Ligand Field Theory (LFT) | Coordination Chemistry Class 12

Ligand Field Theory (LFT)

Combining Crystal Field & Molecular Orbital Theory

1. Evolution from CFT

Crystal Field Theory (CFT) assumes purely electrostatic interactions (Ionic). However, it fails to explain:

The relative strengths of ligands (Spectrochemical Series).
Covalent character in metal-ligand bonds.

                    Ligand Field Theory (LFT) extends CFT by incorporating Molecular Orbital Theory (MOT) principles. It considers the overlap of metal orbitals with Ligand Group Orbitals (LGOs) to form Molecular Orbitals.
                

2. Symmetry and Orbital Matching

In an Octahedral complex ($ML_6$), bonding occurs only between orbitals of matching symmetry. We use Mulliken symbols:

Metal Orbitals	Symmetry Label	Bonding Type
$s$ (spherical)	$a_{1g}$	$\sigma$ (Sigma)
$p_x, p_y, p_z$	$t_{1u}$	$\sigma$ (Sigma)
$d_{x^2-y^2}, d_{z^2}$	$e_g$	$\sigma$ (Sigma)
$d_{xy}, d_{yz}, d_{zx}$	$t_{2g}$	$\pi$ (Pi) or Non-bonding

3. Sigma ($\sigma$) Bonding

The six ligands donate electron pairs into the metal's $s, p$, and $d_{x^2-y^2}, d_{z^2}$ orbitals.

Bonding MOs: $a_{1g}, t_{1u}, e_g$ (Filled with ligand electrons, Low Energy).
Antibonding MOs: $a_{1g}^*, t_{1u}^*, e_g^*$ (High Energy).
Non-bonding: The metal $t_{2g}$ orbitals point between ligands and do not participate in $\sigma$-bonding.

$\Delta_o$ is the energy gap between the Non-bonding $t_{2g}$ and the Antibonding $e_g^*$.

4. Pi ($\pi$) Bonding & Spectrochemical Series

This is the crucial addition by LFT. The metal $t_{2g}$ orbitals can interact with ligand $\pi$-orbitals.

A. $\pi$-Donors (Weak Field)

Ligands like $Cl^-, F^-, OH^-$ have filled p-orbitals.

Interaction pushes metal $t_{2g}$ UP in energy (Antibonding character).
Result: $\Delta_o$ decreases. (Small gap $\to$ High Spin).

B. $\pi$-Acceptors (Strong Field)

Ligands like $CO, CN^-$ have empty $\pi^*$ orbitals (Back-bonding).

Interaction pushes metal $t_{2g}$ DOWN in energy (Bonding character).
Result: $\Delta_o$ increases. (Large gap $\to$ Low Spin).

                    Summary of Field Strength:

                    $\pi$-Donor < $\sigma$-only ($NH_3$) < $\pi$-Acceptor

5. The Nephelauxetic Effect

"Cloud Expanding" Effect.

When electrons form covalent bonds, the electron cloud expands over the ligands, reducing inter-electronic repulsion (Racah parameter $B$).

$B_{complex} < B_{free\_ion}$
The ratio $\beta = B_{complex}/B_{free}$ measures Covalency.
Smaller $\beta$ $\rightarrow$ Greater cloud expansion $\rightarrow$ More Covalent Character.

Practice Quiz

Test your knowledge on LFT and Bonding.

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