7. Crystal Field Theory

Crystal Field Theory :

The drawbacks of VBT of coordination compounds are, to a considerable extent, removed by the Crystal Field Theory.

The crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be  ionic arising purely from electrostatic interaction between the metal ion and the ligand. Ligands are treated as point charges in case of anions or dipoles in case of neutral molecules. The five d orbitals is an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands (either anions or the negative ends of dipolar molecules like NH₃ and H₂O) in a complex, it becomes asymmetrical and the degeneracy of the d orbitals is lost. It results in splitting of the d orbitals. The pattern of spitting depends upon the nature of the crystals field.

(a) Crystal field splitting in octahedral coordination entities :

In an octahedral coordination entity with six ligands surrounding the metal atom/ion, there will be repulsion between the electrons in metal d orbitals and the electrons (or negative charges) of the ligands. Such a repulsion is more when the metal d orbitals is directed towards the ligand than when it is away from the ligand. Thus, the  and  orbitals (axial orbitals) which point towards the axis along the direction of the ligand will experience more repulsion and will be raised in energy ; and the d_xy , d_yz and d_zx orbitals (non-axial) orbitals which are directed between the axis will be lowered in energy relative to the average energy in the spherical crystal field. Thus, the degeneracy of the d orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, t_2g set and two orbitals of higher energy, e_g set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by D0 (the subscript o is for octahedral). Thus, the energy of the two e_g orbitals will increase by (3/5)D0 and that of the three t_2g will decrease by (2/5) D0.

The crystal field splitting, D0, depends upon the fields produced by the ligand and charge on the metal ion. Some ligands are able to produces strong fields in which case, the splitting will be large whereas others produce weak fields and consequently result in small splitting of d orbitals. In general, ligands can be arranged in a series in the orders of increasing field strength as given below :

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Such a series is termed as spectrochemical series. It is an experimentally determined series based on the absorption of light by complexes with different ligands. For d⁴ configuration, the fourth electron will singly occupy eg orbital (according to Hund’s rule) or will undergo pairing in t_2g orbital, which of these possibilities occurs, depends on the relative magnitude of the crystal field splitting, D0 and the pairing energy, P (P represents the energy required for electron pairing in a single orbital). The two possibilites are :

(i) If D0 < P, the fourth electron enters one of the eg orbitals giving the configuration t³_2ge_g¹. Ligands for which D0 < P are known as weak field ligands and form high spin complexes.

(ii) If D0 > P, it becomes more energetically favourable for the fourth electron to occupy a t_2g orbital with configuration t_2g⁴ e_g⁰. Ligands which produce this effect are known as strong field ligands and form low spin complexes.

(b) Crystal field splitting in tetrahedral coordination entities :

In tetrahedral coordination entity formation, the d orbital splitting is inverted and is smaller as compared to the octahedral field splitting. For the same metal, the same ligands and metal-ligand distances, it can be shown that Dt = (4/9)D0. This may attributes to the following two reasons.

(i) there are only four ligands instead of six, so the ligand field is only two thirds the size ; as the ligand field spliting is also the two thirds the size and

(ii) the direction of the orbitals does not concide with the direction of  the ligands. This reduces the crystal field spliting by roughly further two third. So Dt =  ×  = Do.

Consequently, the orbital splitting energies are not sufficiently large for forcing pairing and, therefore, low spin configurations are rarely observed.

Since Dt < Do, crystal field spliting favours the formation of octahedral complexes.