Coordination number, isomerism in transition-metal compounds; CFT (octahedral, tetrahedral and Square Planar)

Coordination Number, Isomerism & Crystal Field Theory

1. Coordination compounds — basics

Complex = central metal ion + ligands (electron-pair donors) in coordination sphere: e.g. $[Cu(NH_3)_4]^{2+}$, $[Fe(CN)_6]^{3-}$.

• Coordination number (CN): number of donor atoms directly bonded to metal. Common: CN = 4 (tetrahedral or square planar), CN = 6 (octahedral).
• Ligand types: monodentate (NH₃, Cl⁻, H₂O), bidentate (en = ethylenediamine, oxalate C₂O₄²⁻), polydentate (EDTA — hexadentate). Chelating ligands form rings → extra stability (chelate effect).
• IUPAC naming: cation first, ligands alphabetical, metal with oxidation state: $[Cu(NH_3)_4]SO_4$ = tetraamminecopper(II) sulphate; $K_4[Fe(CN)_6]$ = potassium hexacyanoferrate(II).

2. Isomerism in transition-metal compounds

(a) Structural: ionization ($[Co(NH_3)_5SO_4]Br$ vs $[Co(NH_3)_5Br]SO_4$), linkage (NO₂⁻ via N = nitro vs via O = nitrito), coordination, hydrate isomerism.
(b) Stereo:

• Geometrical (cis–trans): $[Pt(NH_3)_2Cl_2]$ — cis is the anticancer drug cisplatin, trans is inactive. $[Co(NH_3)_4Cl_2]^+$; octahedral $MA_4B_2$ shows cis–trans; $MA_3B_3$ shows facial (fac) vs meridional (mer).
• Optical: chiral complexes (e.g. $[Co(en)_3]^{3+}$, cis-$[Co(en)_2Cl_2]^+$) rotate plane-polarized light; non-superimposable mirror images ($\Delta$ / $\Lambda$).

3. Crystal Field Theory (CFT)

Ligands = point negative charges that split the five degenerate d-orbitals by repulsion.

(a) Octahedral: orbitals pointing at ligands ($d_{x^2-y^2}, d_{z^2}$ = $e_g$ set) rise; others ($d_{xy}, d_{xz}, d_{yz}$ = $t_{2g}$ set) fall. Gap = $\Delta_o$.

      _ e_g  (2 orbitals, +0.6Δo each)
Δo ↕
     ___ t2g (3 orbitals, −0.4Δo each)

(b) Tetrahedral: reverse pattern, gap $\Delta_t \approx \frac{4}{9}\Delta_o$ — always high spin (gap too small to pair electrons).
(c) Square planar (common for $d^8$: Ni²⁺, Pd²⁺, Pt²⁺): $d_{x^2-y^2}$ highest (points at all 4 ligands); large splitting → usually low-spin, diamagnetic.

4. High-spin vs low-spin, CFSE, spectrochemical series

• Weak-field ligands (I⁻ < Br⁻ < Cl⁻ < F⁻ < H₂O) → small $\Delta$ → high spin (max unpaired). Strong-field (CN⁻, CO, en, NH₃) → large $\Delta$ → low spin (paired).
• CFSE = $(-0.4n_{t2g} + 0.6n_{eg})\Delta_o$ (+ pairing energy $P$ per extra pair).
• Example: $[Fe(CN)_6]^{3-}$ ($d^5$, strong field): $t_{2g}^5$, 1 unpaired, CFSE $= -2.0\Delta_o + 2P$. $[FeF_6]^{3-}$ (weak field): $t_{2g}^3e_g^2$, 5 unpaired, CFSE $= 0$.
• Colour: absorbed photon promotes $t_{2g} \to e_g$ electron; observed colour is complementary. $[Cu(H_2O)_6]^{2+}$ blue, $[CoCl_4]^{2-}$ deep blue.
• Magnetic moment (spin-only): $\mu = \sqrt{n(n+2)}$ BM, $n$ = unpaired electrons.

Exam Points

• IUPAC name + CN + oxidation state of a given complex (3 marks, always asked).
• Cis–trans / fac–mer / optical isomer sketches (3–5 marks).
• Octahedral splitting diagram, spectrochemical series, high-spin vs low-spin decision + CFSE and $\mu$ numerical (5 marks favourite).