# Unit 8: Inorganic Spectroscopy and Magnetism (CH232) ## Electronic Spectra of Transition Metal Complexes - Absorption of visible or UV light promotes electrons to higher levels. Colours arise from **d-d transitions** ($t_{2g} \to e_g$ in octahedral), complementary to the colour absorbed. - **Types of transitions**: - **d-d (ligand field)**: weak, $\varepsilon$ about 1 to 100 L mol$^{-1}$cm$^{-1}$. - **Charge transfer**: ligand to metal (LMCT, e.g. $MnO_4^-$, $CrO_4^{2-}$) and metal to ligand (MLCT, e.g. $[Fe(bipy)_3]^{2+}$); intense, $\varepsilon$ up to $10^4$ or more. - Intraligand and $\pi \to \pi^*$ transitions. ## Selection Rules 1. **Spin rule**: $\Delta S = 0$; spin-forbidden transitions are very weak (high spin $d^5$ Mn2+ is nearly colourless, pale pink). 2. **Laporte rule**: in centrosymmetric molecules $g \to g$ (d-d) transitions are forbidden ($\Delta l = \pm1$). Octahedral complexes are weakly coloured; tetrahedral complexes (no centre) are more intense. Relaxed by **vibronic coupling**. ## Spectroscopic Ground States - Terms from $L$ and $S$: ground state by **Hund's rules** (maximum S, then maximum L). - Free-ion ground terms: $d^1$ $^2D$, $d^2$ $^3F$, $d^3$ $^4F$, $d^4$ $^5D$, $d^5$ $^6S$, $d^6$ $^5D$, $d^7$ $^4F$, $d^8$ $^3F$, $d^9$ $^2D$. - In an octahedral field $D$ splits to $T_{2g}$ and $E_g$; $F$ to $A_{2g}$, $T_{2g}$, $T_{1g}$; $S$ stays $A_{1g}$. - **L-S (Russell-Saunders) coupling**: orbital angular momenta add to $L$, spins add to $S$, then $J = L+S$. ## Spectrochemical Series - Ligands ordered by $\Delta$: $I^- < Br^- < Cl^- < F^- < OH^- < H_2O < NH_3 < en < CN^- < CO$. Strong-field ligands give large $\Delta$ and shift absorption to shorter wavelengths. - Metals: $Mn^{2+} < Ni^{2+} < Co^{2+} < Fe^{3+} < Cr^{3+} < Co^{3+} < Pt^{4+}$. ## Orgel Diagrams for $d^1$ and $d^9$ - Orgel diagrams show energy of terms against $\Delta$ for **high spin** complexes with the same ground-term symmetry. They do not include spin-forbidden transitions or pairing. - $d^1$ octahedral: ground state $^2T_{2g}$, excited $^2E_g$. $d^9$ octahedral: ground state $^2E_g$, excited $^2T_{2g}$ (inverse; hole formalism). $d^1$ tetrahedral resembles $d^9$ octahedral. - One spin-allowed transition: $^2T_{2g} \to {}^2E_g$ ($d^1$). **[Figure: Orgel diagram for $d^1$/$d^9$]** Two lines diverging with increasing $\Delta$: $^2D$ splitting into $T_{2g}$ and $E_g$. ## Spectrum of $[Ti(H_2O)_6]^{3+}$ - $Ti^{3+}$ is $d^1$; ground state $^2T_{2g}$. Single band at about 20,300 cm$^{-1}$ (about 493 nm) from $^2T_{2g} \to {}^2E_g$, so $\Delta_o \approx 20,300$ cm$^{-1}$; absorbs blue-green, appears **purple**. A shoulder arises from **Jahn-Teller** distortion of the excited $^2E_g$ state. ## Magnetic Properties - **Types**: **diamagnetic** (all electrons paired, repelled by field); **paramagnetic** (unpaired electrons, attracted); **ferromagnetic** (parallel alignment, domains, Fe, Co, Ni); **antiferromagnetic** (antiparallel, MnO). - **Magnetic susceptibility** $\chi$ and **Curie law** $\chi = C/T$; $\mu_{eff} = 2.84\sqrt{\chi_M T}$ BM. - **Methods**: **Gouy balance** (force on sample in field), **Faraday method**, Evans NMR method, SQUID. - **Spin-only formula**: $\mu_s = \sqrt{n(n+2)}$ BM, with n unpaired electrons: 1 gives 1.73, 2 gives 2.83, 3 gives 3.87, 4 gives 4.90, 5 gives 5.92 BM. - With orbital contribution: $\mu_{S+L} = \sqrt{4S(S+1)+L(L+1)}$; for first row ions orbital contribution is usually quenched. - Example: $[Fe(CN)_6]^{4-}$ low spin $d^6$, $\mu = 0$; $[FeF_6]^{3-}$ $d^5$ high spin, 5.9 BM. ## Likely Exam Questions 1. State Laporte and spin selection rules. (2 marks) 2. Why are octahedral complexes weakly coloured? 3. Explain the spectrum of $[Ti(H_2O)_6]^{3+}$. 4. Draw and explain the Orgel diagram for $d^1$ and $d^9$. 5. Calculate spin-only magnetic moment for $[Fe(H_2O)_6]^{2+}$. (2 marks) 6. Describe the Gouy method of measuring magnetic susceptibility.