Three-center Two-electron Research Articles

FK4H4-: Planar Tetracoordinate Fluorine Stabilized by Multicenter Ionic Bonding.

Planar tetracoordinate fluorine (ptF) species are very exotic and scarce due to high electronegativity of fluorine. Herein we report the ternary square ptF cluster, D4h FK4H4-, which is composed of a F center, a square K4 ring, and four outer H bridges. It is a true global minimum (GM) structure and possesses good dynamic stability. Bonding analyses indicate that there are four lone pairs for the central F atom, along with four K-H-K three-center two-electron (3c-2e) σ bonds for the peripheral K4H4 ligand ring. The stability of ptF is dominated by multicenter ionic bonds rather than the supposed σ aromaticity of the system. Excitingly, it is a pseudohalogen anion with the VDE 3.57 eV at the CCSD(T) level. The merge of ptF with pseudohalogen anion character makes the FK4H4- cluster an exotic species, which will motivate theoretical and experimental studies on novel ptF species as well as superhalogens.

Three-Supercenter Two-Electron Bonds in C16H10: Two-Dimensional Analogue of Halogen-Bridge Bonding.

Three-center two-electron bridging bonding plays a vital role in rationalizing structures and stabilities of certain molecules. Herein, the π electron rule of pyrene (C16H10) was unraveled based on a newly proposed two-dimensional (2D) superatomic-molecule theory, where the superatomic sextet rule was regarded as a π electron counting target. C16H10 can be taken as a ◊N2◊F2 superatomic molecule, where ◊N and ◊F denote 2D superatoms bearing 3π and 5π electrons, respectively. Interestingly, it represents the first 2D superatomic halogen-bridge molecule, which realizes π electronic shell-closure via two three-supercenter two-electron bridging bonds. Additionally, a N-doped nanoporous graphene with a wide band gap (1.22 eV) was designed based on C16H10, which can be considered as a periodic aggregate of 2D superatomic wires composed of 2π-◊C and bridging ◊F superatoms. This work enriches the 2D superatomic-molecule chemistry and provides a practicable bottom-up assemble approach to obtain 2D functional materials with tunable band gaps.

Toward the Chemical Structure of Diborane: Electronic Force Density Fields, Effective Electronegativity, and Internuclear Turning Surface Properties.

The chemical structure of diborane was elucidated through the superposition of the vector fields of the electron density gradient ∇ρ(r), the electrostatic force Fes(r), and the kinetic force Fk(r), together with the analysis of the cumulative charges of the atoms and pseudoatoms delimited in the aforementioned fields. It was proposed that the Fk-pseudoatomic charge could be employed as a metric for quantifying the ionic component of a related atomic charge. The electron permeability across an internuclear turning surface─specifically, the zero-flux surface in Fk(r)─was characterized by probing it through mapping the total static potential φem(r). The conceptualization of post hoc electronegativity was presented for consideration. Our analysis revealed that the ordinary B-H and bent B-μ-H bonds in diborane demonstrate the polar covalent character with minor contributions of the ionic component. The former bond exhibits a greater electron permeability through the internuclear turning surface, indicating a stronger tendency for electron sharing between the corresponding nucleus-dominated regions. The electron density accumulation along the bent B-μ-H bond path diverges from the minimum action trajectories of the forces Fes(r) and Fk(r). This phenomenon can be associated with the structural strain within the angled, three-center two-electron bonding B-μ-H-B. The internuclear B···B paths were identified in Fes(r) and Fk(r), in contrast to ∇ρ(r). This fact, in conjunction with a pronounced electron permeability through the mutual turning surface between the two boron nuclei, implies a certain degree of electron exchange between the boron-dominated pseudoatomic regions. Furthermore, the anomalous [B-]H···μ-H intermolecular polar interactions were described between the strongly negatively charged hydrogen atoms in the monoclinic crystalline β-phase of diborane. In fact, the ionic contributions to the charges of the hydrogen atoms are shown to be relatively small.

Transition Metal/Lanthanide-Nitrogen Double Bonds Co-stabilized in a Carbon Cage.

Metal-nitrogen double bonds have been commonly reported for conventional metal complexes, but the coexistence of both transition metal-nitrogen and lanthanide-nitrogen double bonds bridged by nitrogen within one compound has never been reported. Herein, by encapsulating a ternary transition metal-lanthanide heteronuclear dimetallic nitride into a C84 fullerene cage, transition metal-nitrogen and lanthanide-nitrogen double bonds are costabilized simultaneously within the as-formed clusterfullerene TiCeN@C1(12)-C84, which is a representative heteronuclear dimetallic nitride clusterfullerene. Its molecular structure was unambiguously determined by single-crystal X-ray diffraction, revealing a slightly bent μ2-bridged nitride cluster with short Ti-N (1.761 Å) and Ce-N (2.109 Å) bond lengths, which are comparable to the corresponding Ti=N and Ce=N double bonds of reported metal complexes and consistent with the theoretically predicted values, confirming their coexistence within TiCeN@C1(12)-C84. Density functional theory (DFT) calculations unveil three-center two-electron (3c-2e) bonds delocalized over the entire TiCeN cluster, which are responsible for costabilization of Ti=N and Ce=N double bonds. An electronic configuration of Ti4+Ce3+N3-@C84 4- is proposed featuring an intramolecular four-electron transfer, drastically different from the analogous actinide dimetallic nitride clusterfullerene (U2)9+N3-@C80 6- and trimetallic nitride clusterfullerene (Sc2)6+Ti3+N3-@C80 6-, indicating the peculiarity of 4-fold negatively charged fullerene cage in stabilizing the heteronuclear dimetallic nitride cluster.

Stability and Electronic Properties of Mixed Rare-Earth Tri-Metallofullerenes YxDy3-x@C80 (x = 1 or 2).

Tri-metallofullerenes, specifically M3@C80 where M denotes rare-earth metal elements, are molecules that possess intriguing magnetic properties. Typically, only one metal element is involved in a given tri-metallofullerene molecule. However, mixed tri-metallofullerenes, denoted as M1xM23-x@C80 (x = 1 or 2, M1 and M2 denote different metal elements), have not been previously discovered. The investigation of such mixed tri-metallofullerenes is of interest due to the potential introduction of distinct properties resulting from the interaction between different metal atoms. This paper presents the preparation and theoretical analysis of mixed rare-earth tri-metallofullerenes, specifically YxDy3-x@C80 (x = 1 or 2). Through chemical oxidation of the arc-discharge produced soot, the formation of tri-metallofullerene cations, namely Y2Dy@C80+ and YDy2@C80+, has been observed. Density functional theory (DFT) calculations have revealed that the tri-metallofullerenes YxDy3-x@C80 (x = 1 or 2) exhibit a low oxidation potential, significantly lower than other fullerenes such as C60 and C70. This low oxidation potential can be attributed to the relatively high energy level of a singly occupied orbital. Additionally, the oxidized species demonstrate a large HOMO-LUMO gap similar to that of YxDy3-xN@C80, underscoring their high chemical stability. Theoretical investigations have uncovered the presence of a three-center two-electron metal-metal bond at the center of Y2DY@C80+ and YDy2@C80+. This unique multi-center bond assists in alleviating the electrostatic repulsion between the metal ions, thereby contributing to the overall stability of the cations. These mixed rare-earth tri-metallofullerenes hold promise as potential candidates for single-molecule magnets.

D 4h H©K4H4-: a planar tetracoordinate hydrogen global minimum.

Herein we report a square-like D4h H©K4H4- anion with one planar tetracoordinate hydrogen (ptH) center, which is the global minimum (GM) structure and possesses good dynamic stability. The planar structure of the system is preserved by four peripheral K-H-K three-center two-electron (3c-2e) σ bonds together with one 5c-2e σ bond over the HK4 core. The multicenter ionic bonds dominate the stability of ptH, while the contribution of qualitative σ aromaticity is extremely limited.

Infrared spectra of SinH4n-1+ ions (n = 2-8): inorganic H-(Si-H)n-1 hydride wires of penta-coordinated Si in 3c-2e and charge-inverted hydrogen bonds.

SinHm+ cations are important constituents in silane plasmas and astrochemical environments. Protonated disilane (Si2H7+) was shown to have a symmetric three-centre two-electron (3c-2e) Si-H-Si bond that can also be considered as a strong ionic charge-inverted hydrogen bond with polarity Siδ+-Hδ--Siδ+. Herein, we extend our previous work to larger SinH4n-1+ cations, formally resulting from adding SiH4 molecules to a SiH3+ core. Infrared spectra of size-selected SinH4n-1+ ions (n = 2-8) produced in a cold SiH4/H2/He plasma expansion are analysed in the SiH stretch range by complementary dispersion-corrected density functional theory calculations (B3LYP-D3/aug-cc-pVTZ) to reveal their bonding characteristics and cluster growth. The ions with n = 2-4 form a linear inorganic H-(Si-H)n hydride wire with adjacent Si-H-Si 3c-2e bridges, whose strength decreases with n, as evident from their characteristic and strongly IR active SiH stretch fundamentals in the range 1850-2100 cm-1. These 3c-2e bonds result from the lowest-energy valence orbitals, and their high stability arises from their delocalization along the whole hydride wire. For SinH4n-1+ with n ≥ 5, the added SiH4 ligands form weak van der Waals bonds to the Si4H19+ chain. Significantly, because the SinH4n-1+ hydride wires are based on penta-coordinated Si atoms leading to supersaturated hydrosilane ions, analogous wires cannot be formed by isovalent carbon.

IR spectrum of SiH3OH2+SiH4: cationic OH⋯HSi dihydrogen bond versus charge-inverted SiH⋯Si hydrogen bond.

The low electronegativity of Si gives rise to a variety of nonconventional intermolecular interactions in clusters of silanes and their derivatives, which have not been well characterized yet. Herein, we characterize the structures of various isomers of bare and Ar-tagged SiH3OH2+SiH4 dimers composed of protonated silanol and silane by infrared photodissociation (IRPD) of mass-selected ions and dispersion-corrected density functional calculations (B3LYP-D3/aug-cc-pVTZ). The analysis of the IRPD spectra recorded in the OH stretch range reveals the competition between two types of nonconventional hydrogen bonds (H-bonds). The first one represents a OH⋯HSi ionic dihydrogen bond (DHB), in which SiH4 interacts with the H2O moiety of SiH3OH2+. The second one represents a charge-inverted SiH⋯Si ionic H-bond (CIHB), in which the SiH4 ligand interacts with the SiH3 moiety of SiH3OH2+. The latter may also be considered as a weak three-centre two-electron (3c-2e) bond. Although both types of H-bonds are computed to have comparable interaction strengths for SiH3OH2+SiH4 (D0 ≈ 35-40 kJ mol-1), DHB isomers dominate the population in the supersonic plasma expansion, while the abundance of CIHB isomers is roughly one order of magnitude lower, probably as a result of entropic factors.

Bilayer Kagome Borophene with Multiple van Hove Singularities.

The appearance of van Hove singularities near the Fermi level leads to prominent phenomena, including superconductivity, charge density wave, and ferromagnetism. Here a bilayer Kagome lattice with multiple van Hove singularities is designed and a novel borophene with such lattice (BK-borophene) is proposed by the first-principles calculations. BK-borophene, which is formed via three-center two-electron (3c-2e) σ-type bonds, is predicted to be energetically, dynamically, thermodynamically, and mechanically stable. The electronic structure hosts both conventional and high-order van Hove singularities in one band. The conventional van Hove singularity resulting from the horse saddle is 0.065eV lower than the Fermi level, while the high-order one resulting from the monkey saddle is 0.385eV below the Fermi level. Both the singularities lead to the divergence of electronic density of states. Besides, the high-order singularity is just intersected to a Dirac-like cone, where the Fermi velocity can reach 1.34 × 106m s-1. The interaction between the two Kagome lattices is critical for the appearance of high-order van Hove singularities. The novel bilayer Kagome borophene with rich and intriguing electronic structure offers an unprecedented platform for studying correlation phenomena in quantum material systems and beyond.

Luminescent cadmium(II) complexes with benzyl and chlorobenzyl benzimidazole derivatives and closo-decaborate anion

New ligands, namely N-[(1-benzyl-1H-benzimidazol-2-yl)methylidene]aniline (L1) and its chloro-derivative N-[(1-(4′-chlorobenzyl)-1H-benzimidazol-2-yl)methylidene]aniline (L2), have been synthesized. Their behavior in the course of cadmium(II) complexation has been studied in the presence of the closo-decaborate anion [B10H10]2–. Mixed-ligand complexes [CdL2[B10H10]] (L = L1, L2) have been isolated, which contain the [B10H10]2– anion coordinated by the metal atom via three-center two-electron (3c2e) CdHB bonds. The structures of both complexes have been determined by single-crystal X-ray diffraction. Based on the data of the UV–vis absorption spectra measured for the synthesized compounds, it has been concluded that the luminescent properties are retained in the complexes under consideration. The intensity of the luminescence and the position of the emission band of the cadmium(II) complexes have been analyzed. Quantum-chemical calculations based on density functional theory (DFT) calculations have allowed us to determine the general relationships between the structural and spectroscopic characteristics.

Spin Crossover in Iron(II) Complexes with Polynitrogen Heterocyclic Ligands and Outer-Sphere Boron Cluster Anions (Review)

The results of synthesis and study of magnetically-active iron(II) complexes with polynitrogen heterocyclic ligands and outer-sphere boron cluster anions have been considered. Derivatives of 1,2,4-triazole, tris(pyrazol-1-yl)methane, and 2,6-bis(imidazol-2-yl)pyridine have been used as ligands, decahydro-closo-decaborate, dodecahydro-closo-dodecaborate, decachloro-closo-decaborate, and 1,5,6,10-tetra(R)-7,8-dicarba-nido-undecaborates (R = H, Cl, Br) have been studied as outer-sphere anions. A number of iron(II) complexes showing spin crossover accompanied by thermochromism in the majority of cases has been obtained. Effect of ligand nature and cluster anion on temperature (Tc) and spin transition character has been considered. In particular, it has been shown that introduction of substituent increasing electron density over the system of conjugated three-centered two-electron bonds in cluster anion leads to increase in the field strength of ligand bound to anion via network of hydrogen bonds.

Deciphering the Impact of Helium Tagging on Flexible Molecules: Probing Microsolvation Effects of Protonated Acetylene by Quantum Configurational Entropy

Helium, the lightest and most weakly interacting noble gas, is well-known for its unsurpassed chemical inertness. In many applications of helium in experimental techniques, such as tagging, messenger, or nanodroplet isolation action spectroscopy of molecules or complexes, it is assumed that the interaction of helium with the respective species, and thus the resulting interaction-induced perturbation, is small enough not to affect their structure and dynamics. Here, we probe the impact of one up to many attached helium atoms on protonated acetylene─an important nonclassical carbocation subject to three-center two-electron bonding in its ground state structure─using highly accurate interaction potentials in conjunction with entropy-based higher-order nonlinear correlation analysis. In particular, using neural network potentials at CCSD(T) accuracy, we disclose the specific structural perturbations due to the tagging of C2H3+ with up to 20 He atoms at a temperature of 1 K. Analysis reveals that microsolvation by helium influences the structure of C2H3+ noticeably, while our investigation of the quantum configurational information entropy additionally shows that correlations between individual orientational degrees of freedom are affected as a function of cluster size. In particular, it is found that the most probable bridge-like structure of the ro-vibrational quantum ground state of C2H3+, which is nonplanar and trans-bent in contrast to the perfectly planar equilibrium structure, becomes increasingly more localized upon adding helium atoms. The remarkably nonlinear behavior of the angular correlations as a function of cluster size is traced back to the buildup of the quantum microsolvation shell that enhances anisotropy up to NHe = 6 while more and more isotropic solvation takes over beyond six. Our approach is general and thus sets the stage to investigate the salient effects on the structure of flexible molecules due to tagging beyond the specific case.

Prediction of a Cyclic Hydrogenated Boron Molecule as a Promising Building Block for Borophane.

We have extensively searched for a cyclic hydrogenated boron molecule that has a three-center two-electron bond at the center. Using first-principles calculations, we discovered a stable molecule of 2:4:6:8:-2H-1,5:1,5-μH-B8H10 and propose its existence. This molecule can be regarded as a building block for sheets of topological hydrogen boride (borophane), which was recently theoretically proposed and experimentally discovered. The electronic structure of the cyclic hydrogenated boron molecule is discussed in comparison with that of cyclic hydrogenated carbon molecules.

Supported or unsupported three-center two-electron bonds? A criterion based on Interference Energy Analysis.

The classification of three-center two-electron (3c2e) bonds into supported (closed) or unsupported (open) was proposed by Lipscomb in his work on boranes and extended to transition metal complexes by Bau and co-workers. The species in which the interactions of the terminal atoms are negligible are called "unsupported bonds." Examples of chemical species that are said to exhibit such bonds are Li2H+, Na2H+, B2H7 -, Al2(CH3)7 -, and [(μ2-H)Cr2(CO)10]- although the general criterion for distinguishing these types of bonds is somewhat qualitative. Besides providing a unifying view of the nature of the chemical bond, in terms of quantum interference among electronic states, the Generalized Product Function Energy Partitioning method through the Interference Energy Analysis (IEA) is also potentially capable of providing a rigorous ground to the concept of supported bonds by looking at the specific interference energies between the orbital pairs associated with the bond. The IEA was performed in the species Li2H+, Na2H+, B2H7 -, C2H7 -, Al2H7 -, and [(μ2-H)Cr2(CO)10]-, as well as along the reaction path Li2H+ → Li2 + + H. The results shown that in all studied A-B-C bonds, the A-C interactions are as important as the A-B/B-C ones, leading to the conclusion that all studied 3c2e bonds are "supported," in the sense that the A-C interaction is not negligible. The particularity of those species in preferring linear geometry is completely explained by quasi-classical effects, more specifically, by minimization of the electron-electron and nucleus-nucleus repulsions.

Elastic Electron Scattering by Diborane(6) and Diborane(4) Molecules

We present integral, differential, and momentum transfer cross sections for elastic electron collisions with the two most stable isomers of the B2H4 molecule, hereafter referred to as isomer I (C2v symmetry) and isomer II (D2d symmetry), and with the B2H6 molecule (D2h symmetry). The isomer I of B2H4 and the B2H6 molecule are known for their electrodeficiency in the "three-center two-electron" (3c-2e) bond, a region in which a hydrogen atom occupies a bridged position between two non-hydrogen atoms. The cross sections were computed by using the Schwinger multichannel method implemented with norm-conserving pseudopotentials, and the scattering calculations were carried out in the static-exchange and static-exchange plus polarization levels of approximation for energies from 0.1 to 50 eV. We discuss the presence of shape resonances in the scattering cross sections. We also made a direct comparison among the cross sections of these three targets.

Bonding Nature of "Ionic Carbenes" in [M3(μ3-CH2)]-Containing Compounds: The Covalent Interaction.

While a series of trinuclear rare-earth metal methylene (divalent >CH2) complexes with the so-called "ionic carbene" have been known for decades, the nature of metal-carbene interactions in this class of compounds remains elusive. Herein, a quantum chemical investigation has been performed to reveal the bonding nature in typical trimetallic "ionic carbene" species with the [M3(μ3-CH2)] (M = Sc, Y, La, and Ac) cluster core. Through various chemical bonding analyses, we have demonstrated that there exists a non-negligible covalent interaction between μ3-CH2 and M3 moieties, and the chemical bonding can be accounted for with two three-center two-electron (3c-2e) bonds. The chemical bonding analyses reveal that the metal d-electron configuration plays an important role in stabilizing various μ3-coordinated carbene complexes. The late transition metals do not favor such a μ3-coordination geometry, thus explaining why ionic carbene complexes are usually found for rare-earth and early transition metals. A series of ionic carbene complexes with early transition metals, lanthanides, and actinides are predicted to be stable as well. These reactive ionic carbene complexes may have characteristic properties for organic synthesis and catalysis.

Bonding in a Crystalline Tri-Thorium Cluster: Not σ-Aromatic But Still Unique.

Very recently, Boronski et al. reported the first thorium–thorium bond in a crystalline cluster prepared under normal experimental conditions. By using a range of experimental techniques and computational models, the authors found that the isolated actinide cluster contains at its heart two paired electrons delocalized over the tri‐thorium ring. The recorded Raman spectrum allegedly confirmed the existence of a σ‐aromatic three‐center two‐electron bond. In the following we demonstrate that the experimentally observed broad inelastic scattering bands between 60 and 135 cm−1, originally assigned by the authors to thorium‐thorium vibrations, represent the combination of Th−Cl stretching and Th−Cl−Th bending modes, and they establish the existence of an unprecedented multicenter charge‐shift bonding (ThCl2)3 rather than the σ‐aromatic bonding Th3. In the light of the presented findings, the latter remains experimentally unproven and computationally questionable.

Computational Prediction of Graphdiyne-Supported Three-Atom Single-Cluster Catalysts

Computational Prediction of Graphdiyne-Supported Three-Atom Single-Cluster Catalysts

Ln3@C80+ (Ln = lanthanide): a new class of stable metallofullerene cations with multicenter metal–metal bonding in the sub-nanometer confined space

Unstable tri-metallofullerenes Ln3@C80 are greatly stabilized in their cationic form. The stability of Ln3@C80+ originates from a three-center two-electron metal–metal bond that compensates for the Coulomb repulsion between the metal ions.

Thorium-thorium bonding marks actinide milestone

Bonds between actinide elements are extremely rare, with barely a handful identified in fleeting or exotic circumstances. Researchers have now created a fully fledged crystalline complex containing thorium-thorium bonds, synthesized and isolated under ordinary experimental conditions ( Nature 2021, DOI: 10.1038/s41586-021-03888-3 ). Stephen T. Liddle of the University of Manchester and colleagues made the new compound by combining a thorium precursor with a tetrasilyl cyclobutadiene dianion—a powerful reducing agent. This formed a complex containing a cluster of three thorium atoms flanked by cyclooctatetraenyl ligands and bridging chlorides. The dark-blue crystals decompose slowly at room temperature but remain stable at –35 °C. The researchers compared crystal structure data and spectroscopy and magnetic measurements with quantum chemical calculations and determined that the thorium cluster contains a three-center two-electron bond and that these delocalized electrons are σ aromatic. “It’s pretty much the last thing that anyone expected,” Liddle says. “It underlines to me