Collective interactions among organometallics are exotic bonds hidden on lab shelves

The Na–B bond in NaBH₃ has been a subject of intense debate, with studies showing that only a small fraction of its bond dissociation energy arises from spin-exchange covalency and that electrostatics and interactions with substituents (H or CN) dominate. This raises the question of where such bonds fit within known bonding types and whether analogous interactions exist in aluminum and carbon analogs, including common organometallic reagents (e.g., Grignard and organolithium species). The study introduces the interaction collectivity index (ICI) to quantify the balance between pairwise (1,2) and collective (longer-range 1,n) interactions, and re-examines bonding in [Mⁿ⁺AH₃]²⁻ⁿ and [Mⁿ⁺AR₃]¹⁻ⁿ systems to identify and characterize collective interactions.

Prior work on NaBH₃ and related [Mⁿ⁺BH₃]²⁻ⁿ complexes using advanced analyses (BOVB, QTAIM, IQA) established that the M–B interaction is atypical: minimal electron density at the bond critical point, small spin-exchange covalent contribution, destabilizing M–B electrostatics, and strong stabilizing interactions between the metal and substituents (e.g., M⋯H). Radenković et al. found that about 68.7% (≈25 kcal·mol⁻¹) of Na–B bond energy arises from dipole–dipole interactions in a Heitler–London resonance structure. Discussions on the limitations of electron-density-based bond descriptors prompted a focus on energetic, orbital-invariant quantities. Literature on ionic vs covalent vs charge-shift bonds provides context for interpreting interatomic exchange-correlation (Vxc) and Coulombic (Vc) components, and for recognizing charge-shift bonding signatures. The study also references debates on interpreting electron-density topologies (promolecule density comparability) and emphasizes real-space energy partitioning via IQA as a robust framework.

• Systems: Optimized structures of [Mⁿ⁺AH₃]²⁻ⁿ (M = Li, Na, K, Mg, Ca, Sr; A = B, Al) and [Mⁿ⁺AR₃]¹⁻ⁿ (M = Li, Na, K, Be, Mg, Ca, Sr; A = C; R = H, CH₃, F, CN, phenyl) at C₃ symmetry; also examined inverted (i-) vs pyramidal geometries. A comparative test set of 53 classical molecules (ionic, covalent, dative, charge-shift) was analyzed to benchmark bonding regimes.
• Electronic structure methods: Geometry optimizations at closed-shell and broken-symmetry DFT levels using M06-2X/def2-TZVPP; frequency analyses to confirm minima (Cs minima selected). Multi-reference diagnostics via T1 at CCSD(T)/def2-SVP; selected systems further analyzed at CCSD, CASSCF(8,8), and DFT levels.
• Energy decomposition: Interacting Quantum Atoms (IQA) partitioning to obtain interatomic interaction energy Vint(A,B) and decompose into Coulombic (Vc) and exchange-correlation (Vxc) components; also considered deformation and promotion energies for fragment bond dissociation energy analysis. Emphasis on Vxc (always stabilizing) as a covalency measure and Vc as electrostatics.
• New metric: Defined exchange-correlation interaction collectivity index ICIxc(Y) = Vxc(Y,{M}) / Vxc(Y,{T}), with {M} being 1,2 neighbors and {T} all atoms except Y. Defined analogous electrostatic ICIC(Y) = Vc(Y,{M}) / Vc(Y,{T}).
• Data analyses: Plotted Vxc vs Vc for 103 AB bonds to map bonding regimes and define empirical thresholds: ionic prototype Vxc ≈ −31 kcal·mol⁻¹ (KCl/LiF upper limit for ionic) and lower bound for conventional covalent Vxc ≈ −94.4 kcal·mol⁻¹ (Se–Se in H₂Se₂). Assessed ICIxc and ICIC across systems.
• Robustness checks: Performed IQA with fuzzy atoms (Becke partitioning, Slater–Bragg radii, k=3) using PROMOLDEN to test sensitivity to atomic basin definitions; compared DFT results to CCSD and CASSCF IQA components.
• Software: Gaussian 16 for electronic structure; AIMAll and PROMOLDEN for QTAIM/IQA and fuzzy atom analyses; AdNDP used for NaBH₃ to compare with real-space insights.

• Bonding map: Conventional bonds cluster distinctly in Vxc vs Vc space: nonpolar covalent bonds have destabilizing Vc and substantial stabilizing Vxc (e.g., Se–Se threshold Vxc = −94.4 kcal·mol⁻¹), ionic bonds have small |Vxc| and large stabilizing Vc (e.g., KCl: Vxc ≈ −31, Vc ≈ −104.7 kcal·mol⁻¹).
• [Mⁿ⁺BH₃]²⁻ⁿ and [Mⁿ⁺AlH₃]²⁻ⁿ occupy a unique region: M–B and many M–Al interactions show destabilizing Vc akin to nonpolar covalent situations but with comparatively small |Vxc|, placing them outside conventional regimes. Example: in NaBH₃, M–B Vc is destabilizing, and stabilization arises from M⋯H interactions.
• Organometallic analogs: M–C interactions in MCF₃ and i-MC(CN)₃ often have strongly destabilizing Vc with insufficient Vxc to compensate; stabilization originates from M⋯F or M⋯CN interactions on the periphery. Example: i-MgCF₃ has Vc(Mg,C) ≈ +403.1 kcal·mol⁻¹ and Vxc(Mg,C) ≈ −2.3 kcal·mol⁻¹; the lowest-energy MgCF₃ isomer has larger Vxc(Mg,C) ≈ −63 but still overshadowed by electrostatics.
• Collectivity indices: Conventional covalent/ionic bonds show ICIxc ≳ 0.9. In contrast, metals in [Mⁿ⁺BH₃]²⁻ⁿ, [Mⁿ⁺AlH₃]²⁻ⁿ, and several organometallics have much smaller ICIxc, indicating pronounced collective interactions. The smallest ICIxc values occur in inverted structures (e.g., i-MCF₃), consistent with multiple bond paths (3,−1 BCPs) and 2e-multicenter MO features. Triphenylmethyl organometallics also show notably low ICIxc among pyramidal species, indicating strong through-space metal–phenyl interactions.
• Electrostatic collectivity (ICIC): Negative ICIC values in [Mⁿ⁺BH₃]²⁻ⁿ, [Mⁿ⁺AlH₃]²⁻ⁿ (most), MCF₃, i-MCF₃, and i-MC(CN)₃ indicate destabilizing 1,2 electrostatics (e.g., M–A) but strongly stabilizing interactions with substituents (M⋯X), mirroring the bonding origin. Positive ICIC > 1 (e.g., in BF₃ for F) reflects stabilizing 1,2 electrostatics with slight destabilizing through-space X⋯X interactions.
• Fluorine–fluorine interactions: Significant 1,3 F⋯F exchange-correlation stabilization in BF₃ and CF₄ reduces ICIxc for F, reminiscent of charge-shift bonding features and suggesting a potential class of 1,3 CSB-like interactions.
• Robustness: Trends in Vxc and ICIxc are consistent across DFT, CCSD, and CASSCF levels, with magnitudes varying moderately. Fuzzy-atom IQA yields similar ICIxc rankings (lowest for inverted species; low values also for triphenylmethyl and selected BH₃/AlH₃ complexes), indicating insensitivity to atom partitioning.
• Quantitative references: Thresholds set at Vxc = −31 kcal·mol⁻¹ (ionic prototype) and −94.4 kcal·mol⁻¹ (lower bound for conventional covalent). Examples of charge-shift bonds show unusually large |Vxc|: F₂ ≈ −227, HO–OH ≈ −225, H₂N–NH₂ ≈ −220 kcal·mol⁻¹, versus ethane C–C ≈ −189.6 kcal·mol⁻¹. Prior VB analysis of NaBH₃ indicated 68.7% of its D_e (≈36.4 kcal·mol⁻¹) stems from dipole–dipole interactions (~25 kcal·mol⁻¹).

The analyses demonstrate that many organometallic and related main-group systems are stabilized not by a traditional pairwise M–A bond but through collective interactions where the metal engages more strongly with substituents around A (X) than with A itself. This resolves the NaBH₃ bonding puzzle by placing it on a spectrum with aluminum and carbon analogs and common reagents (e.g., Grignard/organolithium), explaining stability despite weak or even destabilizing direct M–A pairwise interactions. ICIxc effectively differentiates conventional (pairwise) bonds from collective ones: values near 1 for typical covalent/ionic bonds versus substantially lower values for collective systems, especially inverted geometries and triphenylmethyl species. MO analyses categorize systems into classic 2e–2c, 2e-multicenter, and ionic-like cases, but the real-space energy perspective reveals a common underlying collective stabilization mechanism. The findings suggest that covalent contributions can become long-ranged in these systems, necessitating a global view of interactions (akin to electrostatics in ionic crystals) rather than focusing solely on nearest-neighbor pairs.

This work introduces the exchange-correlation interaction collectivity index (ICIxc) to quantify pairwise versus collective bonding and identifies a broad family of collective interactions across organometallics and [Mⁿ⁺AR₃] species (A = B, Al, C; R = H, F, CN, CH₃, Ph). Collective bonding is characterized by weak or destabilizing direct M–A pair interactions and dominant stabilization via metal–substituent interactions, often with low ICIxc. The bonding map in Vxc–Vc space shows that these systems fall outside conventional ionic/covalent regimes. The concept is robust across theoretical levels and atom partitioning schemes, and highlights notable 1,3 exchange-correlation interactions among close-packed substituents (e.g., F in BF₃/CF₄). Future work should further explore the valence-bond characterization of potential 1,3 charge-shift interactions (e.g., in XF₃/XO₃), expand experimental validation across diverse organometallics, and develop design rules leveraging collective bonding for reactivity and materials applications.

• The covalent-vs-ionic thresholds in Vxc are empirical (based on specific prototypes) and may shift with broader datasets or alternative metrics.
• Although multi-reference effects were probed (CCSD, CASSCF), quantitative energy components vary with method; conclusions rely on consistent trends rather than absolute values.
• The study focuses on systems accessible to the chosen theoretical levels and on strong-bonding cases; weak noncovalent interactions were not explored.
• While robustness to atom partitioning was tested (QTAIM vs fuzzy atoms), IQA-based interpretations still depend on the chosen energy decomposition framework.
• Detailed valence-bond (VB) analysis of proposed 1,3 charge-shift interactions in XF₃/XO₃ is beyond scope and remains to be investigated.