Crystal Field Theory

A coordination compound consists of a metal atom or ion at the centre, surrounded by a number of oppositely charged ions or neutral molecules. A coordinate connection connects these ions or molecules to the metal atom or ion. When dissolved in water, they do not dissociate into simple ions.

Crystal Field Theory

H. Bethe and V. Bleck proposed the crystal field theory (CFT). This theory describes metal complexes’ bonding, characteristics, electronic spectra, and magnetism in greater detail.

Crystal field splitting is the conversion of five degenerate d-orbitals of a metal ion into different sets of orbitals with varying energies in the presence of a crystal field of ligands. Crystal field theory is founded on the splitting of crystal fields.

Postulates of Crystal Field Theory

1. According to the crystal field theory, the metal ion is surrounded by an electric field created by the ligands.
2. In a complex, the attraction between the core metal and the ligand is solely electrostatic. The metal ion is targeted by the negative end of the dipole of the neutral molecule ligand.
3. The transition metal or ion is a positive ion with the same charge as the oxidation state.
4. A specified number of ligands surround the transition metal atom or ion, which can be negative ions or neutral molecules with lone pairs of electrons.
5. The ligands act as point charges that generate an electric field. The energy of the orbitals on the metal atom or ions is changed by this electric field.
6. The electrons on the central metal ion occupy the d-orbitals as far away as possible from the direction of approach of the ligand due to the repulsive attraction between the central metal ion and the ligand.
7. The metal orbital and the ligand orbital have no interaction.
8. All orbitals have the same energy in an isolated metal atom or ion, i.e., all five d orbitals (d_xy, d_xz, d_yz, d_x²–y² and d_z²) are degenerate.
9. The d-orbitals remain degenerate when the core metal atom or ion is surrounded by a spherically symmetrical field of negative charges. The repulsion between the field and the electron on the metal atom or ion, however, raises the energy of the orbitals.
10. The d-orbitals are influenced differently in most transition metal complexes, and their degeneracy is lost due to the field produced by the unsymmetrical ligand.

Spectrochemical Series

The type of the ligand determines the crystal field splitting. Weak field ligands are ligands that cause just a minor crystal field splitting. Strong field ligands are ligands that generate a high crystal field splitting.

The spectrochemical series is the grouping of common ligands in ascending order of crystal field splitting (Δ). In increasing order of crystal field splitting, the spectrochemical series is:

I^–<Br^–<S^2–<Cl^–<NO^–₃<F^–<OH^–<EtOH^–<C₂O^2–₄<H₂O<<EDTA<NH₃<Py<Ethylenediamine<dipyridyl<0–phenanthroline<

NO^–₂<CN^–<CO

Crystal Field Theory for Octahedral Complexes

The ligand is represented by modest negative charges in the octahedral complex ion, while the metal ion is represented by positive change.

• Repulsion between the ligands and the d-orbitals occurs in octahedral complexes as the ligands approach metal ions, raising their energy relative to the free ion. The ligands repel d_x²–y² and d_z² orbitals more strongly than the remaining three d-orbitals, d_xy, d_xz, and d_yz.
• As a result, the energies of the d_xy, d_xz, and d_yz orbitals are lower than the energies of the d_x²–y² and d_z² orbitals.
• Lower-energy d_xy, d_xz, and d_yz orbitals are known as t_2g orbitals, while higher-energy d_x²–y²,d_z² orbitals are known as e_g orbitals.
• Crystal field splitting energy or crystal field stabilisation energy is the difference in energy between the two sets of d- orbitals (CFSE). It is denoted by the letter Δ_O, which stands for the octahedral complex.
• The e_g orbitals have an energy level of +0.6 Δ₀ or 3/5 Δ₀ above the average, whereas the t_2g orbitals have an energy level of –0.4 Δ₀ or –2/5 Δ₀ below the average.

• Strong field ligands have a high Δ₀ value and are low spin complexes in octahedral complexes. [Fe(CN)₆]^4– and [Co(NH₃)₆]³⁺ are two examples. 
• The weak field ligands are high spin complexes with a low Δ₀ value.

Crystal Field Theory for Tetrahedral Complexes

• Tetrahedral complexes have a splitting pattern that is the polar opposite of octahedral complexes. The d_x²–y² and d_z² orbitals in tetrahedral complexes have lower energy than the d_xy, d_xz, and d_yz orbitals.
• Δt(Δt=49 Δ₀) is the energy difference between two energy levels. Electrons do not pair because of the narrow energy gap. Tetrahedral complexes have a high spin structure as a result.

Crystal Field Stabilisation Energy

Crystal field splitting energy or crystal field stabilisation energy is the difference in energy between the two sets of d-orbitals (CFSE). It is denoted by the symbol Δ.

Factors Affecting the Magnitude of Orbital Splitting Energy (Δ)

1. The larger the value of orbital splitting energy, the higher the oxidation state of the central ion.
2. The Δ value of d-block (transition) elements grows from 3d to 4d to 5d. As a result, elements in the second (4d) and third (5d) transition series are more likely to form low spin complexes than those in the first (3d) transition series.
3. The Δ value of the coordinating entity aids in the classification of complexes. The tetrahedral complex has a value that is roughly half that of the octahedral complex.

Limitations of Crystal Field Theory

The crystal field theory was able to satisfactorily describe the coordination compound’s synthesis, structure, optical, and magnetic properties. However, the crystal field hypothesis was unable to account for the following factors.

1. Covalent bonding is found in some transition metal complexes.
2. In the spectrochemical series, the order of the ligands. Because ligands are point charges, anionic ligands should have a stronger splitting effect. The anionic ligands, on the other hand, are at the bottom of the spectrochemical series.

Sample Questions

Question 1: What is crystal field theory?

Answer:

Crystal field splitting is the conversion of five degenerate d-orbitals of a metal ion into different sets of orbitals with varying energies in the presence of a crystal field of ligands. Crystal field theory is founded on the splitting of crystal fields.

Question 2: What are the main features of crystal field theory?

Answer:

According to the crystal field theory, the metal ion is surrounded by an electric field created by the ligands. In a complex, the attraction between the core metal and the ligand is solely electrostatic. The metal ion is targeted by the negative end of the dipole of the neutral molecule ligand. The transition metal or ion is a positive ion with the same charge as the oxidation state. A specified number of ligands surround the transition metal atom or ion, which can be negative ions or neutral molecules with lone pairs of electrons.

The ligands act as point charges that generate an electric field. The energy of the orbitals on the metal atom or ions is changed by this electric field. The electrons on the central metal ion occupy the d-orbitals as far away as possible from the direction of approach of the ligand due to the repulsive attraction between the central metal ion and the ligand.

Question 3: What are the factors affecting crystal field splitting?

Answer:

The crystal field splitting is affected by the type of the ligand and the oxidation state of the central atom. The larger the value of orbital splitting energy, the higher the oxidation state of the central ion. Various ligands have different splitting magnitudes for the same metal ion.

Question 4: How to use crystal field theory?

Answer:

The bonding characteristics, electronic spectra, and magnetism of metal complexes are all explained by crystal field theory. Strong field ligands have a high Δ₀ value and are low spin complexes in octahedral complexes. The weak field ligands are high spin complexes with a low Δ₀ value.

Question 5: What is crystal field stabilisation energy?

Answer:

The difference in energy between the two sets of d-orbitals is known as crystal field splitting energy or crystal field stabilisation energy (CFSE). It’s represented by the symbol Δ.

Question 6: What are the limitations of crystal field theory?

Answer:

The synthesis, structure, optical, and magnetic properties of the coordination compound were all satisfactorily described by the crystal field theory. The crystal field hypothesis, on the other hand, failed to account for the following factors.

1. Some transition metal compounds have covalent bonding.
2. The order of the ligands in the spectrochemical series. Anionic ligands should have a higher splitting impact because they are point charges. The anionic ligands, on the other hand, are found at the bottom of the spectrochemical hierarchy.