Crystal Field Theory (CFT)

• Crystal field theory (CFT) describes the breaking of orbital degeneracy in transition metal complexes due to the presence of ligands.
• CFT arises from electrostatic interactions between metal ion d-electrons and ligands.
• Ligands are treated as point charges creating an electrostatic field.
• CFT explains the colors, magnetism, structure, and stability of coordination compounds.
• The magnitude of crystal field splitting (Δ) depends on the nature of the metal ion, its oxidation state, and the arrangement and nature of the ligands.

d-orbitals

• In an isolated gaseous metal ion, the five d-orbitals are degenerate.
• The five d-orbitals are dxy, dyz, dxz, dx2-y2, and dz2.
• When ligands approach the metal ion, the d-orbitals are no longer degenerate; the degeneracy is lifted.
• Some d-orbitals experience stronger interactions with the ligand field than others.
• Orbitals pointing directly at the ligands experience stronger repulsion and higher energy.
• Orbitals pointing between the ligands experience weaker repulsion and lower energy.

Octahedral complexes

• In an octahedral complex, the metal ion is at the center of an octahedron, and the six ligands are at the vertices.
• The eg set (dz2 and dx2-y2) point directly at the ligands along the x, y, and z axes.
• The t2g set (dxy, dyz, and dxz) point between the ligands.
• The eg set experiences stronger repulsion and is higher in energy.
• The t2g set experiences weaker repulsion and is lower in energy.
• The energy difference between the eg and t2g sets is denoted by Δo (Δoct).
• Δo is the octahedral field splitting parameter.
• The eg set is destabilized by +0.6Δo.
• The t2g set is stabilized by -0.4Δo.

Tetrahedral complexes

• In a tetrahedral complex, the metal ion is at the center of a tetrahedron, and the four ligands are at the vertices.
• None of the d-orbitals point directly at the ligands.
• The t2 set (dxy, dyz, and dxz) are closer to the ligands than the e set (dz2 and dx2-y2).
• The t2 set experiences stronger repulsion and is higher in energy.
• The e set experiences weaker repulsion and is lower in energy.
• The energy difference between the t2 and e sets is denoted by Δt (Δtet).
• Δt is the tetrahedral field splitting parameter.
• The t2 set is destabilized by +0.4Δt.
• The e set is stabilized by -0.6Δt.
• Δt is approximately 4/9 of Δo (Δt ≈ 4/9 Δo).
• Tetrahedral complexes are always high spin because the crystal field splitting is small.

Square planar complexes

• A square planar complex can be derived from an octahedral complex by removing the two ligands along the z-axis.
• The dz2 orbital is stabilized as there is no ligand along the z-axis.
• The dx2-y2 orbital is destabilized as the ligands are along the x and y axes.
• The splitting pattern is more complex than in octahedral or tetrahedral complexes: dx2-y2 > dxy > dz2 > dxz, dyz.

Crystal field stabilization energy

• Crystal field stabilization energy (CFSE) is the stabilization energy of a complex due to the placement of d-electrons in the lower energy d-orbitals in a ligand field.
• CFSE is calculated based on the number of electrons in the t2g and eg orbitals for octahedral complexes.
• For octahedral complexes, CFSE = (-0.4 x number of t2g electrons + 0.6 x number of eg electrons)Δo.
• For tetrahedral complexes, CFSE = (-0.6 x number of e electrons + 0.4 x number of t2 electrons)Δt.
• High spin and low spin configurations are possible for d4 to d7 octahedral complexes.
• The magnitude of Δo determines whether a complex is high spin or low spin.
• If Δo is smaller than the pairing energy (P), the complex is high spin.
• If Δo is larger than the pairing energy (P), the complex is low spin.
• Pairing energy (P) is the energy required to pair two electrons in the same orbital.

Factors affecting Δ

• The nature of the metal ion affects the magnitude of Δ.
• Δ generally increases down a group in the periodic table.
• Δ increases with increasing oxidation state of the metal ion.
• The nature of the ligands has a significant impact on Δ.
• Ligands can be arranged in a spectrochemical series based on their ability to split the d-orbitals.
• A spectrochemical series is a list of ligands ordered according to their increasing field strength: I- < Br- < SCN- < Cl- < F- < OH- < H2O < NH3 < en < NO2- < CN- < CO.
• Ligands on the left side of the series are weak-field ligands, resulting in small Δ and high spin complexes.
• Ligands on the right side of the series are strong-field ligands, resulting in large Δ and low spin complexes.

Jahn-Teller distortion

• The Jahn-Teller theorem states that any non-linear molecular system in a degenerate electronic state will be unstable and undergo distortion to remove the degeneracy.
• Jahn-Teller distortion is most common in octahedral complexes with uneven occupancy of the eg orbitals.
• The distortion usually involves elongation or compression along the z-axis.
• Elongation stabilizes the dz2 orbital and destabilizes the dx2-y2 orbital.
• Compression stabilizes the dx2-y2 orbital and destabilizes the dz2 orbital.
• Jahn-Teller effect is not usually observed when the degeneracy involves only the t2g orbitals because the effect of these orbitals on the bond lengths is smaller.

Applications of CFT

• CFT explains the magnetic properties of coordination compounds.
• Paramagnetic complexes have unpaired electrons.
• Diamagnetic complexes have all electrons paired.
• The number of unpaired electrons can be determined from the electronic configuration, which is influenced by Δ.
• CFT explains the colors of coordination compounds.
• Electronic transitions between the split d-orbitals can absorb light in the visible region.
• The color of the complex is complementary to the color of the absorbed light.
• CFT explains and predicts the geometry of coordination compounds.
• CFSE contributes to the overall stability of the complex and influences its structure.
• CFT is used in catalysis.
• Transition metal complexes are used as catalysts in many chemical reactions.
• Ligand field effects can be used to tune the catalytic activity of the metal center.

Crystal field theory (CFT) explains transition metal complex properties like color and magnetism. CFT arises from electrostatic interactions between metal ion d-electrons and ligands. Ligands are treated as point charges creating an electrostatic field that affects d-orbital degeneracy.