Crystal Field Theory (CFT) | Coordination Compounds Class 12

Crystal Field Theory (CFT)

Bonding, Color & Magnetism in Complexes | Class 12

1. Core Concepts

                    Assumption: CFT treats the metal-ligand bond as purely ionic (electrostatic). Ligands are treated as point charges.
                

When ligands approach the central metal ion, the degeneracy (equal energy) of the five d-orbitals is lifted due to unequal repulsion, causing them to split into different energy levels.

2. Crystal Field Splitting in Octahedral Complexes ($\Delta_o$)

Ligands approach along the axes ($x, y, z$).

$e_g$ orbitals ($d_{x^2-y^2}, d_{z^2}$): Lie along the axes. They experience maximum repulsion and their energy increases.
$t_{2g}$ orbitals ($d_{xy}, d_{yz}, d_{zx}$): Lie between the axes. They experience less repulsion and their energy decreases.

$$ \Delta_o = 10 \, Dq $$ Energy Gap: $E(e_g) = +0.6 \Delta_o$, $E(t_{2g}) = -0.4 \Delta_o$

CFSE Calculation:
$$ CFSE = [-0.4(n_{t2g}) + 0.6(n_{eg})] \Delta_o + nP $$ Where $P$ is pairing energy.

3. Crystal Field Splitting in Tetrahedral Complexes ($\Delta_t$)

Ligands approach from between the axes. The splitting pattern is inverted.

$t_2$ orbitals: Higher Energy (Closer to ligands).
$e$ orbitals: Lower Energy.

$$ \Delta_t \approx \frac{4}{9} \Delta_o $$

Since $\Delta_t$ is always small ($\Delta_t < P$), tetrahedral complexes are almost always High Spin.

4. Electronic Configuration & Spin

The filling of electrons depends on the magnitude of Crystal Field Splitting Energy ($\Delta_o$) vs Pairing Energy ($P$).

A. Strong Field Ligands ($\Delta_o > P$)

Electrons pair up in lower orbitals first. Forms Low Spin Complexes.

B. Weak Field Ligands ($\Delta_o < P$)

Electrons enter higher orbitals before pairing. Forms High Spin Complexes.

                    Spectrochemical Series (Increasing Strength):

                    $I^- < Br^- < Cl^- < F^- < OH^- < H_2O < NH_3 < en < CN^- < CO$

5. Color of Complexes

Color arises due to the d-d transition of electrons. When white light falls on the complex, an electron excites from lower d-orbital to higher d-orbital by absorbing specific wavelength. The complementary color is observed.

Note: Substances with $d^0$ or $d^{10}$ configuration are generally colorless (No d-d transition possible).

Practice Quiz

Test your ability to apply CFT.

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