# Unit 7: Theories of Coordination Chemistry (CH232) ## Valence Bond Theory and its Limitations - Metal provides empty orbitals which hybridise and accept ligand electron pairs. - Hybridisation: $sp^3$ tetrahedral, $dsp^2$ square planar, $d^2sp^3$ (inner orbital, low spin) or $sp^3d^2$ (outer orbital, high spin) octahedral. - Examples: $[Fe(CN)_6]^{4-}$ is $d^2sp^3$, diamagnetic; $[FeF_6]^{3-}$ is $sp^3d^2$, paramagnetic; $[Ni(CN)_4]^{2-}$ is $dsp^2$ square planar; $[NiCl_4]^{2-}$ is $sp^3$ tetrahedral. - **Limitations**: gives no explanation of **colour** or electronic spectra; no quantitative treatment of magnetic properties (temperature dependence); cannot say why some $d^8$ complexes are square planar and others tetrahedral; ignores ligand strength differences (spectrochemical series); no account of thermodynamic and kinetic stability. ## Crystal Field Theory (Elementary) - Metal-ligand bond is purely **electrostatic**: ligands are point negative charges; metal d orbitals are repelled. - In a free ion the five d orbitals are degenerate. A ligand field **splits** them. **Octahedral**: ligands along axes; $e_g$ ($d_{z^2}, d_{x^2-y^2}$) point at ligands and rise by $+0.6\Delta_o$; $t_{2g}$ ($d_{xy}, d_{yz}, d_{xz}$) fall by $-0.4\Delta_o$. **CFSE** $= (-0.4n_{t_{2g}} + 0.6n_{e_g})\Delta_o + $ pairing energies. - **Strong field** ($\Delta_o > P$): pairing, low spin. **Weak field** ($\Delta_o < P$): high spin. This applies to $d^4$ to $d^7$. **[Figure: d-orbital splitting]** Energy level diagram with $t_{2g}$ below and $e_g$ above in octahedral, reversed in tetrahedral. **Tetrahedral**: no ligand along axes; $e$ (lower) and $t_2$ (higher); $\Delta_t = \frac{4}{9}\Delta_o$, so tetrahedral complexes are almost always **high spin**. **Square planar**: four ligands in the xy-plane; $d_{x^2-y^2}$ highest, then $d_{xy}$, $d_{z^2}$, with $d_{xz}, d_{yz}$ lowest. Favoured by strong field $d^8$ ions (Pd(II), Pt(II), Ni(II) with CN-). ## Jahn-Teller Effect - **Statement**: any non-linear molecule in a degenerate electronic state undergoes distortion to remove the degeneracy and lower energy. - Prominent in octahedral complexes with unsymmetrical $e_g$ occupation: $d^9$ (Cu2+), high spin $d^4$ (Cr2+, Mn3+), low spin $d^7$. - Usually **tetragonal elongation** (two long axial bonds); e.g. $[Cu(H_2O)_6]^{2+}$. - Weak distortion when $t_{2g}$ is unsymmetrically filled. ## Factors Affecting Crystal Field Parameters ($\Delta_o$) 1. **Nature of ligand**: spectrochemical series $I^- < Br^- < S^{2-} < Cl^- < F^- < OH^- < C_2O_4^{2-} < H_2O < NCS^- < NH_3 < en < bipy < NO_2^- < CN^- < CO$. 2. **Oxidation state of metal**: higher charge gives larger $\Delta$ (Co3+ > Co2+). 3. **Period of metal**: $\Delta$ increases 3d < 4d < 5d (about 30 to 50 percent each). 4. **Geometry**: $\Delta_t \approx 4/9\Delta_o$. 5. Number of ligands. ## Thermodynamic Stability of Complexes - **Stability constants**: $M + nL \rightleftharpoons ML_n$; stepwise $K_n$ and overall $\beta_n = K_1K_2\cdots K_n$. Larger $\beta$ means greater stability. Typically $K_1 > K_2 > \ldots$ - Factors: charge/size of metal, nature of ligand, **chelate effect**, Irving-Williams order $Mn < Fe < Co < Ni < Cu > Zn$. - Thermodynamic stability (extent of formation) differs from **kinetic stability** (inert vs labile). ## Hard and Soft Acids and Bases (Pearson HSAB) - **Hard acids**: small, high charge, not polarisable (H+, Li+, Al3+, Fe3+, Cr3+). **Soft acids**: large, low charge, polarisable (Ag+, Hg2+, Pt2+, Cu+). - **Hard bases**: F-, OH-, H2O, NH3, O donors. **Soft bases**: I-, CN-, CO, R3P, S donors. - Rule: **hard prefers hard, soft prefers soft**; borderline Fe2+, Cu2+, Br-. - Explains occurrence of ores (hard Ca, Al as oxides/carbonates; soft Hg, Pb as sulphides) and ambidentate bonding. ## Likely Exam Questions 1. State limitations of valence bond theory. (2 marks) 2. Explain crystal field splitting in octahedral and tetrahedral complexes. 3. Why are tetrahedral complexes mostly high spin? (2 marks) 4. Explain the Jahn-Teller effect with an example. 5. What factors affect $\Delta_o$? 6. Write notes on HSAB principle and stability constants.