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Concept 05 / 06Coordination Compounds

Crystal Field Theory: Splitting, Spectrochemical Series, Colour and Magnetism

Crystal field theory as an electrostatic model, splitting of d orbitals in octahedral and tetrahedral fields, crystal field splitting energy and CFSE, pairing energy and high-spin versus low-spin configurations, the spectrochemical series, colour of complexes from d-d transitions, and limitations of CFT.

Figure 1
Crystal field theory (CFT) treats metal-ligand bonding as purely electrostatic: ligands are point charges (anions) or point dipoles (neutral molecules) that repel the metal's d electrons. In a free ion the five d orbitals are degenerate; in a field of ligands, the degeneracy is lifted (crystal field splitting). Octahedral field (see figure). Six ligands approach along the xx, yy and zz axes. The dx2−y2d_{x^{2}-y^{2}} and dz2d_{z^{2}} orbitals point directly at the ligands and are raised in energy (the ege_{g} set); dxyd_{xy}, dyzd_{yz} and dxzd_{xz} point between the ligands and are lowered (the t2gt_{2g} set). The energy gap is Δo\Delta_{o}; relative to the barycentre, ege_{g} is at +0.6Δo+0.6\Delta_{o} and t2gt_{2g} at −0.4Δo-0.4\Delta_{o}. Filling: d1d^{1} to d3d^{3} go into t2gt_{2g}. For d4d^{4}, the fourth electron can either pair in t2gt_{2g} (costing the pairing energy PP) or enter ege_{g} (costing Δo\Delta_{o}): if Δo<P\Delta_{o} < P (weak-field ligands): t2g3eg1t_{2g}^{3}e_{g}^{1}, high spin; if Δo>P\Delta_{o} > P (strong-field ligands): t2g4eg0t_{2g}^{4}e_{g}^{0}, low spin. Similar choices arise for d5d^{5}, d6d^{6} and d7d^{7}. Crystal field stabilisation energy: CFSE =(−0.4x+0.6y)Δo+nP= (-0.4x + 0.6y)\Delta_{o} + nP for t2gxegyt_{2g}^{x}e_{g}^{y} (nn = extra pairs). Tetrahedral field. The ligands lie between the axes, so the splitting is reversed: ee (two orbitals) lower and t2t_{2} (three orbitals) higher. Δt=49Δo\Delta_{t} = \frac{4}{9}\Delta_{o}, so small that pairing is never favoured: tetrahedral complexes are almost always high spin. Spectrochemical series. Ligands arranged in increasing field strength (increasing Δo\Delta_{o}): I−<Br−<SCN−<Cl−<S2−<F−<OH−<C2O42−<H2O<NCS−<edta4−<NH3<en<CN−<CO\mathrm{I^{-} < Br^{-} < SCN^{-} < Cl^{-} < S^{2-} < F^{-} < OH^{-} < C_{2}O_{4}^{2-} < H_{2}O < NCS^{-} < edta^{4-} < NH_{3} < en < CN^{-} < CO}. Weak-field ligands (left) give high-spin complexes; strong-field ligands (right) give low-spin complexes. Δo\Delta_{o} also increases with metal oxidation state and down a group (4d, 5d complexes are low spin). Colour. When white light falls on a complex, an electron can be promoted from t2gt_{2g} to ege_{g} by absorbing light of energy Δo\Delta_{o} (d-d transition); the complex shows the complementary colour. [Ti(H2O)6]3+\mathrm{[Ti(H_{2}O)_{6}]^{3+}} (t2g1t_{2g}^{1}) absorbs blue-green light (about 498 nm498\,\mathrm{nm}) and appears violet. Without ligands no splitting occurs, so anhydrous CuSO4\mathrm{CuSO_{4}} is white and CuSO4⋅5H2O\mathrm{CuSO_{4} \cdot 5H_{2}O} is blue. Changing ligands changes Δo\Delta_{o} and colour: [Ni(H2O)6]2+\mathrm{[Ni(H_{2}O)_{6}]^{2+}} is green, and successive replacement of water by en shifts the colour to blue and then violet ([Ni(en)3]2+\mathrm{[Ni(en)_{3}]^{2+}}), as Δo\Delta_{o} increases. Limitations. Treating ligands as point charges ignores covalent bonding; anionic ligands should then give the largest splitting, but they lie at the weak end of the series; and neutral CO gives the largest splitting. Ligand field and molecular orbital theories address this. Key Takeaways: - Octahedral: ege_{g} up (+0.6Δo+0.6\Delta_{o}), t2gt_{2g} down (−0.4Δo-0.4\Delta_{o}); tetrahedral reversed, Δt=49Δo\Delta_{t} = \frac{4}{9}\Delta_{o}. - Low spin when Δo>P\Delta_{o} > P (strong-field ligands), high spin when Δo<P\Delta_{o} < P. - Spectrochemical series from I−\mathrm{I^{-}} (weakest) to CO (strongest). - Colour: d-d absorption of energy Δo\Delta_{o}; complementary colour observed. - Pitfall: tetrahedral complexes are high spin because Δt\Delta_{t} is small, not because their ligands are weak. Brain-Teaser 1: Write the t2gt_{2g}/ege_{g} configuration and number of unpaired electrons for d6d^{6} ions in (a) [CoF6]3−\mathrm{[CoF_{6}]^{3-}} and (b) [Co(NH3)6]3+\mathrm{[Co(NH_{3})_{6}]^{3+}}. Solution: (a) F−\mathrm{F^{-}} is weak field: t2g4eg2t_{2g}^{4}e_{g}^{2}, 44 unpaired (high spin). (b) NH3\mathrm{NH_{3}} with Co3+\mathrm{Co^{3+}} is strong field: t2g6eg0t_{2g}^{6}e_{g}^{0}, 00 unpaired (low spin, diamagnetic). Brain-Teaser 2: Calculate the CFSE of [Fe(CN)6]4−\mathrm{[Fe(CN)_{6}]^{4-}} in terms of Δo\Delta_{o} and PP. Solution: Fe2+\mathrm{Fe^{2+}} d6d^{6} low spin: t2g6t_{2g}^{6}. CFSE =6×(−0.4Δo)=−2.4Δo= 6 \times (-0.4\Delta_{o}) = -2.4\Delta_{o}, plus 2P2P for the two additional pairings compared with the high-spin arrangement (net CFSE =−2.4Δo+2P= -2.4\Delta_{o} + 2P). Brain-Teaser 3: [Ti(H2O)6]3+\mathrm{[Ti(H_{2}O)_{6}]^{3+}} absorbs at 498 nm498\,\mathrm{nm}. Calculate Δo\Delta_{o} in kJ mol−1\mathrm{kJ\,mol^{-1}}. Solution: E=hcNAλ=6.626×10−34×3×108×6.022×1023498×10−9=2.40×105 J mol−1=240 kJ mol−1E = \frac{hcN_{A}}{\lambda} = \frac{6.626 \times 10^{-34} \times 3 \times 10^{8} \times 6.022 \times 10^{23}}{498 \times 10^{-9}} = 2.40 \times 10^{5}\,\mathrm{J\,mol^{-1}} = 240\,\mathrm{kJ\,mol^{-1}}.

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