# Unit 1: Theories of Metal-Ligand bonding in complexes (CH431) ## Crystal Field Theory (CFT) - Proposed by **Bethe and Van Vleck**. Treats metal-ligand interaction as purely **electrostatic** between metal cation and ligands as **point charges (or dipoles)**; ligands only perturb the metal d orbitals. - In a free ion the five d orbitals are degenerate; in a ligand field they **split** in energy depending on geometry. Splitting depends on metal, oxidation state, ligands and geometry. ## Octahedral Splitting - Ligands approach along the axes. $d_{x^2-y^2}$ and $d_{z^2}$ ($e_g$) point at ligands and are **raised**; $d_{xy}, d_{yz}, d_{xz}$ ($t_{2g}$) lie between axes and are **lowered**. - Splitting energy $\Delta_o$ (10 Dq): $t_{2g}$ at $-0.4\Delta_o$ ($-4$ Dq) and $e_g$ at $+0.6\Delta_o$ ($+6$ Dq) relative to barycentre. - **Crystal field stabilisation energy (CFSE)** = $(-0.4 n_{t2g} + 0.6 n_{eg})\Delta_o + $ pairing terms. - **Strong field (low spin)** when $\Delta_o > P$ (pairing energy); **weak field (high spin)** when $\Delta_o < P$. For $d^4$–$d^7$ both are possible. Example: $[Fe(H_2O)_6]^{2+}$ high spin ($t_{2g}^4e_g^2$), $[Fe(CN)_6]^{4-}$ low spin ($t_{2g}^6$). - **Spectrochemical series**: $I^- < Br^- < Cl^- < F^- < OH^- < C_2O_4^{2-} < H_2O < NCS^- < NH_3 < en < bipy < phen < NO_2^- < CN^- < CO$. - $\Delta_o$ increases with oxidation state, down a group (3d < 4d < 5d, about 30-50%). ## Tetrahedral Splitting - Four ligands on alternate cube corners; $e$ orbitals ($d_{z^2}$, $d_{x^2-y^2}$) lowered by $-0.6\Delta_t$, $t_2$ raised by $+0.4\Delta_t$. - $\Delta_t = \frac{4}{9}\Delta_o$; always **high spin** (small $\Delta_t$). CFSE values are small; hence tetrahedral complexes preferred for $d^0, d^5, d^{10}$ and with large ligands ($[CoCl_4]^{2-}$, $[NiCl_4]^{2-}$). ## Square Planar Splitting - Derived from octahedral by removing the z-axis ligands: energy order approximately $d_{x^2-y^2} \gg d_{xy} > d_{z^2} > d_{xz}, d_{yz}$. - Favoured for **$d^8$ metal ions with strong-field ligands** (large $\Delta$): $[Ni(CN)_4]^{2-}$, $[PtCl_4]^{2-}$, $[Pd(NH_3)_4]^{2+}$, Rh(I), Ir(I), Au(III). Diamagnetic. $[NiCl_4]^{2-}$ is tetrahedral (weak ligand) and paramagnetic. - **[Figure: d-orbital splitting diagram]**: three columns for octahedral, tetrahedral and square planar showing relative levels of d orbitals. ## Limitations of CFT - Considers ligands as point charges, ignoring **covalency** (cannot explain why neutral CO and anionic F- fall at extremes of spectrochemical series). - Cannot explain the **nephelauxetic effect** or charge transfer spectra; ignores **pi-bonding**; assumes metal orbitals only d. - Does not explain stability of complexes with very small difference in electrostatics (low oxidation state complexes). - Lead to **Ligand Field Theory** (CFT with covalency parameters) and **MOT**. ## Jahn-Teller Effect - **Statement**: any non-linear molecule in a degenerate electronic ground state undergoes distortion to remove the degeneracy and lower energy. - Strong in octahedral complexes with **degenerate $e_g$** occupation: $d^9$ ($t_{2g}^6e_g^3$, e.g. $Cu^{2+}$), high-spin $d^4$ ($Cr^{2+}$, $Mn^{3+}$), low-spin $d^7$. - **Manifestation**: **tetragonal distortion** - elongation along z (two long, four short bonds) more common than compression; $d_{z^2}$ lowered, $d_{x^2-y^2}$ raised; $t_{2g}$ degeneracy gives weak effect. - Consequences: unequal bond lengths in $[Cu(H_2O)_6]^{2+}$, broad absorption band, irregular stability constants (Irving-Williams series), variation in CFSE. ## Molecular Orbital Theory (MOT) - Metal valence orbitals ($nd$, $(n+1)s$, $(n+1)p$) and ligand sigma orbitals combine by symmetry to give **bonding, non-bonding and antibonding MOs**. In octahedral: $a_{1g}$, $t_{1u}$, $e_g$ (sigma bonding); the metal $t_{2g}$ are **non-bonding** in sigma-only model; antibonding $e_g^*$ ($\sigma^*$). - 12 electrons from six ligands fill the six bonding MOs; metal d electrons occupy $t_{2g}$ and $e_g^*$. **$\Delta_o$ = energy gap between $t_{2g}$ and $e_g^*$.** - **Pi bonding**: $\pi$-donor ligands (halides) interact with $t_{2g}$ lowering $\Delta_o$ (weak field); **$\pi$-acceptor ligands** (CO, CN-, phosphines) with empty pi* orbitals stabilise $t_{2g}$ and raise $\Delta_o$ (strong field) - explains the spectrochemical series. **Back bonding** in metal carbonyls. - MOT accounts for covalency, magnetic properties, spectra and bonding in low-valent complexes; more complicated than CFT. ## Likely Exam Questions 1. Define CFSE and calculate it for a $d^6$ ion in strong field. (2 marks) 2. Why are tetrahedral complexes mostly high spin? (2 marks) 3. Explain d-orbital splitting in octahedral, tetrahedral and square planar fields. (long) 4. State and explain the Jahn-Teller effect with examples. (long) 5. Discuss limitations of CFT. (long) 6. Explain MO diagram of octahedral complex with sigma and pi bonding. (long)