UPSC Civil Services (Mains), Chemistry optional · 2018 · Paper I

Q8(a)(ii). Number of Re–Re bonds in [Re₂Cl₈]²⁻

Question

Determine the number of metal-metal bond(s) in [Re₂Cl₈]²⁻ (Z=75) using simplified MO energy level diagram.

Each Re(III) is d⁴; the eight d electrons fill σ²π⁴δ²: bond order 4, a quadruple Re–Re bond (one σ, two π, one δ).

2x+8(-1)=-2, so x=+3. Re (Z=75) is [Xe]4f¹⁴5d⁵6s²; Re(III) is 5d⁴: eight d electrons for the Re–Re bond.
Take z along Re–Re. d_(x²-y²) of each Re is used for the four Re–Cl bonds. The other four d orbitals overlap with those of the second Re: d_(z²) (σ), d_(xz) and d_(yz) (two π), d_(xy) face to face (δ).
σ<π<δ<δ*<π*<σ*. Eight electrons: σ²π⁴δ², all antibonding orbitals empty.
bond order=12(8-0)=4: one quadruple Re–Re bond

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

Charge: 2x+8(-1)=-2, so x=+3. Re (Z=75) is [Xe]4f¹⁴5d⁵6s²; Re(III) is 5d⁴: eight d electrons for the Re–Re bond.
Take z along Re–Re. d_(x²-y²) of each Re is used for the four Re–Cl bonds. The other four d orbitals overlap with those of the second Re: d_(z²) (σ), d_(xz) and d_(yz) (two π), d_(xy) face to face (δ).
Energy order: σ<π<δ<δ*<π*<σ*. Eight electrons: σ²π⁴δ², all antibonding orbitals empty.
bond order=12(8-0)=4: one quadruple Re–Re bond
The δ bond needs the d_(xy) orbitals face to face, so the two ReCl₄ units are eclipsed (D₄ₕ) although staggering would reduce Cl…Cl repulsion; Re–Re is very short (224 pm). Diamagnetic; the δ→δ* transition makes it blue.

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