# Crystal Field Theory, Overview, Octahedral Complex, Crystal Field Stabilization Energy Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Crystal Field Theory

• Crystal field theory describes the net change in crystal energy resulting from the orientation of d orbitals of a transition metal cation inside a coordinating group of anions also called ligands.
• Transition metals have tendency to form complexes. A complex may be considered as consisting of a central metal atom or ion surrounded by a number of ligands. The interaction between these ligands with the central metal atom or ion is subject to crystal field theory.
• Crystal field theory was established in 1929 treats the interaction of metal ion and ligand as a purely electrostatic phenomenon where the ligands are considered as point charges in the vicinity of the atomic orbitals of the central atom. Development and extension of crystal field theory taken into account the partly covalent nature of bonds between the ligand and metal atom mainly through the application of molecular orbital theory. Crystal field theory often termed as ligand field theory.

## Overview of Crystal Field Theory

• In order to understand clearly the crystal field interactions in transition metal complexes, it is necessary to have knowledge of the geometrical or spatial disposition of d orbitals. The d-orbitals are fivefold degenerate in a free gaseous metal ion. If a spherically symmetric field of negative ligand filed charge is imposed on a central metal ion, the d-orbitals will remain degenerate but followed by some changes in the energy of free ion.
• A summary of the interactions is given below.

Crystal Field Splitting

• 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.

### High Spin and Low Spin

• The complexion with the greater number of unpaired electrons is known as the high spin complex, the low spin complex contains the lesser number of unpaired electrons. High spin complexes are expected with weak field ligands whereas the crystal field splitting energy is small . The opposite applies to the low spin complexes in which strong field ligands cause maximum pairing of electrons in the set of three atomic orbitals due to large .
• High spin β Maximum number of unpaired electrons.
• Low spin β Minimum number of unpaired electrons.

Example:

High Spin and Low Spin Complex

• Low spin complex
• β High spin complex

The pattern of the splitting of d orbitals depends on the nature of the crystal field.

## Crystal Field Splitting in Octahedral Complex

• In the 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 and orbitals as they point towards the axes along the direction of the ligand.
• Hence, they have higher energy than average energy in the spherical crystal field.
• On the other hand, and orbitals experience lower repulsions as they are directed between the axes.
• Hence, these three orbitals have less energy than the average energy in the spherical crystal field.

Thus, the repulsions in octahedral coordination compound yield two energy levels:

• β set of three orbitals () with lower energy
• β set of two orbitals () with higher energy

Crystal Field Splitting in Octahedral Complex

This splitting of degenerate level in the presence of ligand is known as crystal field splitting. The difference between the energy of and level is denoted by (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.

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