The complex(es) having metal-metal bond order 3.5 is/are [Given: The atomic numbers of Mo, Cr, Mn, and Re are 42, 24, 25, and 75, respectively.]

$[\mathrm{Mo_2(\mu\text{-}HPO_4)_4(H_2O)_2}]^{2-}$

GATE 2025 CY – Question 51

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 · Multiple select

The complex(es) having metal-metal bond order $\ge3.5$ is/are [Given: The atomic numbers of Mo, Cr, Mn, and Re are 42, 24, 25, and 75, respectively.]

$[\mathrm{Mo_2(\mu\text{-}SO_4)_4(H_2O)_2}]^{3-}$
$[\mathrm{Mn_2(CO)_{10}}]$
$[\mathrm{Cr_2(\mu\text{-}O_2CCH_3)_4}]$
$[\mathrm{Mo_2(\mu\text{-}HPO_4)_4(H_2O)_2}]^{2-}$

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Correct answer: (A) $[\mathrm{Mo_2(\mu\text{-}SO_4)_4(H_2O)_2}]^{3-}$; (C) $[\mathrm{Cr_2(\mu\text{-}O_2CCH_3)_4}]$

Explanation

The **metal-metal bond order** in a dimer is found from the number of electrons in the bonding and antibonding $\sigma$, $\pi$ and $\delta$ orbitals formed by the $d$ orbitals.

**A. $[\text{Mo}_2(\text{SO}_4)_4(\text{H}_2\text{O})_2]^{3-}$:** each sulfate is 2−, so $4\times(-2)=-8$ and the dimer is $\text{Mo}_2^{5+}$, a $d^4$-$d^3$ pair, with 7 electrons in $\sigma^2\pi^4\delta^1$. The bond order is $(2+4+1)/2=3.5$. ✓
**B. $[\text{Mn}_2(\text{CO})_{10}]$:** one Mn–Mn single bond. Bond order 1. ✗
**C. $[\text{Cr}_2(\mu\text{-O}_2\text{CCH}_3)_4]$:** the classic quadruple bond, $\sigma^2\pi^4\delta^2$ with 8 electrons. Bond order 4. ✓
**D. $[\text{Mo}_2(\text{HPO}_4)_4(\text{H}_2\text{O})_2]^{2-}$:** here the dimer is $\text{Mo}_2^{6+}$ ($d^3$-$d^3$, 6 electrons in $\sigma^2\pi^4$). The bond order is 3. ✗

Bond order $\geq3.5$: **A and C**.