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.

Colour in coordination compounds:

⇒ The colour of the complex is complementary to that which is absorbed.

⇒ If a complex whose d orbitals are split absorbs a photon of visible light, one or more electrons may momentarily jump from the lower energy d-orbitals to the higher energy ones to transiently create an excited state atom.

⇒ The difference in energy between the atom in the ground state and in the excited state is equal to the energy of the absorbed photon.

⇒ Because only certain wavelengths (λ) of light are absorbed - those matching exactly the energy difference - the compounds appears the appropriate complementary color.

⇒ In the absence of ligand, crystal field splitting doesn’t occur and hence substance is colourless.

Ex: anhydrous CuSO₄ is colourless but CuSO₄.5H₂O is blue in colour.

Coordination Entity	Wavelength of Light Absorbed (nm)	Colour of Light Absorbed	Colour of Coordination Entity
[CoCl(NH₃)₅]²⁺	535	Yellow	Violet
[Co(NH₃)₅(H₂O)]³⁺	500	Blue Green	Red
[Co(NH₃)₆]³⁺	475	Blue	Yellow Orange
[Co(CN)₆]³⁻	310	Ultraviolet	Pale Yellow
[Cu(H₂O)₄]²⁺	600	Red	Blue
[Ti(H₂O)₆]³⁺	498	Blue Green	Purple

Limitations of crystal field theory:

⇒ According to crystal field theory anionic ligands are point charges, then anionic ligands should act as strong ligands and should exert the greatest splitting effect. But, anionic ligands are actually found at the low end of the spectro-chemical series.

⇒ It does not take into account the covalent character of bonding between the ligand and the central atom.