Chemistry · Ch 10 — Coordination Compounds

Summary

Ligands and denticity: a ligand donates a lone pair to the central metal through one or more donor atoms — monodentate (one donor, e.g. $\text{NH}_3$ , $\text{Cl}^-$ ), bidentate (two donors, e.g. $\text{en}$ , oxalate), polydentate (three or more, e.g. hexadentate EDTA $^{4-}$ ). Di-/polydentate ligands are chelating ligands; ambidentate ligands ( $\text{SCN}^-$ , $\text{NO}_2^-$ ) can bind through either of two donor atoms.
Spectrochemical series: ligands rank from weak field ( $\text{I}^- < \text{Br}^- < \text{Cl}^- < \text{F}^-$ ) to strong field ( $\text{NH}_3 < \text{en} < \text{CN}^- \approx \text{CO}$ ), by how strongly they split the metal's d-orbitals.
Coordination number: total donor atoms bonded to the metal — counted per donor atom, not per ligand (a bidentate ligand contributes 2).
Colour arises from $d$ - $d$ electronic transitions across the crystal-field gap $\Delta_o$ ; $d^0$ ( $\text{Sc}^{3+}$ ) and $d^{10}$ ( $\text{Zn}^{2+}$ ) ions are colourless (no possible transition).
Magnetic properties: whether a $d^4$ - $d^7$ complex is paramagnetic (high-spin) or diamagnetic/less-paramagnetic (low-spin) depends on comparing $\Delta_o$ against the pairing energy $P$ ; e.g. weak-field $[\text{CoF}_6]^{3-}$ (4 unpaired) versus strong-field $[\text{Co}(\text{NH}_3)_6]^{3+}$ (0 unpaired).
Shapes: coordination number 2 = linear, 6 = octahedral (almost always); coordination number 4 = tetrahedral (weak field / $sp^3$ ) or square planar (strong field, $d^8$ , $dsp^2$ ), e.g. $[\text{NiCl}_4]^{2-}$ vs $[\text{Ni}(\text{CN})_4]^{2-}$ .
IUPAC nomenclature: cation before anion; ligands alphabetical before metal; anionic ligands end "-o" (chloro, cyano); special names aqua, ammine, carbonyl, nitrosyl; bis/tris/tetrakis for composite ligand names; metal oxidation state in Roman numerals; "-ate" ending for anionic complexes (ferrate, cuprate, argentate).
EAN rule: $\text{EAN} = Z - x + 2(\text{CN})$ ; many stable complexes reach the electron count of the next noble gas (e.g. 36, matching krypton, for $[\text{Fe}(\text{CN})_6]^{4-}$ , $[\text{Co}(\text{NH}_3)_6]^{3+}$ , $[\text{Ni}(\text{CO})_4]$ ).
Werner's theory: a metal shows a primary valence (ionizable, matches oxidation state) and a secondary valence (non-ionizable, fixed, directional, matches coordination number) simultaneously — explains why $\text{CoCl}_3.6\text{NH}_3$ , $.5\text{NH}_3$ , $.4\text{NH}_3$ precipitate 3, 2, 1 mol $\text{AgCl}$ respectively.
Valence bond theory: hybridization of metal orbitals fixes geometry and magnetism — $d^2sp^3$ (inner orbital, low-spin) vs $sp^3d^2$ (outer orbital, high-spin) for octahedral; $dsp^2$ (square planar) vs $sp^3$ (tetrahedral) for 4-coordinate.
Crystal field theory: in an octahedral field, d-orbitals split into lower $t_{2g}$ (3 orbitals, $-0.4\Delta_o$ ) and higher $e_g$ (2 orbitals, $+0.6\Delta_o$ ); in a tetrahedral field the order reverses (lower $e$ , higher $t_2$ ) and $\Delta_t \approx \tfrac{4}{9}\Delta_o$ — always too small for low-spin, so tetrahedral complexes are always high-spin.
CFSE $= (-0.4\,n_{t_{2g}} + 0.6\,n_{e_g})\Delta_o$ ; high-spin vs low-spin for $d^4$ - $d^7$ is decided by comparing $\Delta_o$ against pairing energy $P$ . …

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