# Unit 2: Spectra and magnetism of transition metals (CH314) ## Spectrochemical Series - Ligands in order of increasing field strength: $I^- < Br^- < S^{2-} < SCN^- < Cl^- < NO_3^- < F^- < OH^- < C_2O_4^{2-} < H_2O < NCS^- < py \approx NH_3 < en < bipy < phen < NO_2^- < CN^- < CO$. - Weak field halides and strong field CN- and CO ($\pi$-acceptors). Metal ions order: $Mn^{2+} < Ni^{2+} < Co^{2+} < Fe^{2+} < V^{2+} < Fe^{3+} < Cr^{3+} < V^{3+} < Co^{3+}$. - Strong field gives larger $\Delta$ and absorption at shorter wavelength (higher energy). ## Selection Rules for Electronic Transitions - **Spin selection rule**: $\Delta S = 0$; transitions with spin change are forbidden (very weak, $\varepsilon \approx 0.01$ to 1). $[Mn(H_2O)_6]^{2+}$ ($d^5$ high spin) is pale pink since all d-d transitions are spin forbidden. - **Laporte (orbital) rule**: in a molecule with a centre of symmetry, $g \leftrightarrow g$ transitions are forbidden; allowed only $g \leftrightarrow u$ ($\Delta l = \pm 1$). d-d transitions are Laporte forbidden in octahedral complexes ($\varepsilon$ 1 to 100); tetrahedral complexes have no inversion centre and show intense colours ($\varepsilon$ about 100 to 1000, e.g. $[CoCl_4]^{2-}$ deep blue). - **Relaxation**: **vibronic coupling** (asymmetric vibrations temporarily remove the centre of symmetry), d-p mixing in tetrahedral complexes, and **spin-orbit coupling** (relaxes the spin rule). - Types by intensity: spin-allowed Laporte-forbidden (octahedral d-d), spin-allowed Laporte-allowed (charge transfer), spin-forbidden. ## Colour of Complexes - Colour arises when the d-d transition falls in the visible region; the light absorbed gives the complement colour. $[Ti(H_2O)_6]^{3+}$ absorbs about 500 nm (blue-green) and looks purple; $[Cu(H_2O)_6]^{2+}$ absorbs red and looks blue; $[Cu(NH_3)_4]^{2+}$ deep blue as $\Delta$ is larger. - $d^0$ ($Sc^{3+}$, $Ti^{4+}$) and $d^{10}$ ($Zn^{2+}$, $Cu^+$) ions have no d-d transition and are colourless (unless charge transfer). ## Spectroscopic Ground States and L-S Coupling - **L-S (Russell-Saunders) coupling**: for light atoms the orbital angular momenta couple to total $L$ and spins to total $S$; the **term symbol** $^{2S+1}L_J$. **Hund's rules**: maximum multiplicity, then maximum $L$. - 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: $S \to A_{1g}$; $D \to T_{2g} + E_g$; $F \to A_{2g} + T_{2g} + T_{1g}$; $P \to T_{1g}$. - Example: $d^3$ ($V^{2+}$, $Cr^{3+}$) ground state $^4A_{2g}$ and three spin-allowed bands $^4A_{2g}\to{}^4T_{2g}$, $^4T_{1g}(F)$, $^4T_{1g}(P)$; the first gives $\Delta_o$. ## Charge Transfer Spectra - **LMCT** (ligand to metal): ligand electron moves to metal's empty or partly filled d orbital; high oxidation state metal and reducing ligand: $MnO_4^-$ (purple), $CrO_4^{2-}$ (yellow), $Cr_2O_7^{2-}$ (orange). - **MLCT** (metal to ligand): metal electron to ligand $\pi^*$; low oxidation state metals with $\pi$-acceptor ligands: $[Fe(phen)_3]^{2+}$, $[Ru(bipy)_3]^{2+}$. - **Metal-to-metal (intervalence)** e.g. Prussian blue. - Features: very intense bands ($\varepsilon \approx 10^3$ to $10^5$), allowed by both rules, usually in UV or visible. ## Types of Magnetism - **Diamagnetism**: all electrons paired; weakly repelled; $\chi$ negative and independent of T. - **Paramagnetism**: unpaired electrons; attracted; $\chi$ positive; temperature dependent. - **Ferromagnetism**: parallel alignment of spins in domains (Fe, Co, Ni, $CrO_2$); lost above the **Curie temperature**. - **Antiferromagnetism**: antiparallel coupling (MnO, $Cr_2O_3$); above the **Neel temperature** becomes paramagnetic. - **Ferrimagnetism**: unequal antiparallel moments ($Fe_3O_4$, ferrites). ## Temperature Dependence: Curie and Curie-Weiss Laws - **Curie law**: $\chi_M = \frac{C}{T}$ for magnetically dilute paramagnets; $\mu_{eff} = 2.828\sqrt{\chi_MT}$ BM. - **Curie-Weiss law**: $\chi_M = \frac{C}{T - \theta}$; $\theta$ is the Weiss constant; **$\theta > 0$** ferromagnetic interaction, **$\theta < 0$** antiferromagnetic. - Plot of $1/\chi$ vs T is a straight line with intercept at $\theta$. ## Measurement of Magnetic Susceptibility - **Gouy method**: a long cylindrical sample hangs between the poles of an electromagnet with one end in a strong field and the other at negligible field; the **apparent change in mass** $\Delta w$ with the field on and off is related to susceptibility: $\chi_g = \frac{\beta\Delta w + \ldots}{\ldots}$ (calibrated using $Hg[Co(NCS)_4]$ or $[Ni(en)_3]S_2O_3$). Simple but needs relatively large sample (about 1 g). **[Figure: Gouy balance]** Sample tube suspended from a balance between magnet poles. - **Faraday method**: small sample in a **non-uniform field** with constant $H\,dH/dx$; force is measured on a microbalance; requires only milligram quantities and is more sensitive. - Diamagnetic corrections (Pascal's constants) are applied; $\mu_s = \sqrt{n(n+2)}$. ## Likely Exam Questions 1. State the Laporte and spin selection rules. Why do octahedral complexes show weak colour? 2. Write the spectrochemical series. (2 marks) 3. Explain LMCT and MLCT with examples. 4. Describe the term symbols and ground states for $d^n$ ions. 5. State Curie and Curie-Weiss laws. 6. Explain the Gouy and Faraday methods.