Crystal Field Theory

Valence Bond Theory failed to explain the stability of coordination compounds and the differences between strong and weak ligands. Later on, Crystal field theory was proposed which described the metal-ligand bond as an ionic bond arising purely from the electrostatic interactions between the metal ions and ligands. Crystal field theory considers anions as point charges and neutral molecules as dipoles. When transition metals are not bonded to any ligand, their d orbitals are degenerate that is they have the same energy. When they start bonding with other ligands, due to different symmetries of the d orbitals and the inductive effect of the ligands on the electrons, the d orbitals split apart and become non-degenerate. The pattern of the splitting of d orbitals depends on upon the nature of crystal field. The splitting in various crystal fields is discussed below:

Crystal Field Theory for Octahedral Coordination Compounds:

Crystal Field Theory

Crystal Field Theory – Octahedral

In case of an octahedral coordination compound having six ligands surrounding the metal atom/ion, we observe repulsion between the electrons in d orbitals and ligand electrons. This repulsion is experienced more in the case of dx2-y2 and dz2 orbitals as they point towards the axes along the direction of ligand. Hence, they have higher energy than average energy in spherical crystal field. On the other hand, dxy, dyz and dxz orbitals experience lower repulsions as they are directed between the axes. Hence, these three orbitals have less energy than the average energy in spherical crystal field. Thus, the repulsions in octahedral coordination compound yield two energy levels:

  • t2g– set of three orbitals (dxy, dyz and dxz) with lower energy
  • eg – set of two orbitals (dx2-y2 and dz2) with higher energy

This splitting of degenerate level in the presence of ligand is known as crystal field splitting. The difference between energy of t2g and eg level is denoted by “Δo” (subscript o stands for octahedral). Some ligands tend to produce strong fields thereby causing large crystal field splitting whereas some ligands tend to produce weak fields thereby causing small crystal field splitting. Thus, the crystal field splitting depends on upon the field produced by the ligand and the charge on the metal ion. An experimentally determined series based on absorption of light by coordination compound with different ligands known as spectrochemical series has been proposed. Spectrochemical series arranges ligands in order of their field strength as:

I– < Br– < Cl– < SCN– < F– < OH– <C2O42-< H2O<NCS– < EDTA4- < NH3 < en < CN< CO

Filling of d-orbitals takes place in the following manner; the first three electrons are arranged in t2g level as per the Hund’s rule. The fourth electron can either enter into t2g level giving a configuration of t2g4eg0 or can enter the eg orbital giving a configuration of t2g3eg1. This depends on two parameters magnitude of crystal field splitting, Δo and pairing energy, P. The possibilities of two cases can better be explained as:

  • Δo > P – Electron enters in the t2g level giving a configuration of t2g4eg0. Ligands producing this configuration are known as strong field ligands and form low spin complexes.
  • Δo < P – Electron enters in the eg level giving a configuration of t2g3eg1. Ligands producing this configuration are known as weak field ligands and form high spin complexes.

Learn more about Limitations of Crystal Field Theory with Byju’s.

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