Introduction

In this particular article, Theory of Crystal field stabilization energy we are going to discuss crystal field stabilization energy in octahedral and Tetrahedral Complexes.

Crystal Field Stabilization Energy in Octahedral Complexes

In the octahedral complex, the d- orbitals of the metal cation are split into two sets of different energies, t₂g of lower energy and eg of higher energy. The separation between these two sets is equal to ∆₀. The t₂g set has an energy of -0.4∆₀ and the eg set has an energy of + 0.6∆₀ relative to the barycenter. Minus and plus signs indicate a decrease and increase in energy relative to the barycenter respectively. The complex ion with one electron in one of the t₂g orbitals has an energy of -0.4∆₀ relative to the barycenter. This indicates that in a complex ion of d¹ configuration 0.4 ∆₀ energy is released. This released energy is called the crystal field stabilization energy of the complex ion.

For d¹ complex, electronic configuration is not t¹₂g e⁰g

CFSE = -0.4 × 1 ∆₀ = -0.4 ∆₀

For d² complex, electronic configuration is not t²₂g e⁰g

CFSE = -0.4 × 2 ∆₀ = -0.8 ∆₀

For d³ complex, electronic configuration is not t³₂g e⁰g

CFSE = -0.4 × 3 ∆₀ = -1.2 ∆₀

For d⁴ high spin complex, electronic configuration is t³g e¹g

CFSE = 0.4 ×3 + 0.6 × 1 ∆₀ =- 0.6  ∆₀

Thus for a dⁿ high spin complex with electronic configuration t₂gªegº,

CFSE = { -0.4p + 0.6 q} ∆₀

Since no pairing of d- electrons occurs in high spin complexes, therefore no pairing energy is involved in CFSE.

For low spin Complexes of d⁴, d⁵, d⁶ and d⁷ metal ion, the pairing of electrons occurs in t₂g orbitals. To pair up the two electrons in an orbital, an extra energy is required which is called as pairing energy (P). Therefore, for d⁴ low spin complex, the electronic configuration is t⁴₂g e⁰g.

and CFSE= { -0.4 × 4 + 0.6 ×0 } ∆₀ + P

= – 1.6 ∆₀ + P

For d⁵ low spin Complex, the electronic configuration is t⁵₂g e⁰g. In this case, four electrons are forced to pair up in two different orbitals of the t₂g set.

Therefore CFSE = { -0.4 × 5 + 0.6 ×0 } ∆₀ +2p

= – 2.0 ∆₀+ 2p

For dⁿ low spin octahedral complexes with electronic configuration t₂gªegº,

CFSE = { -0.4p + 0.6 q} ∆₀ + mp

Where p and q are the number of electrons in t₂g and eg orbitals respectively.

m = number of pairs of electrons caused by the ligands.

P is the mean pairing energy. The required pairing energy is compensated from CFSE.

Let us illustrate the difference in calculation of CFSE of some high spin and low spin complexes.

(1) For d⁶ low spin octahedral complex, the electronic configuration is t⁶₂g e⁰g.

CFSE = { -0.4 × 6 + 0.6 ×0 } ∆₀

= [−0.4×4 + 0.6 ×2]∆₀

=− 0.4 ∆₀

In this case, no pairing energy is included because no pairing of electrons is caused by the ligands. Though it has one pair of electrons it is not caused by the ligands. This part was already present in d-orbitals as shown below :

For d⁶ low spin octahedral complex, the electronic configuration is t⁶₂g e⁰g

CFSE = [−0.4 ×6 + 0.6 ×0 ]∆₀+ 2P

= − 2.4 ∆₀+ 2P

In this case, there are three pairs of electrons but only two are caused by the ligands and one was already present in d-orbitals.

The CFSE’s of d¹ to d¹⁰ high spin and low spin complexes are given in the table.

Crystal Field Stabilization Energy in Tetrahedral Complexes :

In a tetrahedral complex, the d- orbitals of the metal cation are split into two sets of different energies, e of lower energy and t₂ of higher energy. The separation between these two sets is equal to ∆ t. The e set has an energy of -0.6 ∆t and the t₂ has an energy of + 0.4 ∆t relative to the barycenter. For a dⁿ tetrahedral complex with e⁰t₂ª  configuration,

CFSE = {-0.6 p + 0.4 q} ∆t

={-0.6 p + 0.4 q} ×4/9 ∆₀ (∴ ∆ t = 4/9 ∆₀)

={-0.27  p + 0.18 q} ∆₀

Since tetrahedral complexes are high spin and no pairing of d- electrons occurs (∆t < p ). Therefore no pairing energy is included in the above equation. The CFSE value of tetrahedral complexes of d¹to d¹⁰ metal ions is given in the table.

Theory of Crystal field stabilization energy

The conclusion of the Theory of Crystal field stabilization energy

In this particular article Theory of Crystal field stabilization energy, we have discussed crystal field stabilization energy in octahedral complexes and crystal field stabilization energy in tetrahedral complexes in the easiest way possible.

2 Replies to “Theory of crystal field stabilization energy”

Leave a Reply

Your email address will not be published. Required fields are marked *