Crystal - Field Splitting Energy

The crystal field theory in short represented as CFT was originally proposed for explaining the optical properties of crystalline solids. It was applied to the study of coordination compounds. The valence bond theory considers the bonding between the metal ion and the ligands as purely covalent. On the other hand, crystal field theory is based on the assumption that the metal ion and the ligands act as point charges and the interactions between them are purely electrostatic. 

What is Crystal Field Splitting Energy?

The division of the d-orbitals of the central metal ions divides into two sets of different energy levels. This separation in the energy of the d-orbital is called crystal field splitting energy.

Crystal Field Stabilizing Energy

Let’s define the Crystal Field Stabilization Energy, the distribution of electrons will take place in such a way that it will gain stability with respect to the berry center. And this increased stability or an overall decrease in energy is known as Crystal Field Stabilization Energy. In short Crystal Field Stabilization Energy is represented as CFSE.

In the case of negative ligands such as chloride ion, bromide ion, and cyanide ion the interaction with the metal ions are ion-ion interactions. If the ligands are neutral molecules such as water molecule, ammonia molecule, and carbon monoxide molecule the interaction with metal ions are ion-dipole interactions. For example, in the case of complex ions [Co F₆]^-3 the interactions are between Co⁺³ and F^- ions whereas in [Co (NH₃)₆]⁺³, the interactions are between the negatively charged end of ammonia molecules and Co⁺³ ions.

d Orbital Splitting

In the case of free metal ions, all the five d-orbitals that have the same energies are called degenerate orbitals. This indicates that an electron can occupy any one of these five d-orbitals with equal ease. However, on the approach of the ligands, the orbital electrons will be repelled by the lone pairs or negative charges of the ligands. The electronic repulsion will increase the energy of the d-orbitals. If all the ligands approaching the central metal are at an equal distance from each of the d-orbitals, the energy of each orbital will increase by the same amount due to the spherical field or symmetrical field of ligands. As a result, these orbitals will remain degenerate, but their energy will be higher than the free ions. But we know that d-orbitals have different orientations and, therefore, these orbitals will experience different interactions from the ligands. The orbitals facing the ligands will be more repelled, and their energies will be higher in comparison to their positions in a symmetrical region. 

The orbitals away from the ligands' approach, on the other hand, will have fewer interactions with the negative charge of donor atoms, and therefore their energies will be lower than in a spherical region. Therefore, due to the electrical field of the ligands, the energies of the five d-orbitals will split up (d-orbital splitting). This conversion of five degenerate-orbitals of the metal ion into different sets of orbitals having different energies in the presence of the electrical field of ligands is called crystal field splitting. This concept forms the basis of crystal field theory. 

Image Showing d Orbital Splitting

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In the d-orbital splitting of the coordination compounds, the interaction between the ligand and the metal ion causes the five d-orbitals to split up. The number of ligands and their arrangement around the central metal ion will have a different effect on the relative energies of the five d-orbitals. In other words, the crystal field splitting can vary depending on the coordination number of the compound structure. For example, in the case of octahedral complexes, the five d-orbitals split up into two sets; one set consisting of two orbitals dx²-y² and dz² of higher energy and another set consisting of three orbitals dxy, dyz, and dzx of the lower energy.

Crystal Field Splitting Energy Formula

The energy difference between the two sets of energy levels is called crystal field splitting energy and is represented as Δ0, this subscript ‘o’ stands for octahedral. It assesses the ligands' crystal field power. The average energy of the d-orbitals does not change as a result of the crystal field breaking. This is known as the barycentre rule, which is similar to the center of gravity rule. This means that the three orbitals lie at an energy that is ⅖ Δ0 below the average d-orbital energy and the two d-orbitals lie t an energy ⅗ Δ0 above the average energy. 

CFSE Formula for Octahedral Complex is Given Below:

CFSE = (-0.4x + 0.6y) Δ0

In the above formula, x represents the electrons in the t2g set.

Y represents the number of electrons in the eg set.

Calculating Crystal Field Stabilization Energy Tetrahedral

CFSE = (-0.6y + 0.4x) Δ0

In the above formula, x represents the electrons in the t2g set.

Y represents the number of electrons in the eg set.

Splitting in an Octahedral Field

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Crystal field splitting energy for high spin d4 octahedral complexes is known as the splitting in the octahedral field. In the octahedral complex, MX6, all the five d-orbitals will not remain of the same energy. This can be easily understood by considering the shapes of these orbitals. The lobes of dz2 and dx²-y² orbitals point directly towards the corner of the octahedron where the negative charges of the approaching ligands are present. The remaining three orbitals; dxy, dyz, and dzy have thor lobes not towards ligands but in between the point charges. This means that the electrons in dxy, dyz, and dzx orbitals will be repelled less by the negative point charges of the ligands than those in two d-orbitals (dxy, dyz, and dzx) experience less repulsion from the ligands and are stable and of lower energy than the two d-orbitals (dxy, dyz, and dzx) and (dx2-y2 and dz2) in the octahedral field.

Splitting in Tetrahedral Field

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It can be shown from the geometry that in tetrahedral complexes, the two d-orbitals (dx2-y2 and dz2) become more stable and of lower energy and the three orbitals (dxy, dyz, and dzx) become less stable and of higher energy. The difference between these two sets is called crystal field splitting in the tetrahedral field.

Factors Affecting Crystal Field Splitting Energy

Various factors influence the magnitude of splitting energy

1. Nature of the Ligand-  the crystal field splitting energy depends upon the nature of the ligand. The greater the ease with which the ligands can approach the metal ion and interact with it, the greater will be the CFSE. 

2. Oxidation State of the Metal Ion- In general, the higher the oxidation state or the charge on the metal ion, the greater will be the value of CFSE.

3. Nature of the Metal Ion- for the analogous entities within the group, the CFSE value differs. The CFSE value for a similar complex in the same oxidation state increases by 30-50% on going from 3d series. This increase is most of the same amount going from 4d-series to 5d-series. As a consequence of this, coordination entities of the second and third transition series have a greater tendency to form low spin complexes as compared to the first transition series.

4. The Geometry of the Coordination Entity- The CFSE value for tetrahedral coordination entities is about half the Crystal Field Splitting Energy value for octahedral species.  

Did You Know?

• It has been observed that the splitting in tetrahedral complexes is considerably less than in octahedral complexes.

• It may be noted that the splitting of d-orbitals in square planar complexes is complicated and has not been mentioned in the present text.