Chen and Sakaki's 2017 DFT study attributed the exceptional reactivity of the Mo–Mo quintuple bond in Mo2(N^N)2 (N^N = bis(2,6-diisopropylphenyl)formamidinate) toward H–H, C–H, and O–H σ-bond cleavage to strong polarization of dδ-type metal–metal orbitals in the transition state — a frustrated-Lewis-pair-like arrangement of donor and acceptor regions on the two molybdenum atoms — and derived from it a design principle: unsymmetrical chelate ligands that pre-polarize the Mo–Mo bond already in the ground state should lower σ-bond activation barriers further. The study's computational predictions (barrierless H–H cleavage to cis-dihydride intermediates, kinetically feasible methane C–H and methanol O–H activation, THF-assisted cis-to-trans isomerization) and the design principle remain untested: no subsequent study has synthesized designed unsymmetrical-chelate metal–metal multiple-bond complexes and compared their σ-bond activation reactivity with symmetric controls, observed the predicted cis-dihydride or C–H/O–H activation products experimentally, subjected the σ-activation transition states to higher-level computations on the full experimental complex, or systematically mapped the mechanism's scope across other metals, bond orders, and ligand environments. The open problem is to establish — or refute and bound — the transition-state-polarization mechanism and the derived ground-state pre-polarization design principle as a validated account of σ-bond activation at metal–metal multiple bonds, at the source's full generality.

Background

Metal–metal multiple bonds are shared-electron bonds between two transition-metal atoms. They progress from Cotton's quadruple bonds (one σ, two π, and one δ bonding pair; eight electrons) to quintuple bonds, formally σ2π4δ4\sigma^2\pi^4\delta^4 with ten bonding electrons, first realized for Cr–Cr in 2005 and for Mo–Mo in 2009 by two-electron reduction of quadruply bonded dimolybdenum amidinate precursors (Tsai et al.). An amidinate (here, formamidinate) ligand is the monoanion [RN−C(H)−NR]−[\mathrm{RN{-}C(H){-}NR}]^{-}, which bridges both metal atoms through its two nitrogen donors; with two such ligands a Mo(I)–Mo(I) core, formally d5d^5–d5d^5, carries ten electrons that fill the five Mo–Mo bonding orbitals. The resulting complex Mo2{μ-κ2-HC(N-2,6-iPr2C6H3)2}2\mathrm{Mo_2\{\mu\text{-}\kappa^2\text{-}HC(N\text{-}2,6\text{-}iPr_2C_6H_3)_2\}_2} (abbreviated Mo2(N∧N)2\mathrm{Mo_2(N^{\wedge}N)_2} below) is a low-coordinate, air-sensitive species with one of the shortest known Mo–Mo distances.

Historically, metal–metal multiple bonds were characterized mainly structurally, and their reactions generally required highly reactive reagents. A landmark exception came from Carmona's group in 2013: Mo2(N∧N)2\mathrm{Mo_2(N^{\wedge}N)_2} cleaves H2_2 at 1 bar and 25 °C in THF (tetrahydrofuran) to give the trans-dihydride [Mo2(H)2(N∧N)2(thf)2]\mathrm{[Mo_2(H)_2(N^{\wedge}N)_2(thf)_2]} bearing a Mo–Mo quadruple bond, and UV irradiation reductively eliminates H2_2 to restore the quintuple bond — an oxidative-addition/reductive-elimination pair that interconverts quadruple and quintuple metal–metal bonds. Whether such metal–metal multiple bonds could also cleave the much stronger C–H and O–H σ-bonds of stable substrates, and which electronic feature makes them reactive, remained open. In mononuclear σ-bond activation, reactivity is conventionally rationalized through the frontier-orbital (HOMO/LUMO) energies of the reacting metal complex.

Chen and Sakaki (2017) addressed these questions with density-functional theory (DFT, ωB97XD functional) on a truncated model of Mo2(N∧N)2\mathrm{Mo_2(N^{\wedge}N)_2} (the iPr groups of the real ligands replaced by Me) with implicit solvation (CPCM) and, where relevant, explicitly coordinated THF. They found: (i) H–H cleavage is essentially barrierless and gives a cis-dihydride intermediate; the experimentally observed trans product forms only after cis→trans isomerization, whose computed barrier is 36.9 kcal/mol without coordinating solvent but about 6.2 kcal/mol with THF assistance — rationalizing the observed solvent acceleration; (ii) cleavage of a methane C–H bond (ΔG‡≈22.5\Delta G^{\ddagger} \approx 22.5 kcal/mol) and a methanol O–H bond (ΔG‡≈8.1\Delta G^{\ddagger} \approx 8.1 kcal/mol in the computed reaction profile; the paper's abstract quotes 9.0 kcal/mol) is predicted to be kinetically feasible, forecasting genuine alkane and alcohol σ-bond activation by a metal–metal multiple bond; (iii) a direct comparison with the mononuclear complex RhCl(PMe3)2\mathrm{RhCl(PMe_3)_2} shows that frontier-orbital energy positions do not explain the Mo2_2 system's superior reactivity. Instead, fragment orbital-population analysis showed that in the crucial transition states the dδ-type orbitals of the Mo–Mo quintuple bond polarize strongly: an occupied dδ-type orbital (the HOMO of the complex) donates into the substrate σ∗(X−H)\sigma^{*}(\mathrm{X{-}H}) orbital while a dδ*-type orbital (the LUMO+2) accepts density from σ(X−H)\sigma(\mathrm{X{-}H}), creating spatially separated donor and acceptor regions on the two different Mo atoms. This arrangement functions analogously to a frustrated Lewis pair (FLP — a combination of a Lewis acid and a Lewis base that cannot quench each other sterically and therefore jointly cleaves σ-bonds), even though the ground-state Mo–Mo bond is formally nonpolar. Because reciprocal polarization of the several d–d bonding/antibonding orbital pairs is energetically easy, the authors concluded that transition-state polarization is the origin of the high reactivity — easy polarization of the dδ-type orbitals being, in their account, an advantage of the metal–metal multiple bond, since such polarization is impossible in a mononuclear metal complex — and drew a design consequence: metal–metal complexes with unsymmetrical chelate ligands, which pre-polarize the dδ orbitals already in the ground state, should need less additional polarization en route to the transition state and therefore cleave σ-bonds even more readily.

What the source study did not settle — and what later literature has not settled — defines the open problem: the computations used truncated ligands, a single DFT protocol, implicit solvation, and a single-reference method (leaving absolute barrier heights, relative transition-state energies, dynamical, entropic, and possible multiconfigurational effects unvalidated for the full experimental complex); the predicted cis-dihydride intermediates and the C–H/O–H activation products have never been observed experimentally, nor have the conditions for observing them been determined; the unsymmetrical-chelate design principle awaits synthetic realization and testing; and the scope of the polarization mechanism across other metals, metal–metal bond orders, and ligand environments is conjectural.

Problem Statement

The problem is the open question left by Chen and Sakaki's computational study of σ-bond cleavage by the Mo–Mo quintuple bond, kept at the source's generality. Its single overarching objective is to establish — or refute and bound — the transition-state-polarization mechanism and the ground-state pre-polarization design principle as a validated account of σ-bond activation at metal–metal multiple bonds. The question is open in the following specific respects:

(1) Mechanism validation for the Mo2 quintuple-bond system, in two sub-claims. (1a) Experimental: determine whether the predicted cis-dihydride intermediates of H2 addition to Mo2(N∧N)2\mathrm{Mo_2(N^{\wedge}N)_2} are formed, and the conditions (temperature, H2 pressure, solvent coordination, added ligands) under which they, or the predicted C–H (methane, ΔG‡≈22.5\Delta G^{\ddagger} \approx 22.5 kcal/mol) and O–H (methanol, ΔG‡≈8–9\Delta G^{\ddagger} \approx 8\text{--}9 kcal/mol) activation products, can be generated and characterized. (1b) Computational: establish whether the computed mechanisms and barrier heights hold for the full experimental complex, with its real iPr-substituted ligands, explicit solvation, and the dynamical, entropic, and possible multiconfigurational effects in the transition states that the truncated-model single-reference DFT treatment cannot capture. Item (1) is settled only when both (1a) and (1b) are resolved, affirmatively or by a bounded refutation; neither sub-claim alone settles it.

(2) Design-principle test. Determine whether metal–metal multiply bonded complexes bearing designed unsymmetrical chelate ligands that pre-polarize the metal–metal dδ orbitals in the ground state activate σ-bonds (H–H, C–H, O–H) more readily than the corresponding complexes with symmetric chelate ligands.

(3) Scope and limits of the mechanism. Here “other metals, metal–metal bond orders, and ligand environments” names the three dimensions along which the mechanism's generality is at issue, not three separate surveys: determine whether the transition-state-polarization mechanism, and the pre-polarization design principle derived from it, extend beyond the Mo2 quintuple-bond system, and bound the conditions under which they operate or fail. The choice of representative cases along these dimensions is left to the solver; the item is settled once the mechanism's validity or failure has been established or bounded for a representative set spanning all three dimensions — at least one metal other than Mo, at least one metal–metal bond order other than quintuple, and at least one ligand environment other than the formamidinate (N^N) environment of the source system — an exhaustive survey being unnecessary.

These items are one problem: without (1) the mechanism remains an unvalidated computation; without (2) its central design consequence remains an untested prediction; without (3) the generality claimed for the mechanism and the design principle is unestablished. The objective is resolved only when all three items are settled, affirmatively or by a bounded refutation; settling any single item alone does not resolve it.

References

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