All-boron aromatic clusters as potential new inorganic ligands and building blocks in chemistry

Unravelling the effect of successive electron injection into the smallest cyclic boron cluster, B3n (n = +2, +1, 0, -1, -2, -3) through electronic structure analysis

With an aim to study the effect of successive electron injection or abstraction on the electronic structure of the cyclic boron clusters; B3n (where n = +2, +1, 0, -1, -2, -3) have been explored using DFT methodology. A total of nine clusters have been studied including the minimum energy ground states and a few closely lying ground states. Through real space functions like electron density, Electron Localization Function (ELF), Localized Orbital Locator (LOL), and Phase-space-defined Fisher Information Density (PS-FID) an in-depth study has been carried out to understand how the electronic character evolves with the successive electron injection into the cluster. Based on Atoms in Molecules (AIM) theory evolution of electron density at critical points and basins has also been studied. Global indices have also been calculated using Conceptual Density Functional Theory (CDFT) to understand cluster's reactivity and stability. IR spectrum has been computed for future experimental verification. B3 clusters fall into two main symmetry classes: six of them have D3h symmetry (B3+2, both the singlet and triplet states of B3+1, B30, B3-1 and the triplet state of B3-3) and three have C2v symmetry (B3-2 and two singlet states of B3-3). It has been found that the B3-1 cluster has the minimum energy among all the structures with the most electron delocalization in the centre.

Structure- and Size-Dependent Properties of BnCu20/- (n = 2-14) Clusters: DFT Calculations

The structural and stability properties of two Cu atoms doped boron clusters (BnCu2 with n = 2-14) are investigated by a genetic algorithm method in combination with density functional theory (DFT) calculations. The lowest energy clusters of neutral clusters (BnCu20) adopt two-dimensional (2D) structures for n ≤ 6, 10, and 12. For anionic clusters (BnCu2-) the structural patterns are similar, however, the Cu atoms tend to pair up and form dimers instead of islands. The stability of the clusters, evaluated through the binding energy, second-order energy difference, and ionization energy, reveals that the neutral clusters B4Cu20, B6Cu20, and B8Cu20, as well as the anionic clusters B9Cu2-, B11Cu2-, and B13Cu2-, have greater chemical and thermodynamic stability than their neighbors in size. The favored structures for these clusters are found to be related with stable boron motifs which correspond to magic clusters. Moreover, the Cu2-Bn interaction of the clusters were analyzed using the Energy Decomposition Analysis (EDA) and Natural Bond Order (NBO) charges, which supported the current findings. According to the AdNDP analyses, the stability of the clusters can be understood by the presence of delocalized sigma orbitals along the boron backbone.

Evolution of B13n (n = + 3 to - 3) wheel with electron injection/abstraction: an insight from electronic structure analysis

CONTEXT

The planar B13+1 cluster, a prototypical molecular 'Wankel motor', has captivated the scientific community with its exceptional stability as well as rotor action. The present study is an exploration of how incremental electron injection/abstraction influences the electronic structure of B13 clusters with B13+1 as a reference one. It has been found that seven different charge states (from + 3 to - 3) of B13 cluster are possible, among which B13-1 triplet is the lowest energy cluster. For B13n clusters, n =  + 3 to - 2, the clusters are planar and possess C2v symmetry and their relative atomic arrangement is similar to B13+1 ground state (GS) structure in which a triangular boron core is encircled by ten peripheral boron atoms. B13-3 cluster has a different geometric arrangement of atoms like that of the B13+1 transition state (TS) structure; remains planar, possesses C2v symmetry. The different atomic arrangement of B13-3 can be assigned to the electronic structural relaxation to reduce the electronic stress arising from high negative charge. B13+1 cluster is characterized by a unique electron density distribution in the cluster plane which is analogous to a 'tri-spoke wheel' configuration. In it, three spokes of electron dense lines connect the triangular core to the nearly circular periphery. The present study unveils how the injection or abstraction of electrons modifies the electronic topology in the cluster plane and how the spoke-wheel geometry evolves. It has been found that, in the + 3 and + 2 charge states, the wheel consists of four and five spokes respectively. On the other hand, for all other clusters, the overall electronic topology resembles that of the tri-spoke wheel-like B13+1 cluster. AIM analysis helped to trace out and characterize the evolution of the spoke-wheel topology with electron density at ring critical points and the bond paths.

METHODS

Density Functional Theory (DFT), utilizing the 6-311 + G(d) basis set and the PBE1PBE hybrid density functional, has been employed to determine the minimum energy structures of B13 clusters with different charged states. The calculations have been performed using a superfine integration grid and very tight optimization settings, as implemented in GAUSSIAN 09 Revision D.01. To address potential instabilities in SCF calculations, wavefunction stability has been thoroughly analysed. AIM analysis and various real-space functions, including electron density, Localized Orbital Locator (LOL), Phase-Space defined Fisher Information Density (PS-FID), and Electron Localization Function (ELF), have been investigated. Multiwfn 3.8 was utilized for plotting these functions.

Boron-based B3Zn6- alloy cluster as a hybrid between prismatic and sandwich-like structures: Stabilization of a linear B3 chain motif using electronic transmutation

Doping boron clusters with metallic elements can tune the structural, electronic, and bonding properties. We report on the computational design of a zinc-rich D3h (1A1') B3Zn6- alloy cluster, whose global-minimum structure is a hybrid between prismatic, sandwich-like, and core-shell tubular geometries. The binary cluster features a linear B3 chain along its C3 axis, as well as three lateral Zn-Zn dimers, in which a central B atom is sandwiched by two quasi-planar BZn3 units in an eclipsed form. Chemical bonding analyses show that the B3 chain motif has Lewis-type B-B σ single bonds and a pair of orthogonal three-center two-electron (3c-2e) π bonds, collectively leading to a B-B bond order of two. Stabilizing a boron single chain is scarce in the literature, as is observing a series of double B=B bonds in a monoatomic chain fashion. The triangular pyramid BZn3 units are each in a unique triplet σ2σ*1σ*1 configuration, thus rendering σ aromaticity to the cluster according to the reversed 4n Hückel rule. It is proposed that the alloy cluster can be rationalized using the concept of electronic transmutation, wherein a close chemical analogy to the carbon dioxide (CO2) molecule is established.

Observation of the Smallest Three-Dimensional Neutral Boron Cluster

Despite major progress in the investigation of boron cluster anions, direct experimental study of neutral boron clusters remains a significant challenge because of the difficulty in size selection. Here we report a size-specific study of the neutral B9 cluster using threshold photoionization with a tunable vacuum ultraviolet free electron laser. The ionization potential of B9 is measured to be 8.45±0.02 eV and it is found to have a heptagonal bipyramid D7h structure, quite different from the planar molecular wheel of the B9 - anionic cluster. Chemical bonding analyses reveal superior stability of the bipyramidal structure arising from delocalized σ and π bonding interactions within the B7 ring and between the B7 ring and the capping atoms. Photoionization of B9 breaks the single-electron B-B bond of the capping atoms, which undergo off-axis distortion to enhance interactions with the B7 ring in the singlet ground state of B9 +. The single-electron B-B bond of the capping atoms appears to be crucial in stabilizing the D7h structure of B9. This work opens avenues for direct size-dependent experimental studies of a large variety of neutral boron clusters to explore the stepwise development of network structures.

B92: a complete coating icosahedral B12 core-shell structure

Using first-principles calculations, this study unveils a spherically aromatic core-shell B12@B80 structure featuring a B12 icosahedral core, which is the smallest complete coating icosahedral B12 core-shell Bn cluster to date. Detailed orbital and bonding analyses reveal that the icosahedral B12 core exhibits prominent superatomic behavior with the electronic configuration 1S21P61D101F8.

Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based B8Al3+ Cluster

We studied the boron-based composite cluster B8Al3+ doped with Al atoms. The global minimum structure of the B8Al3+ cluster is a three-layer structure, consisting of three parts: an Al2 unit, a B8 ring and an isolated Al atom. Charge calculations analysis shows that the cluster can be expressed as [Al]+[B8]2-[Al2]2+, has 6π/6σ double aromaticity and follows the (4n+2) Hückel rule. Born-Oppenheimer molecular dynamics (BOMD) simulation shows that the B8Al3+ cluster has dynamic fluxionality properties. Remarkably, at the single-point coupled cluster singles, doubles and triples (CCSD(T)) level, the energy barrier for intramolecular rotation is merely 0.19 kcal mol-1. [B8]2- molecular wheels have magical 6π/6σ double aromaticity properties, providing a continuous cloud of delocalized electrons, which is a key factor in the dynamic fluxionality of the cluster. The B8Al3+ cluster provides a new example of dynamic structural fluxionality in molecular systems.

Amidinato silylene-based inorganic aromatic rings

Aromaticity is a key concept that underpins the behavior and applications of a wide range of chemical compounds. Its impact on stability, reactivity, biological functions, material properties, and environmental persistence underscores the importance of understanding and harnessing aromaticity in chemistry and materials sciences. We have been pioneers in the field of silylene chemistry and recently, our silylene molecules have been used to synthesize several inorganic aromatic ring compounds. Aromaticity in inorganic compounds is not commonly observed; hence, inorganic aromatic rings derived from silylene would further enhance our understanding of aromaticity and stability. Herein, we discuss the inorganic aromatic rings which have been synthesized from amidinato silylene.

Borophene nanoclusters: Energetics and structures from analytical potentials

Boron shows a variety of properties, determining a chemistry rich and complementary to that of carbon, the neighbor atom in the Periodic Table. In this work, we investigated the strength and nature of the interaction involving B12 or B36 monomer, which represent molecular prototypes of borophene, the two-dimensional allotrope of elemental boron. For the representation of the intermolecular interaction, we developed new potential energy surfaces (PESs) that are based on accurate ab initio or density functional theory data. It is shown that borophene molecules are bound by weak intermolecular interactions of van der Waals nature, perturbed by antiaromatic effects. Moreover, the proposed PESs are given in an analytical form proper to investigate the structures and energetics of (B12)n and (B36)n clusters (with n = 2-10) by applying a global geometry optimization procedure. It is found that the most stable structures of (B12)n favor close contacts between the edges of the monomers, leading to cage-like clusters as n increases, and conversely, (B36)n clusters are mainly composed of stacked or herringbone structures. These results suggest the possibility to produce a novel class of two-dimensional borophene materials, exhibiting different features compared to graphene like structures, which could be of interest for the nanotechnology.

Observation of Aromatic B13(CO)n+ (n = 1-7) as Boron Carbonyl Analogs of Benzene

CO as a typical σ-donor is one of the most important ligands in chemistry, while planar B13+ is experimentally known as the most prominent magic-number boron cluster analogous to benzene. Joint gas-phase mass spectroscopy, collision-induced dissociation, and first-principles theory investigations performed herein indicate that B13+ reacts with CO successively under ambient conditions to form a series of boron carbonyl complexes B13(CO)n+ up to n = 7, presenting the largest boron carbonyl complexes observed to date with a quasi-planar B13+ core at the center coordinated by nCO ligands around it. Extensive theoretical analyses unveil both the chemisorption pathways and bonding patterns of these aromatic B13(CO)n+ monocations which, with three delocalized π bonds well-retained over the slightly wrinkled B13+ moiety, all prove to be boron carbonyl analogs of benzene tentatively named as boron carbonyl aromatics (BCAs). Their π-isovalent B12(CO)n (n = 1-6) complexes with a quasi-planar B12 coordination center are predicted to be stable neutral BCAs.

Does Aromaticity Play a Role in Electronic and Structural Properties of YBn (n=2-14) Clusters?

Nanoclusters exhibit electronic, optical, and magnetic properties that differ significantly from those of extended and molecular systems with comparable stoichiometries. In this work, we examined the structural, energetic, and electronic characteristics of yttrium-doped boron clusters (YBn, where n ranges from 2 to 14) with the aid of robust wavefunction analysis tools. Special emphasis is placed on the elucidation of the potential aromatic character exhibited by the resultant molecules and how it can affect their chemical bonding and stability. Our results revealed that the YBn stability is governed by the maximization of the ionic Y-B interactions. This circumstance is evidenced from the lowest-energy conformations, which manifest as half-sandwich structures wherein the majority of boron atoms are bonded to yttrium. The stabilization of such chemical contacts comes at the expense of a notorious depletion of the Y local electron density, crystallizing in a considerable ionic character, close to Y2++B n 2 - ${{\rm{B}}_{\rm{n}}^{2 - } }$ . Such a prominent charge transfer is coupled to the enhancement of the electron delocalization within the Bn lattice, resulting in quite remarkable local and global aromatic characters. Altogether, this study shows how the toolkit of real space chemical bonding descriptors can offer valuable insights into the structural and electronic properties, along with the chemical bonding, of YBn clusters, contributing to a more comprehensive understanding of their behavior.

MB38(M=Be and Zn): A Quasi-Planar Structure Rather Than a Core-Shell Octahedral Borospherene Structure

In a recent paper (ChemPhysChem, 2023, 24, e202200947), based on the results computed using DFT method, the perfect core-shell octahedral configuration Be@B38 and Zn@B38 was reported to be the global minima of the MB38(M=Be and Zn) clusters. However, this paper presents the lower energy structures of MB38(M=Be and Zn) clusters as a quasi-planar configuration, the Be atom is found to reside on the convex surface of the quasi-planar B38 isomer, while the Zn atom tends to be attached to the top three B atoms of the quasi-planar B38 isomer. Our results show that quasi-planar MB38(M=Be and Zn) at DFT method have lower energy than core-shell octahedral configuration M@B38(M=Be and Zn). Natural atomic charges, valence electron density, electron localization function (ELF) analyses identify the MB38(M=Be and Zn) to be charge transfer complexes (Be2+B38 2-and Zn1+B38 1-) and suggest primarily the electrostatic interactions between doped atom and B38 fragment. The photoelectron spectra of the corresponding anionic structures were simulated, providing theoretical basis for future structural identification.

Theoretical Investigation on One-Electron ϕ···ϕ Bonding in Diuranium Inverse Sandwich U2B6 Complex Enabled by a B6 Ring

Traditional σ, π, and δ types of covalent chemical bonding have been extensively studied for nearly a century. In contrast, ϕ-type bonding involving nf (n = 4, 5) orbitals has received less attention due to their high contraction and minimal orbital overlap. Herein, we theoretically predict a singly occupied ϕ···ϕ bonding between two 5f orbitals, facilitated by B6 group orbitals in the hexa-boron diuranium inverse sandwich structure of U2B6. From ab initio quantum chemical calculations, the global minimum structure has a septuplet state with D6h symmetry. Chemical bonding analyses reveal that the 5f and 6d atomic orbitals of the two uranium atoms interact with the ligand orbitals of the central B6 ring, exhibiting favorable energy matching and symmetry compatibility to form delocalized σ-, π-, δ-, and ϕ-type bonding orbitals. Notably, even though the ϕ···ϕ bonding orbital is singly occupied, it still has a significant role in stability and cannot be overlooked. Furthermore, the U2B6 cluster model can be viewed as a building block of UB2 solid materials from both geometric and electronic perspectives. This work predicts the first example of ϕ···ϕ bonding, highlighting the complexity and diversity of chemical bonds formed in actinide boride clusters.

Fluxional Behavior and Stability of the Cu2B8- Cluster: A Copper Borozene with a Freely Rotating Cu2 Dimer

We demonstrate that Cu2B8- exhibits distinct fluxional behavior, akin to that of a functional stirrer, with the Cu2 dimer freely rotating on the B8 molecular wheel. This behavior is confirmed by Born-Oppenheimer molecular dynamics simulations. The initiation of this dynamic motion is facilitated by an ultrasoft vibrational mode (less than 10 cm-1), resulting in a negligible rotational barrier of 0.03 kcal/mol, as calculated at the single-point CCSD(T) level. The high stability of Cu2B8- arises from the strong interlayer electrostatic interaction between Cu2 and B8, due to charge transfer from Cu2 to B8, along with additional covalent interactions from the delocalized π electrons of the B8 wheel to the Cu2 dimer. Notably, the Cu2 dimer in Cu2B8- features a two-center one-electron Cu-Cu single bond, while the B82- moiety displays double aromaticity, characterized by the presence of six delocalized π electrons and six delocalized σ electrons.

Borozenes: Benzene-Like Planar Aromatic Boron Clusters

ConspectusWith three valence electrons and four valence orbitals, boron (2s22p1) is an electron-deficient element, resulting in interesting chemical bonding and structures in both borane molecules and bulk boron materials. The electron deficiency leads to electron sharing and delocalization in borane compounds and bulk boron allotropes, characterized by polyhedral cages, in particular, the ubiquitous B12 icosahedral cage. During the past two decades, the structures and bonding of size-selected boron clusters have been elucidated via combined photoelectron spectroscopy and theoretical investigations. Unlike bulk boron materials, finite boron clusters have been found to possess 2D structures consisting of B3 triangles, dotted with tetragonal, pentagonal, or hexagonal holes. The discovery of the planar B36 cluster with a central hexagonal hole provided the first experimental evidence for the viability of 2D boron nanostructures (borophene), which have been synthesized on inert substrates. The B7-, B8-, and B9- clusters were among the first few boron clusters to be investigated by joint photoelectron spectroscopy and theoretical calculations, and they were all found to possess 2D structures with a central B atom inside a Bn ring. Recently, the B73- (C6v), B82- (D7h), and B9- (D8h) series of closed-shell species were shown to possess similar π bonding akin to that in the C5H5-, C6H6, and C7H7+ series, respectively, and the name "borozene" was coined to highlight their analogy to the classical aromatic hydrocarbon molecules.Among the borozenes, the D7h B82- species is unique for its high stability originating from both its double aromaticity and the fact that the B7 ring has the perfect size to host a central B atom. The B82- borozene has been realized experimentally in a variety of MB8 and M2B8 complexes. In particular, the B82- borozene has been observed to stabilize the rare valence-I oxidation state of lanthanides in LnB8- complexes, as well as a Cu2+ species in Cu2B8-. The B6 ring in B73- is too small to host a B atom, resulting in a slight out-of-plane distortion. Interestingly, the bowl-shaped B7 borozene is perfect for coordination to a metal atom, leading to the observation of a series of highly stable MB7 borozene complexes. On the other hand, the B8 ring is slightly too large to host the central B atom, such that a low-lying and low-symmetry isomer also exists for B9-. Even though most 2D boron clusters are aromatic, the B73-, B82-, and B9- borozenes are special because of their high symmetries and their analogy to the series of C5H5-, C6H6, and C7H7+ prototypical aromatic compounds. This Account discusses recent experimental and theoretical advances on the investigations of various borozene complexes. It is expected that many new borozene compounds can be designed and may be eventually synthesized.

Intercluster B-H and B-B aggregation in iso- and trans-[B20H18]2-. Spherical aromaticity in borane dimers

The formation of molecular-based functional materials is a key step towards the development of technologies at the nanoscale. Recently, it has been shown that after oxidation of closo-[B10H10]2- anions, an induced aggregation of two cluster units is achieved, retaining their parent B10 backbones as persistent building blocks. Such characterization provides an interesting scenario to further understand relevant factors leading to aggregation in a minimal structure involving two units. Here, we explore the interaction between closo-[B10H10]2- units in two isomers, namely, iso- and trans-[B20H18]2-, involving different intercluster contacts based on B-B and B-H interactions, respectively. Our results show that the inherent spherical aromatic characteristics of the parent closo-[B10H10]2- cluster are persistent in both iso- and trans-[B20H18]2- isomers as an interplay between the spherical aromatic properties from both B10 motifs, leading to an overlap of the shielding regions from shielding cone properties, ascribed as a dual spherical-spherical aromatic cluster. From 11B-NMR features, it came out that trans-[B20H18]2- involves larger differences in comparison to closo-[B10H10]2-, owing to the variation of the B10-B10 backbone provided by the intercluster B-interaction, thus resulting in a more effective aggregation connecting such building units, towards boron-based cluster materials.

Structural Evolution of Small-Sized Phosphorus-Doped Boron Clusters: A Half-Sandwich-Structured PB15 Cluster

The present study is a theoretical investigation into the structural evolution, electronic properties, and photoelectron spectra of phosphorus-doped boron clusters PBn0/- (n = 3-17). The results of this study revealed that the lowest energy structures of PBn- (n = 3-17) clusters, except for PB17-, exhibit planar or quasi-planar structures. The lowest energy structures of PBn (n = 3-17), with the exceptions of PB7, PB9, and PB15, are planar or quasi-planar. The ground state of PB7 has an umbrella-shaped structure, with C6V symmetry. Interestingly, the neutral cluster PB15 has a half-sandwich-like structure, in which the P atom is attached to three B atoms at one end of the sandwich, exhibiting excellent relative and chemical stability due to its higher second-order energy difference and larger HOMO-LUMO energy gap of 4.31 eV. Subsequently, adaptive natural density partitioning (AdNDP) and electron localization function (ELF) analyses demonstrate the bonding characteristics of PB7 and PB15, providing support for the validity of their stability. The calculated photoelectron spectra show distinct characteristic peaks of PBn- (n = 3-17) clusters, thus providing theoretical evidence for the future identification of doped boron clusters. In summary, our work has significant implications for understanding the structural evolution of doped boron clusters PBn0/- (n = 3-17), motivating further experiments regarding doped boron clusters.

MB16 - (M=Sc, Y, La): Perfect Bowl-Like Boron Clusters

The introduction of transition-metal doping has engendered a remarkable array of unprecedented boron motifs characterized by distinctive geometries and bonding, particularly those heretofore unobserved in pure boron clusters. In this study, we present a perfect (no defects) boron framework manifesting an inherently high-symmetry, bowl-like architecture, denoted as MB16 - (M=Sc, Y, La). In MB16 -, the B16 is coordinated to M atoms along the C5v-symmetry axis. The bowl-shaped MB16 - structure is predicted to be the lowest-energy structure with superior stability, owing to its concentric (2 π+10 π) dual π aromaticity. Notably, the C5v-symmetry bowl-like B16 - is profoundly stabilized through the doping of an M atom, facilitated by strong d-pπ interactions between M and boron motifs, in conjunction with additional electrostatic stabilization by an electron transfer from M to the boron motifs. This concerted interplay of covalent and electrostatic interactions between M and bowl-like B16 renders MB16 - a species of exceptional thermodynamic stability, thus making it a viable candidate for gas-phase experimental detection.

Searching for stable copper borozene complexes in CuB7- and CuB8. Phys Chem Chem Phys 2024;26:12928-12938. [PMID: 38456623 DOI: 10.1039/d4cp00296b]

Copper has been shown to be an important substrate for the growth of borophenes. Copper-boron binary clusters are ideal platforms to study the interactions between copper and boron, which may provide insight about the underlying growth mechanisms of borophene on copper substrates. Here we report a joint photoelectron spectroscopy and theoretical study on two copper-doped boron clusters, CuB7- and CuB8-. Well resolved photoelectron spectra are obtained for the two clusters at different wavelengths and are used to understand the structures and bonding properties of the two CuBn- clusters. We find that CuB8- is a highly stable borozene complex, which possesses a half-sandwich structure with a Cu+ species interacting with the doubly aromatic η8-B82- borozene. The CuB7- cluster is found to consist of a terminal copper atom bonded to a double-chain B7 motif, but it has a low-lying isomer composed of a half-sandwich structure with a Cu+ species interacting with an open-shell η7-B72- borozene. Both ionic and covalent interactions are found to be possible in the binary Cu-B clusters, resulting in different structures.

Electronic Control of the Position of the Pb Atom on the Surface of B8 Borozene in the PbB8 Cluster

Spontaneous symmetry-breaking is common in chemical and physical systems. Here, we show that by adding an electron to the C7v PbB8 cluster, which consists of a planar B8 disk with the Pb atom situated along the C7 axis, the Pb atom spontaneously moves to the off-axis position in the PbB8- anion. Photoelectron spectroscopy of PbB8- reveals a broad ground-state transition and a large energy gap, suggesting a highly stable closed-shell PbB8 borozene complex and a significant geometry change upon electron detachment. Quantum chemistry calculations indicate that the lowest unoccupied molecular orbital of the C7v PbB8 cluster is a degenerate π orbital mainly consisting of the Pb 6px and 6py atomic orbitals. Occupation of one of the 6p orbitals spontaneously break the C7v symmetry in the anion due to the Jahn-Teller effect. The large amplitude of the position change of Pb in PbB8- relative to PbB8 is surprising owing to bonding interactions between the Pb 6p orbital with the π orbital of the B8 borozene.

Build Borophite from Borophenes: A Boron Analogue Graphite

Unlike graphene derived from graphite, borophenes represent a distinct class of synthetic two-dimensional materials devoid of analogous bulk-layered allotropes, leading to covalent bonding within borophenes instead of van der Waals (vdW) stacking. Our investigation focuses on 665 vdW-stacking boron bilayers to uncover potential bulk-layered boron allotropes through vdW stacking. Systematic high-throughput screening and stability analysis reveal a prevailing inclination toward covalently bonded layers in the majority of boron bilayers. However, an intriguing outlier emerges in δ5 borophene, demonstrating potential as a vdW-stacking candidate. We delve into electronic and topological structural similarities between δ5 borophene and graphene, shedding light on the structural integrity and stability of vdW-stacked boron structures across bilayers, multilayers, and bulk-layered allotropes. The δ5 borophene analogues exhibit metallic properties and characteristics of phonon-mediated superconductors, boasting a critical temperature near 22 K. This study paves the way for the concept of "borophite", a long-awaited boron analogue of graphite.

Unraveling the Mechanism of Doping Borophene

We elucidate the doping mechanism of suitable elements into borophene with first-principles density functional theory calculation. During doping with nitrogen (N), the sp2 orbitals are responsible for arranging themselves to accommodate the electron of the N atom. Doping dramatically changes structure and electronic properties from corrugated and metallic borophene to flat and insulating h-BN with 100 % N-doping. We extend the mechanism of N-doping in borophene to doping of non-metallic and metallic ad-atoms on borophene. Our findings will help to design boron-based 2D materials.

Boron-based ternary MgTa2B6 cluster: a turning nanoclock with dynamic structural fluxionality

Boron-based complex clusters are a fertile ground for the exploration of exotic chemical bonding and dynamic structural fluxionality. Here we report on the computational design of a ternary MgTa2B6 cluster via global structural searches and quantum chemical calculations. The cluster turns out to be a new member of the molecular rotor family, closely mimicking a turning clock at the subnanoscale. It is composed of a hexagonal B6 ring with a capping Ta atom at the top and bottom, whereas the Mg atom is linked to one Ta site as a radial Ta-Mg dimer. These components serve as the dial, axis, and hand of a nanoclock, respectively. Chemical bonding analyses reveal that the inverse sandwich Ta2B6 motif in the cluster features 6π/6σ double aromaticity, whose electron counting conforms to the (4n + 2) Hückel rule. The Ta-Mg dimer has a Lewis-type σ bond, and the Mg site has negligible bonding with B6 ring. The ternary cluster can be formulated as an [Mg]0[Ta2B6]0 complex. Molecular dynamics simulations suggest that the cluster is structurally fluxional analogous to a nanoclock, even at a low temperature of 100 K. The Ta-Mg hand turns almost freely around the Ta2 axis and along the B6 dial. The tiny intramolecular rotation barrier is less than 0.3 kcal mol-1, being dictated by the bonding nature of double 6π/6σ aromaticity. The present system offers a new type of molecular rotor in physical chemistry.

Investigation of Pb-B Bonding in PbB2(BO)n- (n = 0-2): Transformation from Aromatic PbB2- to Pb[B2(BO)2]-/0 Complexes with BB Triple Bonds

Boron has been found to be able to form multiple bonds with lead. To probe Pb-B bonding, here we report an investigation of three Pb-doped boron clusters, PbB2-, PbB3O-, and PbB4O2-, which are produced by a laser ablation cluster source and characterized by photoelectron spectroscopy and ab initio calculations. The most stable structures of PbB2-, PbB3O-, and PbB4O2- are found to follow the formula, [PbB2(BO)n]- (n = 0-2), with zero, one, and two boronyl ligands coordinated to a triangular and aromatic PbB2 core, respectively. The PbB2- cluster contains a BB double bond and two Pb-B single bonds. The coordination of BO is observed to weaken Pb-B bonding but strengthen the BB bond in [PbB2(BO)n]- (n = 1, 2). The anionic [PbB2(BO)2]- and its corresponding neutral closed-shell [PbB2(BO)2] contain a BB triple bond. A low-lying Y-shaped isomer is also observed for PbB4O2-, consisting of a central sp2 hybridized B atom bonded to two boronyl ligands and a PbB unit.

Advances for Triangular and Sandwich-Shaped All-Metal Aromatics

Much experimental work has been contributed to all-metal σ, π and δ-aromaticity among transition metals, semimetallics and other metals in the past two decades. Before our focused investigations on the properties of triangular and sandwich-shaped all-metal aromatics, A. I. Boldyrev presented general discussions on the concepts of all-metal σ-aromaticity and σ-antiaromaticity for metallo-clusters. Schleyer illustrated that Nucleus-Independent Chemical Shifts (NICS) were among the most authoritative criteria for aromaticity. Ugalde discussed the earlier developments of all-metal aromatic compounds with all possible shapes. Besides the theoretical predictions, many stable all-metal aromatic trinuclear clusters have been isolated as the metallic analogues of either the σ-aromatic molecule's [H3]+ ion or the π-aromatic molecule's [C3H3]+ ion. Different from Hoffman's opinion on all-metal aromaticity, triangular all-metal aromatics were found to hold great potential in applications in coordination chemistry, catalysis, and material science. Triangular all-metal aromatics, which were theoretically proved to conform to the Hückel (4n + 2) rule and possess the smallest aromatic ring, could also play roles as stable ligands during the formation of all-metal sandwiches. The triangular and sandwich-shaped all-metal aromatics have not yet been specifically summarized despite their diversity of existence, puissant developments and various interesting applications. These findings are different from the public opinion that all-metal aromatics would be limited to further applications due to their overstated difficulties in synthesis and uncertain stabilities. Our review will specifically focus on the summarization of theoretical predictions, feasible syntheses and isolations, and multiple applications of triangular and sandwich shaped all-metal aromatics. The appropriateness and necessities of this review will emphasize and disseminate their importance and applications forcefully and in a timely manner.

Two-Dimensional Transition Metal Boron Cluster Compounds (MBnenes) with Strain-Independent Room-Temperature Magnetism

Two-dimensional (2D) metal borides (MBenes) with unique electronic structures and physicochemical properties hold great promise for various applications. Given the abundance of boron clusters, we proposed employing them as structural motifs to design 2D transition metal boron cluster compounds (MBnenes), an extension of MBenes. Herein, we have designed three stable MBnenes (M4(B12)2, M = Mn, Fe, Co) based on B12 clusters and investigated their electronic and magnetic properties using first-principles calculations. Mn4(B12)2 and Co4(B12)2 are semiconductors, while Fe4(B12)2 exhibits metallic behavior. The unique structure in MBnenes allows the coexistence of direct exchange interactions between adjacent metal atoms and indirect exchange interactions mediated by the clusters, endowing them with a Néel temperature (TN) up to 772 K. Moreover, both Mn4(B12)2 and Fe4(B12)2 showcase strain-independent room-temperature magnetism, making them potential candidates for spintronics applications. The MBnenes family provides a fresh avenue for the design of 2D materials featuring unique structures and excellent physicochemical properties.

Li6 E5 Li6 : Tetrel Sandwich Complexes with 10-π-Electrons

When (4n +2) π-electrons are located in single planar ring, it conventionally qualifies as aromatic. According Hückel's rule, systems possessing ten π-electrons should be aromatic. Herein we report a series of D5h  Li6 E5 Li6 sandwich structures, representing the first global minima featuring ten π-electrons E5 10- ring (E=Si-Pb). However, these π-electrons localize as five π-lone-pairs rather than delocalized orbitals. The high symmetry structure achieved is a direct consequence of σ-aromaticity, particularly favored in elements from Si to Pb, resulting in a pronounced diatropic ring current flow that contributes to the enhanced stability of these systems.

A Neutral Planar Four-Membered Si2B2 2π-Aromatic Ring

The synthesis of the first inorganic four-membered neutral 2π-aromatic compound 2 is reported. This unique ring has been synthesized from a simple and straightforward reaction of amidinato-silylene with dichlorophenylborane, followed by the reduction with KC8 in THF. Compound 2 has been fully characterized by single-crystal X-ray diffraction (SC-XRD), NMR spectroscopy, and mass spectrometry. The computational calculations reveal that the Si2B2 ring is a π-delocalized system resulting from the interaction of pπ orbital of B and Si-N σ* orbitals having pseudo π symmetry. Compound 2 is the first known example of a neutral planar inorganic analogue of cyclobutenyl dication.

PB12+ and P2B12+/0/-: The Novel B12 Cage Doped by Nonmetallic P Atoms

A new kind of nonmetallic atom-doped boron cluster is described herein theoretically. When a phosphorus atom is added to the B12 motif and loses an electron, a novel B12 cage is obtained, composed of two B3 rings at both ends and one B6 ring in the middle, forming a triangular bifrustum. Interestingly, this B12 cage is formed by three B7 units joined together from three directions at an angle of 120°. When two P atoms are added to the B12 motif, this novel B12 cage is also obtained, and two P atoms are attached to the B3 rings at both ends of the triangular bifrustum, forming a triangular bipyramid (Johnson solid). Amazingly, the global minimums of neutral, monocationic, and monoanionic P2B12+/0/- have the same cage structure with a D3h symmetry; this is the smallest boron cage with the same structure. The P atom has five valence electrons, according to adaptive natural density partitioning bonding analyses of cage PB12+ and P2B12, in addition to one lone pair, the other three electrons of the P atom combine with an electron of each B atom on the B3 ring to form three 2c-2e σ bonds and form three electron sharing bonds with B atoms through covalent interactions, stabilizing the B12 cage. The calculated photoelectron spectra can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of PnB12- (n = 1-2).

Boron-based Pd3B26 alloy cluster as a nanoscale antifriction bearing system: tubular core-shell structure, double π/σ aromaticity, and dynamic structural fluxionality

Boron-based nanoclusters show unique geometric structures, nonclassical chemical bonding, and dynamic structural fluxionality. We report here on the theoretical prediction of a binary Pd3B26 cluster, which is composed of a triangular Pd3 core and a tubular double-ring B26 unit in a coaxial fashion, as identified through global structural searches and electronic structure calculations. Molecular dynamics simulations indicate that in the core-shell alloy cluster, the B26 double-ring unit can rotate freely around its Pd3 core at room temperature and beyond. The intramolecular rotation is virtually barrier free, thus giving rise to an antifriction bearing system (or ball bearing) at the nanoscale. The dimension of the dynamic system is only 0.66 nm. Chemical bonding analysis reveals that Pd3B26 cluster possesses double 14π/14σ aromaticity, following the (4n + 2) Hückel rule. Among 54 pairs of valence electrons in the cluster, the overwhelming majority are spatially isolated from each other and situated on either the B26 tube or the Pd3 core. Only one pair of electrons are primarily responsible for chemical bonding between the tube and the core, which greatly weaken the bonding within the Pd3 core and offers structural flexibility. This is a key mechanism that effectively diminishes the intramolecular rotation barrier and facilitates dynamic structural fluxionality of the system. The current work enriches the field of nanorotors and nanomachines.

Structural Evolution and Electronic Properties of Two Sulfur Atom-Doped Boron Clusters

We present a theoretical study of structural evolution, electronic properties, and photoelectron spectra of two sulfur atom-doped boron clusters S2Bn0/- (n = 2-13), which reveal that the global minima of the S2Bn0/- (n = 2-13) clusters show an evolution from a linear-chain structure to a planar or quasi-planar structure. Some S-doped boron clusters have the skeleton of corresponding pure boron clusters; however, the addition of two sulfur atoms modified and improved some of the pure boron cluster structures. Boron is electron-deficient and boron clusters do not form linear chains. Here, two sulfur atom doping can adjust the pure boron clusters to a linear-chain structure (S2B20/-, S2B30/-, and S2B4-), a quasi-linear-chain structure (S2B6-), single- and double-chain structures (S2B6 and S2B9-), and double-chain structures (S2B5, and S2B9). In particular, the smallest linear-chain boron clusters S2B20/- are shown with an S atom attached to each end of B2. The S2B2 cluster possesses the largest highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap of 5.57 eV and the S2B2- cluster possesses the largest average binding energy Eb of 5.63 eV, which shows the superior chemical stability and relative stability, respectively. Interestingly, two S-atom doping can adjust the quasi-planar pure boron clusters (B7-, B10-, and B120/-) to a perfect planar structure. AdNDP bonding analyses reveal that linear S2B3 and planar SeB11- have π aromaticity and σ antiaromaticity; however, S2B2, planar S2B6, and planar S2B7- clusters have π antiaromaticity and σ aromaticity. Furthermore, AdNDP bonding analyses reveal that planar S2B4, S2B10, and S2B12 clusters are doubly (π and σ) aromatic, whereas S2B5-, S2B8, S2B9-, and S2B13- clusters are doubly (π and σ) antiaromatic. The electron localization function (ELF) analysis shows that S2Bn0/- (n = 2-13) clusters have different electron delocalization characteristics, and the spin density analysis shows that the open-shell clusters have different characteristics of electron spin distribution. The calculated photoelectron spectra indicate that S2Bn- (n = 2-13) have different characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these doped boron clusters. Our work enriches the new database of geometrical structures of doped boron clusters, provides new examples of aromaticity for doped boron clusters, and is promising to offer new ideas for nanomaterials and nanodevices.

Nanoclusters and nanoalloys of group 13 elements (B, Al, and Ga): benchmarking of methods and analysis of their structures and energies

We investigated the structural and energetic properties of nanoclusters and nanoalloys composed of group 13 elements (B, Al, and Ga) up to a cluster size of 12. We conducted a comprehensive benchmark analysis of density functional and post-Hartree-Fock methods to identify efficient and accurate approaches for studying these systems using our benchmark dataset (BAlGa16) consisting of sixteen dimers and trimers. We compared different density functionals and post-Hartree-Fock methods using bond length and binding energy as parameters. B2PLYP closely follows CCSD(T) for geometry optimization, while REVPBE, BPBE, and PBE show cost-accuracy balanced performances. MRACPF was used as the reference for benchmarking energies, with NEVPT2 being the most accurate method, followed by CCSD(T) and DLPNO-CCSD(T). M06 and range-separated hybrid functionals perform well. Based on a cost-accuracy analysis, we recommend M06/def2-SVP as the preferred method. Additionally, we explored the structural evolution of pure, binary, and ternary clusters of group 13 elements up to 12 atoms, uncovering global and local minima. Ga clusters exhibited more rectangular faces compared to the predominantly trigonal faces of B and Al clusters. Binary clusters showed B in center positions, while Ga preferred outer positions, confirming the higher cohesion of B. The most favorable size of binary clusters (12) exhibited similar compositions of Al and Ga atoms. Compositions with 16.67-40% B, 16.67-60% Al, and 20-50% Ga were estimated to have negative mixing energies, indicating their relative stability.

A DFT study to investigate the physical, electrical, optical properties and thermodynamic functions of boron nanoclusters (MxB2n0; x=1,2, n=3,4,5)

First Principle DFT calculations employing the B3LYP/LanL2DZ/SDD level of theory were used to analyze the various characteristics of boron nanoclusters (B6, B8, and B10). These pure structures were further doped with four transition metals (Ta, Ti, Tc, and V) to examine the enhancement of the pure structures' structural, electrical, and optical features. To study structural stability, we have estimated cohesion energy and imaginary frequencies. Cohesion energies were entirely negative, with a range of -3.37 eV to -8.07 eV, and most constructions had no imaginary frequencies, indicating their structural occurrences. The calculated adsorption energy suggests that the order of stability of the pristine boron nanoclusters is B10>B8>B6, and TcB10 and Tc2B10 are the more stable structures. Mulliken charge, DOS, HOMO-LUMO, and the HOMO-LUMO gap have all been examined in-depth to provide insight into electrical characteristics. UV-Vis and CD measurements show the doped boron nanoclusters have excellent optical properties. Aside from calculating thermodynamic functions, we have also calculated the global DFT parameters, which give us a deep quantum mechanical understanding of the optimized structure for further research and applications in the field of science and technology.

Boron-Based Inverse Sandwich V2B7- Cluster: Double π/σ Aromaticity, Metal-Metal Bonding, and Chemical Analogy to Planar Hypercoordinate Molecular Wheels

Inverse sandwich clusters composed of a monocyclic boron ring and two capping transition metal atoms are interesting alloy cluster systems, yet their chemical bonding nature has not been sufficiently elucidated to date. We report herein on the theoretical prediction of a new example of boron-based inverse sandwich alloy clusters, V₂B₇^-, through computational global-minimum structure searches and quantum chemical calculations. This alloy cluster has a heptatomic boron ring as well as a perpendicular V₂ dimer unit that penetrates through the ring. Chemical bonding analysis suggests that the inverse sandwich cluster is governed by globally delocalized 6π and 6σ frameworks, that is, double 6π/6σ aromaticity following the (4n + 2) Hückel rule. The skeleton B-B σ bonding in the cluster is shown not to be strictly Lewis-type two-center two-electron (2c-2e) σ bonds. Rather, these are quasi-Lewis-type, roof-like 4c-2e V-B₂-V σ bonds, which amount to seven in total and cover the whole surface of inverse sandwich in a truly three-dimensional manner. Theoretical evidence is revealed for a 2c-2e Lewis σ single bond within the V₂ dimer. Direct metal-metal bonding is scarce in inverse sandwich alloy clusters. The present inverse sandwich alloy cluster also offers a new type of electronic transmutation in physical chemistry, which helps establish an intriguing chemical analogy between inverse sandwich clusters and planar hypercoordinate molecular wheels.

Photoelectron Spectroscopy and Theoretical Study of Di-Copper-Boron Clusters: Cu2B3- and Cu2B4. J Phys Chem A 2023. [PMID: 37235389 DOI: 10.1021/acs.jpca.3c02417]

Copper has been found to be able to mediate the formation of bilayer borophenes. Copper-boron binary clusters are ideal model systems to probe the copper-boron interactions, which are essential to understand the growth mechanisms of borophenes on copper substrates. Here, we report a joint photoelectron spectroscopy and theoretical study on two di-copper-doped boron clusters: Cu₂B₃^- and Cu₂B₄^-. Well-resolved photoelectron spectra are obtained, revealing the presence of a low-lying isomer in both cases. Theoretical calculations show that the global minimum of Cu₂B₃^- (C_2v, ¹A₁) contains a doubly aromatic B₃^- unit weakly interacting with a Cu₂ dimer, while the low-lying isomer (C_2v, ¹A₁) consists of a B₃ triangle with the two Cu atoms covalently bonded to two B atoms at two vertexes. The global minimum of Cu₂B₄^- (D_2h, ²A_g) is found to consist of a rhombus B₄ unit covalently bonded to the two Cu atoms at two opposite vertexes, whereas in the low-lying isomer (C_s, ²A'), one of the two Cu atoms is bonded to two B atoms.

Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based Na5B7 Sandwich Cluster

Doping alkali metals into boron clusters can effectively compensate for the intrinsic electron deficiency of boron and lead to interesting boron-based binary clusters, owing to the small electronegativity of the former elements. We report on the computational design of a three-layered sandwich cluster, Na5B7, on the basis of global-minimum (GM) searches and electronic structure calculations. It is shown that the Na5B7 cluster can be described as a charge-transfer complex: [Na4]2+[B7]3-[Na]+. In this sandwich cluster, the [B7]3- core assumes a molecular wheel in shape and features in-plane hexagonal coordination. The magic 6π/6σ double aromaticity underlies the stability of the [B7]3- molecular wheel, following the (4n + 2) Hückel rule. The tetrahedral Na4 ligand in the sandwich has a [Na4]2+ charge-state, which is the simplest example of three-dimensional aromaticity, spherical aromaticity, or superatom. Its 2σ electron counting renders σ aromaticity for the ligand. Overall, the sandwich cluster has three-fold 6π/6σ/2σ aromaticity. Molecular dynamics simulation shows that the sandwich cluster is dynamically fluxional even at room temperature, with a negligible energy barrier for intramolecular twisting between the B7 wheel and the Na4 ligand. The Na5B7 cluster offers a new example for dynamic structural fluxionality in molecular systems.

Theory of sigma bond resonance in flat boron materials

In chemistry, theory of aromaticity or π bond resonance plays a central role in intuitively understanding the stability and properties of organic molecules. Here we present an analogue theory for σ bond resonance in flat boron materials, which allows us to determine the distribution of two-center two-electron and three-center two-electron bonds without quantum calculations. Based on this theory, three rules are proposed to draw the Kekulé-like bonding configurations for flat boron materials and to explore their properties intuitively. As an application of the theory, a simple explanation of why neutral borophene with ~1/9 hole has the highest stability and the effect of charge doping on borophene's optimal hole concentration is provided with the assumption of σ and π orbital occupation balance. Like the aromaticity theory for carbon materials, this theory greatly deepens our understanding on boron materials and paves the way for the rational design of various boron-based materials.

Electron Propagator Theory of Vertical Electron Detachment Energies of Anions: Benchmarks and Applications to Nucleotides

A new generation of ab initio electron-propagator self-energy approximations that are free of adjustable parameters is tested on a benchmark set of 55 vertical electron detachment energies of closed-shell anions. Comparisons with older self-energy approximations indicate that several new methods that make the diagonal self-energy approximation in the canonical Hartree-Fock orbital basis provide superior accuracy and computational efficiency. These methods and their acronyms, mean absolute errors (in eV), and arithmetic bottlenecks expressed in terms of occupied (O) and virtual (V) orbitals are the opposite-spin, non-Dyson, diagonal second-order method (os-nD-D2, 0.2, OV²), the approximately renormalized quasiparticle third-order method (Q3+, 0.15, O²V³) and the approximately renormalized, non-Dyson, linear, third-order method (nD-L3+, 0.1, OV⁴). The Brueckner doubles with triple field operators (BD-T1) nondiagonal electron-propagator method provides such close agreement with coupled-cluster single, double, and perturbative triple replacement total energy differences that it may be used as an alternative means of obtaining standard data. The new methods with diagonal self-energy matrices are the foundation of a composite procedure for estimating basis-set effects. This model produces accurate predictions and clear interpretations based on Dyson orbitals for the photoelectron spectra of the nucleotides found in DNA.

Two-layer molecular rotors: A zinc dimer rotating over planar hypercoordinate motifs

Multi-layer molecular rotors represent a class of unique combination of topology and bonding, featuring a barrier-free rotation of one layer with respect to other layers. This emerging fluxional behavior has been found in a few doped boron clusters. Herein, we strongly enrich this intriguing family followed by an effective design strategy, summarized as essential factors: i) considerable electrostatic interactions originated from a strong charge transfer between layers; ii) the absence of strong covalent bonds between layers; and iii) fully delocalized σ/π electrons from at least one layer. We found that planar hypercoordinate motifs consisting of monocyclic boron rings and metals with σ + π dual aromaticity can be regarded as one promising layer, which can support the suspended X₂ (X = Zn, Cd, Hg) dimers. By detailed investigations of thermodynamic and kinetic stabilities of 60 species, eventually, MB₇ X₂ ^- and MB₈ X₂ (X = Zn, Cd; M = Be, Ru, Os; Be works only for Zn-based cases) clusters were verified to be the global-minimum two-layer molecular rotors. Especially, their electronic structure analyses vividly confirm the practicability of the electronic structure requirements mentioned above for designing multi-layer molecular rotors.

Be3B11- cluster: a dynamically fluxional beryllo-borospherene

The beryllium-doped Be₃B₁₁^- cluster has two nearly isoenergetic isomers, adopting the smallest trihedral spherical geometries with a boron single-chain skeleton. The B₁₁ skeleton in the global minimum (C_2v, ¹A₁) comprises three conjoined boron rings (one B₈/two B₇) on the waist, sharing two B₃ equilateral triangles at the top and bottom, respectively. However, the local minimum (C_s, ¹A') has one deformed B₄ pyramid at the top. The drastic structural transformation of B₁₁ skeletons from perfectly planar B₁₁ clusters mainly profited from robust electrostatic interaction between Be atoms and B₁₁ skeletons. The dynamic simulations suggest that two species can interconvert via a novel mechanism, that is "triangle-pyramid-triangle", which facilitates the free migration of boron atoms in the B₁₁ skeleton, thereby showing the fascinating dynamic fluxionality. The chemical bonding analyses reveal that the B₁₁ skeleton is covered by two types of delocalized π bonds in an orthogonal direction, which leads to its spherical aromaticity.

The dodeca-coordinated La©B8C4 +/0/- molecular wheels: conflicting aromaticity versus double aromaticity

The transition-metal centered boron molecular wheels have attracted the attention of chemists. The highest deca-coordination number for central metal atoms was observed in D _10h Ta©B₁₀ ^- and Nb©B₁₀ ^- molecular wheels. Here, we report a theoretical study of La©B₈C₄ ^q (q = +1, 0, -1) clusters with the dodeca-coordinated La atom. The La©B₈C₄ ^q clusters adopt fascinating molecular wheel structures, showing a La atom enclosed by a perfect B₈C₄ monocyclic ring. The cationic La©B₈C₄ ⁺ cluster has a C _4v symmetry with the distinctly out-of-plane distortion of the La atom (0.70 Å), which is gradually flattened by the sequential reduction reaction. The distortion of the La atom from the plane in the neutral La©B₈C₄ cluster decreases to 0.46 Å. The La©B₈C₄ ^- species turns out to be perfectly planar. Chemical bonding analyses indicate that the neutral La©B₈C₄ and anionic La©B₈C₄ ^- possess 10σ and 9π/10π double aromaticity, respectively, obeying the principle of double aromaticity. However, the cationic La©B₈C₄ ⁺ has 10σ and 8π conflicting aromaticity, representing a counterexample in planar hyper-coordinated molecular wheels. The dodeca-coordination number in La©B₈C₄ ^q (q = +1, 0, -1) clusters is unprecedented, which provides a new idea and concept for searching planar hyper-coordinated systems.

Chemical bonding and dynamic structural fluxionality of a boron-based Al2B8 binary cluster: the robustness of a doubly 6π/6σ aromatic [B8]2- molecular wheel

Despite the isovalency between Al and B elements, Al-doping in boron clusters can deviate substantially from an isoelectronic substitution process. We report herein on a unique sandwich di-Al-doped boron cluster, Al₂B₈, using global structural searches and quantum chemical calculations. The cluster features a perfectly planar B₈ molecular wheel, with two isolated Al atoms symmetrically floating above and below it. The two Al atoms are offset from the center of the molecular wheel, resulting in a C _2v symmetry for the cluster. The Al₂B₈ cluster is shown to be dynamically fluxional even at far below room temperature (100 K), in which a vertical Al₂ rod slides or rotates freely within a circular rail on the B₈ plate, although there is no direct Al-Al interaction. The energy barrier for intramolecular rotation is only 0.01 kcal mol^-1 at the single-point CCSD(T) level. Chemical bonding analysis shows that the cluster is a charge-transfer complex and can be formulated as [Al]⁺[B₈]^2-[Al]⁺. The [B₈]^2- molecular wheel in sandwich cluster has magic 6π/6σ double aromaticity, which underlies the dynamic fluxionality, despite strong electrostatic interactions between the [Al]⁺, [B₈]^2-, and [Al]⁺ layers.

A plier-shaped binary molecular wheel B7Mg4+ cluster: hybrid in-plane heptacoordination, double π/σ aromaticity, and electronic transmutation

A plier-shaped charge-transfer [Mg2]2+[Mg2B7]− complex cluster exhibits double 6π/6σ aromaticity, whose hybrid molecular wheel structure is rationalized using the concept of electronic transmutation.

Structural Evolution and Electronic Properties of Selenium-Doped Boron Clusters SeBn0/- (n = 3-16)

A theoretical research of structural evolution, electronic properties, and photoelectron spectra of selenium-doped boron clusters SeBn0/- (n = 3-16) is performed using particle swarm optimization (CALYPSO) software in combination with density functional theory calculations. The lowest energy structures of SeBn0/- (n = 3-16) clusters tend to form quasi-planar or planar structures. Some selenium-doped boron clusters keep a skeleton of the corresponding pure boron clusters; however, the addition of a Se atom modified and improved some of the pure boron cluster structures. In particular, the Se atoms of SeB7-, SeB8-, SeB10-, and SeB12- are connected to the pure quasi-planar B7-, B8-, B10-, and B12- clusters, which leads to planar SeB7-, SeB8-, SeB10-, and SeB12-, respectively. Interestingly, the lowest energy structure of SeB9- is a three-dimensional mushroom-shaped structure, and the SeB9- cluster displays the largest HOMO-LUMO gap of 5.08 eV, which shows the superior chemical stability. Adaptive natural density partitioning (AdNDP) bonding analysis reveals that SeB8 is doubly aromatic, with 6 delocalized π electrons and 6 delocalized σ electrons, whereas SeB9- is doubly antiaromatic, with 4 delocalized π electrons and 12 delocalized σ electrons. Similarly, quasi-planar SeB12 is doubly aromatic, with 6 delocalized π electrons and 14 delocalized σ electrons. The electron localization function (ELF) analysis shows that SeBn0/- (n = 3-16) clusters have different local electron delocalization and whole electron delocalization effects. The simulated photoelectron spectra of SeBn- (n = 3-16) have different characteristic bands that can identify and confirm SeBn- (n = 3-16) combined with future experimental photoelectron spectra. Our research enriches the geometrical structures of small doped boron clusters and can offer insight for boron-based nanomaterials.

Theoretical Investigation of Geometries and Bonding of Indium Hydrides in the In2Hx and In3Hy (x = 0-4,6; y = 0-5) Series

Boron hydrides have been an object of intensive theoretical and experimental investigation for many decades due to their unusual and somewhat unique bonding patterns. Despite boron being a neighboring element to carbon, boron hydrides almost always form non-classical structures with multi-center bonds. However, we expect indium to form its interesting molecules with non-classical patterns, though such molecules still need to be extensively studied theoretically. In this work, we investigated indium hydrides of In₂H_x (x = 0-4,6) and In₃H_y (y = 0-5) series via DFT and ab initio quantum chemistry methods, performing a global minimum search, chemical bonding analysis, and studies of their thermodynamical stability. We found that the bonding pattern of indium hydrides differs from the classical structures composed of 1c-2e lone pairs and 2c-2e bonds and the bonding pattern of earlier investigated boron hydrides of the B_nH_n+2 series. The studied stoichiometries are characterized by multi-center bonds, aromaticity, and the tendency for indium to preserve the 1c-2e lone pair.

Effect of Nature of Substituents on Coordination Properties of Mono- and Disubstituted Derivatives of Boron Cluster Anions [BnHn]2– (n = 10, 12) and Carboranes with exo-Polyhedral B–X Bonds (X = N, O, S, Hal)

This review systematizes data on the coordination ability of mono- and disubstituted derivatives of boron cluster anions and carboranes in complexation with transition metals. Boron clusters anions [BnHn]2–, monocarborane anions [CBnHn–1]–, and dicarboranes [C2BnHn–2] (with non-functionalized carbon atoms) (n = 10, 12) containing the B–X exo-polyhedral bonds (X = N, O, S, Hal) are discussed. Synthesis and structural features of complexes known to date are described. The effect of complexing metal and substituent attached to the boron cage on the composition and structures of the final complexes is analyzed. It has been established that substituted derivatives of boron cluster anions and carboranes can act as both ligands and counterions. A complexing agent can coordinate substituted derivatives of the boron cluster anions due to three-center two-electron 3c2e MHB bonds, by the substituent functional groups, or a mixed type of coordination can be realized, through the BH groups of the boron cage and the substituent. As for B-substituted carboranes, complexes with coordinated substituents or salts with non-coordinated carborane derivatives have been isolated; compounds with MHB bonding are not characteristic of carboranes.

Unprecedented Prediction of a B160 Cluster Stuffed by Dual-Icosahedron B12

Serving as the premise to understand bulk allotropes, boron clusters have been intriguing experimentalists and theoreticians to study their geometries and chemical bonding. Here, we designed a complete core-shell B₁₆₀ cluster stuffed by two B₁₂ cores, which is energetically preferable over the bilayer structure of the same size. The unprecedented peanutlike structure with C_i symmetry has superior stability and exhibits superatomic electronic configuration and spherical aromaticity. Our theoretical work not only proposed the core-shell structure of dual icosahedrons for the first time but also indicated the multi-B₁₂ core-shell structural pattern in boron particles, bridging to boron crystalline structures.