Let's address each part step-by-step for the **[CoF₆]³⁻** complex: --- ## 1. Molecular Orbital Diagram for Sigma Bonding in [CoF₆]³⁻ - **Central atom:** Co³⁺ (Cobalt in +3 state; d⁶ configuration) - **Ligand:** F⁻ (Fluoride ion, weak field, σ-donor) - **Geometry:** Octahedral ### Construction - The 6 F⁻ ligands provide 6 pairs of electrons for bonding (σ-donation). - The metal uses its 4s, 4p, and 3d orbitals for bonding. - Only the \( t_{2g} \) and \( e_g \) symmetry-adapted combinations of d orbitals participate. ``` Ligand group orbitals (LGOs): σ1 σ2 σ3 σ4 σ5 σ6 Metal orbitals: 4s 4p_x 4p_y 4p_z 3d_x2-y2 3d_z2 3d_xy 3d_xz 3d_yz MO formation (Octahedral, Oh symmetry): - σ LGOs combine with 4s, 4p, and eg (d_x2-y2, d_z2) orbitals → σ bonding and antibonding MOs. - t2g (d_xy, d_xz, d_yz) remain non-bonding (do not participate in sigma bonding). ``` ### **Molecular Orbital Diagram** (Text Representation) ``` σ* (antibonding, eg*) | ----- | | | | (eg*: from 4s, 4p, d_x2-y2, d_z2) ----- | t2g (non-bonding: d_xy, d_xz, d_yz) | ----- | | | | (eg: from 4s, 4p, d_x2-y2, d_z2) ----- | σ (bonding) ``` --- ## 2. Label and Allocate Electrons - **Co³⁺:** 3d⁶ configuration (6 d electrons) - **6 F⁻ ligands:** Each donates 2 electrons = 12 electrons (for σ bonding) - **Total electrons in bonding MOs:** 12 (from ligands) + 6 (from Co³⁺ d electrons in t2g) = 18 electrons Electrons fill: - Lower σ bonding MOs (from LGOs, 4s, 4p, eg) - t2g (non-bonding) filled next (6 electrons: all paired) - eg* (antibonding) is empty (no electrons) --- ## 3. High Spin or Low Spin? Calculate CFSE - F⁻ is a **weak field ligand** → **High Spin** complex - 3d⁶ high spin: Electron configuration in t2g and eg* is: - t2g: 4 electrons (↑↓ ↑ ↑) - eg*: 2 electrons (↑ ↑) But in octahedral field splitting: - **t2g**: 3 orbitals, eg: 2 orbitals - For high spin \( d^6 \): t2g⁴ eg² **CFSE (Crystal Field Stabilization Energy):** \[ CFSE = [(\text{No. e⁻ in t2g}) \times (-.4\Delta_o)] + [(\text{No. e⁻ in eg}) \times (.6\Delta_o)] \] For high spin d⁶: t2g⁴ eg² \[ CFSE = (4 \times -.4\Delta_o) + (2 \times .6\Delta_o) = -1.6\Delta_o + 1.2\Delta_o = -.4\Delta_o \] --- ## 4. Which Metal Orbitals Are Used in Forming MOs? - **4s, 4p, and eg (d_x2-y2, d_z2) orbitals** of Co³⁺ form bonding and antibonding MOs with ligand orbitals. --- ## 5. How Many MOs Are Formed? - **6 ligand orbitals** (one from each F⁻) combine with the metal 4s, 4p, and eg orbitals. - This results in **6 molecular orbitals** (3 bonding, 3 antibonding). --- ## 6. Which Metal d Orbitals Remain Non-Bonding? - **t2g (d_xy, d_xz, d_yz)** orbitals do **not** participate in sigma bonding (remain non-bonding). --- ## 7. Nature of ‘Crystal Field’ Orbitals - **t2g:** Non-bonding (in crystal field theory, these are the 'crystal field' orbitals) - **eg:** Antibonding (since they interact directly with ligand σ orbitals) --- ## **Summary Table** | Question | Answer | |----------|--------| | 1 | See MO diagram above (sigma bonding, octahedral) | | 2 | MOs labeled, electrons allocated as above (t2g⁴ eg² for high-spin d⁶) | | 3 | High spin, CFSE = –.4Δ₀ | | 4 | Metal 4s, 4p, d_x2-y2, d_z2 (eg) used in MOs | | 5 | 6 MOs formed from 6 ligand orbitals | | 6 | t2g (d_xy, d_xz, d_yz) remain non-bonding | | 7 | t2g = non-bonding (crystal field), eg = antibonding | --- ### **Final Answers** 1. Draw an MO diagram: See above (octahedral, sigma-bonding, t2g non-bonding, eg bonding/antibonding). 2. Label and allocate: t2g⁴ eg² (high spin), electrons from Co³⁺ and F⁻. 3. High spin; CFSE = –.4Δ₀. 4. 4s, 4p, d_x2-y2, d_z2 (eg) orbitals used. 5. 6 molecular orbitals formed (from 6 ligand orbitals). 6. t2g (d_xy, d_xz, d_yz) remain non-bonding. 7. Crystal field orbitals are non-bonding (t2g); eg are antibonding. --- **If you need a hand-drawn MO diagram, let me know!**