Metastable Charged Dimers in Organometallic Species: A Look into Hydrogen Bonding between Metallocene Derivatives

Multiply charged complexes bound by noncovalent interactions have been previously described in the literature, although they were mostly focused on organic and main group inorganic systems. In this work, we show that similar complexes can also be found for organometallic systems containing transition metals and deepen in the reasons behind the existence of these species. We have studied the structures, binding energies, and dissociation profiles in the gas phase of a series of charged hydrogen-bonded dimers of metallocene (Ru, Co, Rh, and Mn) derivatives isoelectronic with the ferrocene dimer. Our results indicate that the carboxylic acid-containing dimers are more strongly bonded and present larger barriers to dissociation than the amide ones and that the cationic complexes tend to be more stable than the anionic ones. Additionally, we describe for the first time the symmetric proton transfer that can occur while in the metastable phase. Finally, we use a density-based energy decomposition analysis to shine light on the nature of the interaction between the dimers.

Anion⋯anion interaction within Ch(CH3)X4- (Ch = S, Se, Te; X = Cl, Br, I) dimers stabilized by chalcogen bonds

In a crystal, a pair of homoanions (Te(C₆H₅)Cl₄^-) are arranged in a parallel manner, close enough to interact with each other. Quantum chemical analysis indicates the existence of two strong noncovalent chalcogen bonds engaging the σ-hole of the chalcogen atoms from one unit and electron density accumulated on the Cl atom of the neighboring unit. In a solid, chalcogen bonds are supported by a multitude of HBs between interacting (Te(C₆H₅)Cl₄^-) anions and the C₅H₅NBr⁺ counterions. These studies are extended to the model homodimers [(Ch(CH₃)X₄)^-]₂, where Ch represents an atom of group 16 (S, Se, and Te) while X = Cl, Br, and I. In these model systems, the aromatic ring was replaced by a methyl group and the counterions were not included. The consequence of this is a different noncovalent bond network in comparison to the system in a solid (the absence of intermolecular HBs and the presence of dihalogen bonds). The tendency for more exoenergetic complexation increases in the Cl < Br < I series. The chalcogen size effect is much smaller. However, critical to the stability of this system is overcoming the Coulomb repulsion between the two monoanions. This is possible because of the polarizable environment that exists in the crystal due to the presence of counter ions.

The Role of Hydrogen Bonds in Interactions between [PdCl4]2- Dianions in Crystal

[PdCl₄]^2- dianions are oriented within a crystal in such a way that a Cl of one unit approaches the Pd of another from directly above. Quantum calculations find this interaction to be highly repulsive with a large positive interaction energy. The placement of neutral ligands in their vicinity reduces the repulsion, but the interaction remains highly endothermic. When the ligands acquire a unit positive charge, the electrostatic component and the full interaction energy become quite negative, signalling an exothermic association. Raising the charge on these counterions to +2 has little further stabilizing effect, and in fact reduces the electrostatic attraction. The ability of the counterions to promote the interaction is attributed in part to the H-bonds which they form with both dianions, acting as a sort of glue.

Anti-Electrostatic Pi-Hole Bonding: How Covalency Conquers Coulombics

Intermolecular bonding attraction at π-bonded centers is often described as "electrostatically driven" and given quasi-classical rationalization in terms of a "pi hole" depletion region in the electrostatic potential. However, we demonstrate here that such bonding attraction also occurs between closed-shell ions of like charge, thereby yielding locally stable complexes that sharply violate classical electrostatic expectations. Standard DFT and MP2 computational methods are employed to investigate complexation of simple pi-bonded diatomic anions (BO-, CN-) with simple atomic anions (H-, F-) or with one another. Such "anti-electrostatic" anion-anion attractions are shown to lead to robust metastable binding wells (ranging up to 20-30 kcal/mol at DFT level, or still deeper at dynamically correlated MP2 level) that are shielded by broad predissociation barriers (ranging up to 1.5 Å width) from long-range ionic dissociation. Like-charge attraction at pi-centers thereby provides additional evidence for the dominance of 3-center/4-electron (3c/4e) nD-π*AX interactions that are fully analogous to the nD-σ*AH interactions of H-bonding. Using standard keyword options of natural bond orbital (NBO) analysis, we demonstrate that both n-σ* (sigma hole) and n-π* (pi hole) interactions represent simple variants of the essential resonance-type donor-acceptor (Bürgi-Dunitz-type) attraction that apparently underlies all intermolecular association phenomena of chemical interest. We further demonstrate that "deletion" of such π*-based donor-acceptor interaction obliterates the characteristic Bürgi-Dunitz signatures of pi-hole interactions, thereby establishing the unique cause/effect relationship to short-range covalency ("charge transfer") rather than envisioned Coulombic properties of unperturbed monomers.

Search for an exothermic halogen bond between anions

A halogen-bonded complex containing a pair of anions can be made more stable than the isolated anions if the Lewis acid is a long carbon chain, fully substituted by CN groups, with an I atom on one end and a COO− group on the other, with Cl− as base.

Inter-anion chalcogen bonds: Are they anti-electrostatic in nature?

Inter-anion hydrogen and halogen bonds have emerged as counterintuitive linkers and inspired us to expand the range of this unconventional bonding pattern. Here, the inter-anion chalcogen bond (IAChB) was proposed and theoretically analyzed in a series of complexes formed by negatively charged bidentate chalcogen bond donors with chloride anions. The kinetic stability of IAChB was evidenced by the minima on binding energy profiles and further supported by ab initio molecular dynamic simulations. The block-localized wave function (BLW) method and its subsequent energy decomposition (BLW-ED) approach were employed to elucidate the physical origin of IAChB. While all other energy components vary monotonically as anions get together, the electrostatic interaction behaves exceptionally as it experiences a Coulombic repulsion barrier. Before reaching the barrier, the electrostatic repulsion increases with the shortening Ch⋯Cl^- distance as expected from classical electrostatics. However, after passing the barrier, the electrostatic repulsion decreases with the Ch⋯Cl^- distance shortening and subsequently turns into the most favorable trend among all energy terms at short ranges, representing a dominating force for the kinetic stability of inter-anions. For comparison, all energy components exhibit the same trends and vary monotonically in the conventional counterparts where donors are neutral. By comparing inter-anions and their conventional counterparts, we found that only the electrostatic energy term is affected by the extra negative charge. Remarkably, the distinctive (nonmonotonic) electrostatic energy profiles were reproduced using quantum mechanical-based atomic multipoles, suggesting that the crucial electrostatic interaction in IAChB can be rationalized within the classical electrostatic theory just like conventional non-covalent interactions.

Classical Electrostatics Remains the Driving Force for Interanion Hydrogen and Halogen Bonding

Interanion hydrogen bonding (IAHB) and halogen bonding (IAXB) have emerged as a counterintuitive linker in a range of fascinating applications. Despite the overall repulsive (positive) binding energy, anions are trapped in a local minimum with its corresponding transition state (TS) preventing dissociation. In other words, the adduct of anions is metastable. Seemingly, the electrostatic paradigm and force field description of hydrogen/halogen bonding (HB/XB) are challenged, because of the preconceived Coulombic repulsion. Aiming at an insightful understanding of these interanion phenomena, we employed the energy decomposition approach based on the block-localized wavefunction method (BLW-ED) to investigate a series of exemplary interanion complexes. As expected, the key distinction from the conventional HB/XB lies in the electrostatic interaction, which is not increasingly repulsive as anions gradually approach to each other. Rather, there is a Coulombic barrier at a certain point. After this point, the electrostatic repulsion diminishes with the decreasing distance between anions. Differently, other energy components vary monotonically just like in conventional cases. The nonmonotonic characteristic of the electrostatic interaction in interanion complexes was reproduced using the multipole expansion in AMOEBA polarizable force field in which the state-specified atomic multipoles were adopted. This suggests that the nonmonotonicity can be well interpreted by classical electrostatic theory and there is no conceptual difference between conventional HB/XB and IAHB/IAXB. The stability of IAHB/IAXB depends on the competition between the local attractive HB/XB and the global Coulombic repulsion of net charges, though there is cooperativity between these two contrasting forces. This concise model was supported by the attractive IAHB/IAXB in modified molecular capsules, which exhibit strong quadruple HB/XBs and a considerable distance between charged substituents.

Experimental and theoretical evidence of attractive interactions between dianions: [PdCl4]2-⋯[PdCl4]2

Inspection of the arrangement of tetrachloridopalladate(II) centers in a crystalline solid places the Cl of one [PdCl₄]^2- directly above the Pd center of its neighbor. A survey of the CSD provides 22 more examples of such MX₄^2-⋯MX₄^2- complexes, with M being a Group 10 metal and X = Cl, Br, or I. Quantum calculations attribute this arrangement to a π-hole bond wherein Cl lone pairs of one unit transfer charge to vacant orbitals above the Pd center of its neighbor. The stabilizing effect of this bond must overcome the strong Coulombic repulsion between the two dianions, which is facilitated by a polarizable environment as would be present in a crystal, but much more so when the effects of the neighboring counterions are factored in. These conclusions are extended to other [MX₄]^2- homodimers, where M represents other members of Group 10, namely Ni and Pt.

Anion⋅⋅⋅Anion Interactions Involving σ-Holes of Perrhenate, Pertechnetate and Permanganate Anions

In this communication experimental and theoretical results are reported affording strong evidence that interactions between electron rich atoms and the metal of tetroxide anions of group 7 elements are a new case of attractive and σ‐hole interactions. Single crystal X‐ray analyses, molecular electrostatic potentials, quantum theory of atoms‐in‐molecules, and noncovalent interaction plot analyses show that in crystalline permanganate and perrhenate salts the metal in Mn/ReO₄⁻ anion can act as electron acceptors, the oxygen of another Mn/ReO₄⁻ anion can act as the donor and supramolecular anionic dimers or polymers are formed. The name matere bond (MaB) is proposed to categorize these noncovalent interactions and to differentiate them from the classical metal‐ligand coordination bond.

Triel bonds within anionanion complexes

The ability of two anions to interact with one another is tested in the context of pairs of TrX₄^- homodimers, where Tr represents any of the triel atoms B, Al, Ga, In, or Tl, and X refers to a halogen substituent F, Cl, or Br. None of these pairs engage in a stable complex in the gas phase, but the situation reverses in water where the two monomers are held together by Tr⋯X triel bonds, complemented by stabilizing interactions between X atoms. Some of these bonds are quite strong, notably those involving TrF₄^-, with interaction energies surpassing 30 kcal mol^-1. Others are very much weaker, with scarcely exothermic binding energies. The highly repulsive electrostatic interactions are counteracted by large polarization energies.

Ability of Lewis Acids with Shallow σ-Holes to Engage in Chalcogen Bonds in Different Environments

Molecules of the type XYT = Ch (T = C, Si, Ge; Ch = S, Se; X,Y = H, CH₃, Cl, Br, I) contain a σ-hole along the T = Ch bond extension. This hole can engage with the N lone pair of NCH and NCCH₃ so as to form a chalcogen bond. In the case of T = C, these bonds are rather weak, less than 3 kcal/mol, and are slightly weakened in acetone or water. They owe their stability to attractive electrostatic energy, supplemented by dispersion, and a much smaller polarization term. Immersion in solvent reverses the electrostatic interaction to repulsive, while amplifying the polarization energy. The σ-holes are smaller for T = Si and Ge, even negative in many cases. These Lewis acids can nonetheless engage in a weak chalcogen bond. This bond owes its stability to dispersion in the gas phase, but it is polarization that dominates in solution.

Anion⋅⋅⋅Anion Coinage Bonds: The Case of Tetrachloridoaurate

Interactions in crystalline tetrachloridoaurates of acetylcholine and dimethylpropiothetine are characterized by Au⋅⋅⋅Cl and Au⋅⋅⋅O short contacts. The former interactions assemble the AuCl4 - units into supramolecular anionic polymers, while the latter interactions append the acetylcholine and propiothetine units to the polymer. The distorted octahedral geometry of the bonding pattern around the gold center is rationalized on the basis of the anisotropic distribution of the electron density, which enables gold to behave as an electrophile (π-hole coinage-bond donor). Computational studies prove that gold atoms in negatively charged species can function as acceptors of electron density. The attractive nature of the Au⋅⋅⋅Cl/O interactions described here complement the known aurophilic bonds involved in gold-centered interactions.

Anion-Anion Interactions in Aerogen-Bonded Complexes. Influence of Solvent Environment

Ab initio calculations are applied to the question as to whether a AeX₅^- anion (Ae = Kr, Xe) can engage in a stable complex with another anion: F^-, Cl^-, or CN^-. The latter approaches the central Ae atom from above the molecular plane, along its C₅ axis. While the electrostatic repulsion between the two anions prevents their association in the gas phase, immersion of the system in a polar medium allows dimerization to proceed. The aerogen bond is a weak one, with binding energies less than 2 kcal/mol, even in highly polar aqueous solvent. The complexes are metastable in the less polar solvents THF and DMF, with dissociation opposed by a small energy barrier.

Anionanion (MX3-)2 dimers (M = Zn, Cd, Hg; X = Cl, Br, I) in different environments

The possibility that MX3- anions can interact with one another is assessed via ab initio calculations in gas phase as well as in aqueous and ethanol solution. A pair of such anions can engage in two different dimer types. In the bridged configuration, two X atoms engage with two M atoms in a rhomboid structure with four equal M-X bond lengths. The two monomers retain their identity in the stacked geometry which contains a pair of noncovalent MX interactions. The relative stabilities of these two structures depend on the nature of the central M atom, the halogen substituent, and the presence of solvent. The interaction and binding energies are fairly small, generally no more than 10 kcal mol-1. The large electrostatic repulsion is balanced by a strong attractive polarization energy.

Anion-anion and anion-neutral triel bonds

The ability of a TrCl4- anion (Tr = Al, Ga, In, Tl) to engage in a triel bond with both a neutral NH3 and CN- anion is assessed by ab initio quantum calculations in both the gas phase and in aqueous medium. Despite the absence of a positive σ or π-hole on the Lewis acid, strong triel bonds can be formed with either base. The complexation involves an internal restructuring of the tetrahedral TrCl4- monomer into a trigonal bipyramid shape, where the base can occupy either an axial or equatorial position. Although this rearrangement requires a substantial investment of energy, it aids the complexation by imparting a much more positive MEP to the site that is to be occupied by the base. Complexation with the neutral base is exothermic in the gas phase and even more so in water where interaction energies can exceed 30 kcal mol-1. Despite the long-range coulombic repulsion between any pair of anions, CN- can also engage in a strong triel bond with TrCl4-. In the gas phase, complexation is endothermic, but dissociation of the metastable dimer is obstructed by an energy barrier. The situation is entirely different in solution, with large negative interaction energies of as much as -50 kcal mol-1. The complexation remains an exothermic process even after the large monomer deformation energy is factored in.

Origins and properties of the tetrel bond

The tetrel bond (TB) recruits an element drawn from the C, Si, Ge, Sn, Pb family as electron acceptor in an interaction with a partner Lewis base. The underlying principles that explain this attractive interaction are described in terms of occupied and vacant orbitals, total electron density, and electrostatic potential. These principles facilitate a delineation of the factors that feed into a strong TB. The geometric deformation that occurs within the tetrel-bearing Lewis acid monomer is a particularly important issue, with both primary and secondary effects. As a first-row atom of low polarizability, C is a reluctant participant in TBs, but its preponderance in organic and biochemistry make it extremely important that its potential in this regard be thoroughly understood. The IR and NMR manifestations of tetrel bonding are explored as spectroscopy offers a bridge to experimental examination of this phenomenon. In addition to the most common σ-hole type TBs, discussion is provided of π-hole interactions which are a result of a common alternate covalent bonding pattern of tetrel atoms.

Understanding noncovalent bonds and their controlling forces

The fundamental underpinnings of noncovalent bonds are presented, focusing on the σ-hole interactions that are closely related to the H-bond. Different means of assessing their strength and the factors that control it are discussed. The establishment of a noncovalent bond is monitored as the two subunits are brought together, allowing the electrostatic, charge redistribution, and other effects to slowly take hold. Methods are discussed that permit prediction as to which site an approaching nucleophile will be drawn, and the maximum number of bonds around a central atom in its normal or hypervalent states is assessed. The manner in which a pair of anions can be held together despite an overall Coulombic repulsion is explained. The possibility that first-row atoms can participate in such bonds is discussed, along with the introduction of a tetrel analog of the dihydrogen bond.

Metastable Dianions and Dications

A theoretical study of metastable dianions and dications has been carried out at the CCSD(T)//MP2 level. MX₃ ^2- and LX₄ ^2- (M=Li and Na, L=Be and Mg, X=F and Cl) have been considered as dianions, M₃ X²⁺ (M=Li and Na, X=F and Cl), YH₃ ²⁺ and ZH₄ ²⁺ (Y=F and Cl and Z=O, S) as dications. Minima structures are found in all cases, but they are less stable than the corresponding dissociated pair of mono-ions. The dissociation profile of the molecules in two mono-ions has been explored showing in all cases a maximum that prevent their spontaneous dissociation. The strength and nature of the chemical bond in the dianions and dications have been analyzed with the QTAIM, NBO and LMOEDA method and compared to the corresponding monoanions and monocations.