Coordination Compounds - Crystal Field Theory (CFT)

Crystal Field Theory (CFT) treats the interaction between the metal ion and the ligands as a purely electrostatic one, where ligands are considered as point charges.

In a free metal ion, all five $d$-orbitals are degenerate (have equal energy). In an octahedral field, these split into two sets: $t_{2g}$ ($d_{xy}, d_{yz}, d_{zx}$) of lower energy and $e_g$ ($d_{x^2-y^2}, d_{z^2}$) of higher energy.

The energy difference between the two sets of split $d$-orbitals is denoted as $\Delta_o$ (Octahedral Crystal Field Splitting Energy).

Spectrochemical Series: Ligands are arranged in order of increasing field strength: $I^- < Br^- < SCN^- < Cl^- < S^{2-} < F^- < OH^- < C_2O_4^{2-} < H_2O < NCS^- < edta^{4-} < NH_3 < en < CN^- < CO$.

In Tetrahedral complexes, the splitting is inverted: $e$ orbitals ($d_{x^2-y^2}, d_{z^2}$) have lower energy than $t_2$ orbitals ($d_{xy}, d_{yz}, d_{zx}$). The splitting energy is $\Delta_t$.

Strong field ligands result in $\Delta_o > P$ (Pairing energy), favoring low-spin complexes (pairing occurs). Weak field ligands result in $\Delta_o < P$, favoring high-spin complexes.

The color of coordination compounds arises from $d-d$ transitions, where an electron absorbs light to move from a lower energy $d$-orbital to a higher energy $d$-orbital.