GATE 2026 CY – Question 59

Inorganic Chemistry · Transition Metals: Coordination chemistry – structure and isomerism, theories of bonding (VBT, CFT, and MOT). Metal-metal multiple bonds. Energy level diagrams in various crystal fields, CFSE, applications of CFT, Jahn-Teller distortion. Electronic spectra of transition metal complexes: spectroscopic term symbols, selection rules, Orgel and Tanabe-Sugano diagrams, nephelauxetic effect and Racah parameter, charge-transfer spectra. Magnetic properties of transition metal complexes. Ray-Dutt and Bailar twists, Reaction mechanisms: kinetic and thermodynamic stability, associative, dissociative substitution and redox reactions. · 2 marks · Numerical answer

The sum of metal–metal bond orders in $[\mathrm{Os_2Cl_8}]^{2-}$, $[\mathrm{Re_2Cl_8}]^{2-}$, $[\mathrm{W_2(NMe_2)_6}]$, and $[\mathrm{Mo(C_5H_5)(CO)_2}]_2$ is _____ (integer).

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Correct answer: 13

Explanation

The metal-metal bond order is found from the number of electrons in the metal-based bonding and antibonding orbitals.

**$[\text{Os}_2\text{Cl}_8]^{2-}$:** the oxidation state of Os is +3 ($d^5$ each) with 10 $d$ electrons in the dimer, filling $\sigma^2\pi^4\delta^2\delta^{*2}\pi^{*0}$. The bond order is $(2+4+2-2)/2=3$.
**$[\text{Re}_2\text{Cl}_8]^{2-}$:** Re(III) is $d^4$; the 8 electrons fill $\sigma^2\pi^4\delta^2$, the **quadruple bond**, bond order 4.
**$[\text{W}_2(\text{NMe}_2)_6]$:** W(III) is $d^3$; the 6 electrons fill $\sigma^2\pi^4$, a **triple bond**, bond order 3.
**$[\text{CpMo(CO)}_2]_2$** (so-called $\text{Cp}_2\text{Mo}_2(\text{CO})_4$): each Mo fragment has 15 electrons and needs 3 more to reach 18, so a **triple bond** Mo≡Mo, bond order 3.

**Sum:**
$$3+4+3+3=\mathbf{13}.$$