A Conceptual DFT Study of Phosphonate Dimers: Dianions Supported by H-Bonds

Hydrogen Bonds Are Never of an "Anti-electrostatic" Nature: A Brief Tour of a Misleading Nomenclature

A large amount of scientific works have contributed through the years to rigorously reflect the different forces leading to the formation of hydrogen bonds, the electrostatic and polarization ones being the most important among them. However, we have witnessed lately with the emergence of a new terminology, anti-electrostatic hydrogen bonds (AEHBs), that seems to contradict this reality. This nomenclature is used in the literature to describe hydrogen bonds between equally charged systems to justify the existence of these species, despite numerous proofs showing that AEHBs are, as any other hydrogen bond between neutral species, mostly due to electrostatic forces. In this Viewpoint, we summarize the state of the art regarding this issue, try to explain why this terminology is very misleading, and strongly recommend avoiding its use based on the hydrogen bond physical grounds.

A library of vinyl phosphonate anions dimerize with cyanostars, form supramolecular polymers and undergo statistical sorting

Supramolecular dimers are elementary units allowing the build-up of multi-molecule architectures. New among these are cyanostar-stabilized dimers of phosphate and phosphonate anions. While the anion dimerization at the heart of these assemblies is reliable, the covalent synthesis leading to this class of designer anions serves as a bottleneck in the pathway to supramolecular assemblies. Herein, we demonstrate the reliable synthesis of 14 diverse anionic monomers by Heck coupling between vinyl phosphonic acid and aryl bromide compounds. When this synthesis is combined with reliable anion dimerization, we show formation of supramolecular dimers and polymers by co-assembly with cyanostar macrocycles. The removal of the covalent bottleneck opened up a seamless synthetic route to iterate through three monomers affording the solubility needed to characterize the mechanism of supramolecular polymerization. We also test the idea that the small size of these vinyl phosphonates provide identical dimer stabilities across the library by showing how mixtures of anions undergo statistical (social) self-sorting. We exploit this property by preparing soluble copolymers from the mixing of different monomers. This multi-anion assembly shows the utility of a library for programming properties.

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.

Does a halogen bond require positive potential on the acid and negative potential on the base?

It is usually expected that formation of a halogen bond (XB) requires that a region of positive electrostatic potential associated with a σ or π-hole on the Lewis acid will interact with the negative potential of the base, either a lone pair or π-bond region. Quantum calculations of model systems suggest this not to be necessary. The placement of electron-withdrawing substituents on the base can reverse the sign of the potential in its lone pair or π-bond region to positive, and this base can nonetheless engage in a XB with the positive σ-hole of a Lewis acid. The reverse scenario is also possible in certain circumstances, as a negatively charged σ-hole can form a XB with the negative lone pair region of a base. Despite these classical Coulombic repulsions, the overall electrostatic interaction is attractive in these XBs, albeit only weakly so. The strengths of these bonds are surprisingly insensitive to changes in the partner molecule. For example, even a wide range in the depth of the σ-hole of the approaching acid yields only a minimal change in the strength of the XB to a base with a positive potential.

The transition state region in nonsynchronous concerted reactions

The critical and vanishing points of the reaction force F(ξ) = -dV(ξ)/dξ yield five important coordinates (ξ_R, ξ_R^* , ξ_TS, ξ_P^* , ξ_P) along the intrinsic reaction coordinate (IRC) for a given concerted reaction or reaction step. These points partition the IRC into three well-defined regions, reactants (ξ_R→ξ_R^* ), transition state (ξ_R^* →ξ_P^* ), and products (ξ_P^* →ξ_P), with traditional roles of mostly structural changes associated with the reactants and products regions and mostly electronic activity associated with the transition state (TS) region. Following the evolution of chemical bonding along the IRC using formal descriptors of synchronicity, reaction electron flux, Wiberg bond orders, and their derivatives (or, more precisely, the intensity of the electron activity) unambiguously indicates that for nonsynchronous reactions, electron activity transcends the TS region and takes place well into the reactants and products regions. Under these circumstances, an extension of the TS region toward the reactants and products regions may occur.

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.

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.

A novel series of pyrazole derivatives toward biological applications: experimental and conceptual DFT characterization

A new series of 13 pyrazole-derivative compounds with potential antifungal activity were synthetized with good yields. The series have the (E)-2-((1-(R)-3,5-dimethyl-1H-pyrazol-4-yl)diazenyl)phenol general structure and were characterized by means of X-ray diffraction, UV-Vis, FTIR, ¹H-NMR, ¹³C-NMR, and two-dimensional NMR experiments. This experimental characterization was complemented by DFT simulations. A deep insight regarding molecular reactivity was accomplished employing a conceptual DFT approach. In this sense, dual descriptors were calculated at HF and DFT level of theory and GGV spin-density Fukui functions. The main reactive region within the molecules was mapped through isosurface and condensed representations. Finally, chemical descriptors that have previously shown to be close related to biological activity were compared within the series. Thus, higher values of chemical potential ω and electrophilicity χ obtained for compounds 10, 9, 8, 6 and 7, in this order, suggest that these molecules are the better candidates as biological agents.

Competition between Inter and Intramolecular Tetrel Bonds: Theoretical Studies Complemented by CSD Survey

Crystal structures document the ability of a TF₃ group (T=Si, Ge, Sn, Pb) situated on a naphthalene system to engage in an intramolecular tetrel bond (TB) with an amino group on the adjoining ring. Ab initio calculations evaluate the strength of this bond and evaluate whether it can influence the ability of the T atom to engage in a second, intermolecular TB with another nucleophile. A very strong CN^- anionic base can approach the T either along the extension of a T-C or T-F bond and form a strong TB with an interaction energy approaching 100 kcal/mol, although this bond is weakened a bit by the presence of the internal T⋅⋅⋅N bond. The much less potent NCH base engages in a correspondingly longer and weaker TB, less than 10 kcal/mol. Such an intermolecular TB is weakened by the presence of the internal TB, to the point that it only occurs for the two heavier tetrel atoms Sn and Pb.

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.

Interaction between Trinuclear Regium Complexes of Pyrazolate and Anions, a Computational Study

The geometry, energy and electron density properties of the 1:1, 1:2 and 1:3 complexes between cyclic (Py-M)3 (M = Au, Ag and Cu) and halide ions (F-, Cl- and Br-) were studied using Møller Plesset (MP2) computational methods. Three different configurations were explored. In two of them, the anions interact with the metal atoms in planar and apical dispositions, while in the last configuration, the anions interact with the CH(4) group of the pyrazole. The energetic results for the 1:2 and 1:3 complexes are a combination of the specific strength of the interaction plus a repulsive component due to the charge:charge coulombic term. However, stable minima structures with dissociation barriers for the anions indicate that those complexes are stable and (Py-M)3 can hold up to three anions simultaneously. A search in the CSD confirmed the presence of (Pyrazole-Cu)3 systems with two anions interacting in apical disposition.

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.

Stabilisation of dianion dimers trapped inside cyanostar macrocycles

Interanionic H-bonds (IAHBs) are unfavourable interactions in the gas phase becoming favoured when anions are in solution. Dianion dimers are also susceptible to being trapped inside the cavities of cyanostar (CS) macrocycles, and thus, the formation of 2 : 2 anion : cyanostar aggregates is mainly supported by three kinds of interactions: IAHBs between the dianions, π-π stacking between the confronted cyanostars, and the presence of an intricate network of multiple C(sp²)HO H-bonds between cyanostar ligands and the anionic moieties. An analysis of the interaction energies supported by NBO reveals a slight cooperative effect of the CSs on the IAHB stabilisation.