Stabilization of fullerene-like boron cages by transition metal encapsulation

Conformational Preference of Lithium Polysulfide Clusters Li2Sx (x = 4-8) in Lithium-Sulfur Batteries

Structures are of fundamental importance for diverse studies of lithium polysulfide clusters, which govern the performance of lithium-sulfur batteries. The ring-like geometries were regarded as the most stable structures, but their physical origin remains elusive. In this work, we systematically explored the minimal structures of Li2Sx (x = 4-8) clusters to uncover the driving force for their conformational preferences. All low-lying isomers were generated by performing global searches using the ABCluster program, and the ionic nature of the Li···S interactions was evidenced with the energy decomposition analysis based on the block-localized wave function (BLW-ED) approach and further confirmed with the quantum theory of atoms in molecule (QTAIM). By analysis of the contributions of various energy components to the relative stability with the references of the lowest-lying isomers, the controlling factor for isomer preferences was found to be the polarization interaction. Notably, although the electrostatic interaction dominates the binding energies, it contributes favorably to the relative stabilities of most isomers. The Li+···Li+ distance is identified as the key geometrical parameter that correlates with the strength of the polarization of the Sx2- fragment imposed by the Li+ cations. Further BLW-ED analyses reveal that the cooperativity of the Li+ cations primarily determines the relative strength of the polarization.

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).

OEEF-Driven Intramolecular Self-Redox of Superalkali Rb3BeB6Be'Rb'3: A High-Performance Candidate for NLO Molecular Switch

To provide a novel intramolecular self-redox switch, a boron-based sandwich-like complex Rb3BeB6Be'Rb'3 is achieved by using theoretical computations. An applicable oriented external electric field (OEEF) can result in the occurrence of intramolecular self-redox (IMSR) with a long-range electron transfer from tetrahedral Be'Rb'3 to Rb3Be and subsequently [Rb3Be]3+[B6]6-[Be'Rb'3]3+ (D3d) changes to [Rb3Be]2+[B6]6-[Be'Rb'3]4+ (C3v), accompanying high-performance NLO switchable effect for both static and dynamic first hyperpolarizability (β0). [Rb3Be]3+[B6]6-[Be'Rb'3]3+ (off-form) owns zero of dipole moment (μ0) and β0, while [Rb3Be]2+[B6]6-[Be'Rb'3]4+ (on-form) exhibits a μ0 of 3.36 D and a β0e of 2.18 × 105 au. The different dynamic first hyperpolarizabilities between [Rb3Be]3+[B6]6-[Be'Rb'3]3+ and [Rb3Be]2+[B6]6-[Be'Rb'3]4+ are also significant. This indicates that Rb3BeB6Be'Rb'3 is a potential candidate for an IMSR NLO switch.

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.

Geometric and electronic diversity of metal doped boron clusters

Being intermediate between small compounds and bulk materials, nanoparticles possess unique properties different from those of atoms, molecules, and bulk matter. In the past two decades, a combination of cluster structure prediction algorithms and experimental spectroscopy techniques was successfully used for exploration of the ground-state structures of pure and metal-doped boron clusters. The fruitfulness of this dual approach is well illustrated by the discovery of intriguing microstructures and unique physicochemical properties such as aromaticity and bond fluxionality for both boron and metal-doped boron clusters. Our review starts with an overview of geometrical configurations of pure boron clusters B_n, which are presented by planar, nanotube, bilayer, fullerene-like and core-shell structures, in a wide range ofnvalues. We consider next recent advances in studies of boron clusters doped with metal atoms paying close and thoughtful attention to modifications of geometric and electronic structures of pure boron clusters by heteroatoms. Finally, we discuss the possibility of constructing boron-based nanomaterials with specific functions from metal-boron clusters. Despite a variety of fruitful results obtained in numerous studies of boron clusters, the exploration of boron-based chemistry has not yet reached its peak. The intensive research continues in this area, and it should be expected that it brings exciting discoveries of intriguing new structures.

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 SeB_n^0/- (n = 3-16) is performed using particle swarm optimization (CALYPSO) software in combination with density functional theory calculations. The lowest energy structures of SeB_n^0/- (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 SeB_n^0/- (n = 3-16) clusters have different local electron delocalization and whole electron delocalization effects. The simulated photoelectron spectra of SeB_n^- (n = 3-16) have different characteristic bands that can identify and confirm SeB_n^- (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.

Construction of the Largest Metal-Centered Double-Ring Tubular Boron Clusters Based on Actinide Metal Doping

Metal doping has been considered to be an effective approach to stabilize various boron clusters. In this work, we constructed a series of largest metal-centered double-ring tubular boron clusters An@B₂₄ (An = Th, Pa, Pu, and Am). Extensive global minimum structural searches combined with density functional theory predicted that the global minima of An@B₂₄ (An = Th, Pu, and Am) are double-ring tubular structures. Formation energy analysis indicates that these boron clusters are highly stable, especially for Th@B₂₄ and Pa@B₂₄. Detailed bonding analysis shows that the significant stability of An@B₂₄ is determined by the covalent character of the An-B bonding, which stems from the interactions of An 5f and 6d orbitals and B 2p orbitals. These results show that actinide metal doping is a feasible route to construct stable large metal-centered double-ring tubular boron clusters, offering the possibility to design boron nanomaterials with special physiochemical properties.

Structures, and electronic and spectral properties of single-atom transition metal-doped boron clusters MB24 - (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni)

A theoretical study of geometrical structures, electronic properties, and spectral properties of single-atom transition metal-doped boron clusters MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) is performed using the CALYPSO approach for the global minimum search, followed by density functional theory calculations. The global minima obtained for the MB₂₄ ^- (M = Sc, Ti, V, and Cr) clusters correspond to cage structures, and the MB₂₄ ^- (M = Mn, Fe, and Co) clusters have similar distorted four-ring tubes with six boron atoms each. Interestingly, the global minima obtained for the NiB₂₄ ^- cluster tend to a quasi-planar structure. Charge population analyses and valence electron density analyses reveal that almost one electron on the transition-metal atoms transfers to the boron atoms. The electron localization function (ELF) of MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) indicates that the local delocalization of MB₂₄ ^- (M = Sc, Ti, V, Cr, and Ni) is weaker than that of MB₂₄ ^- (M = Mn, Fe, and Co), and there is no obvious covalent bond between doped metal and B atoms. The spin density and spin population analyses reveal that open-shell MB₂₄ ^- (M = Ti, Cr, Fe, and Ni) has different spin characteristics which are expected to lead to interesting magnetic properties and potential applications in molecular devices. The polarizability of MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) shows that MB₂₄ ^- (M = Mn, Fe, and Co) has larger first hyperpolarizability, indicating that MB₂₄ ^- (M = Mn, Fe, and Co) has a strong nonlinear optical response. Hence, MB₂₄ ^- (M = Mn, Fe, and Co) might be considered as a promising nonlinear optical boron-based nanomaterial. The calculated spectra indicate that MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) has different and meaningful characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these single-atom transition metal-doped boron clusters. Our work enriches the database of geometrical structures of doped boron clusters and can provide an insight into new doped boron clusters.

Structural transformations in boron clusters induced by metal doping

In the last decades, experimental techniques in conjunction with theoretical analyses have revealed the surprising structural diversity of boron clusters. Although the 2D to 3D transition thresholds are well-established, there is no certainty about the factors that determine the geometry adopted by these systems. The structural transformation induced by doping usually yields a minimum energy structure with a boron skeleton entirely different from that of the bare cluster. This review summarizes those clusters no larger than 40 boron atoms where one or two dopants show a radical transformation of the structure. Although the structures of these systems are not easy to predict, they often adopt familiar shapes such as umbrella-like, wheel, tubular, and cages in various cases.

Exploring the structure and electronic properties of germanium doped boron clusters using density functional theory based global optimization method

Density functional theory calculations to investigate the effect of single and double germanium atom doping on the geometric structure and electronic properties of boron clusters with 10 to 20 atoms.

Theoretical probing of twenty-coordinate actinide-centered boron molecular drums

The exploration of metal-doped boron clusters has a great significance in the design of high coordination number (CN) compounds. Actinide-doped boron clusters are probable candidates for achieving high CNs. In this work, we systematically explored a series of actinide metal atom (U, Np, and Pu) doped B₂₀ boron clusters An@B₂₀ (An = U, Np, and Pu) by global minimum structural searches and density functional theory (DFT). Each An@B₂₀ cluster is confirmed to be a twenty-coordinate complex, which is the highest CN obtained in the chemistry of actinide-doped boron clusters so far. The predicted global minima of An@B₂₀ are tubular structures with actinide atoms as centers, which can be considered as boron molecular drums. In An@B₂₀, U@B₂₀ has a relatively high symmetry of C₂, while both Np@B₂₀ and Pu@B₂₀ exhibit C₁ symmetry. Extensive bonding analysis demonstrates that An@B₂₀ has σ and π delocalized bonding, and the U-B bonds possess a relatively higher covalency than the Np-B and Pu-B bonds, resulting in the higher formation energy of U@B₂₀. Therefore, the covalent character of An-B bonding may be crucial for the formation of these high CN actinide-centered boron clusters. These results deepen our understanding of actinide metal doped boron clusters and provide new clues for developing stable high CN boron-based nanomaterials.

Structural and Electronic Properties of Single-Atom Transition Metal-Doped Boron Clusters MB24 (M = Sc, V, and Mn)

A theoretical study of geometrical structures, electronic properties, and spectral properties of single-atom transition metal-doped boron clusters MB24 (M = Sc, V, and Mn) is performed using the CALYPSO approach for the global minimum search, followed by density functional theory calculations. The global minima obtained for the VB24 and MnB24 clusters correspond to cage structures. Interestingly, the global minima obtained for the ScB24 cluster tend to a three-ring tubular structure. Population analyses and valence electron density analyses reveal that partial electrons on transition-metal atoms transfer to boron atoms. The localized orbital locator of MB24 (M = Sc, V, and Mn) indicates that the electron delocalization of ScB24 is stronger than that of VB24 and MnB24, and there is no obvious covalent bond between doped metals and B atoms. The spin density and spin population analyses reveal that MB24 (M = Sc, V, and Mn) have different spin characteristics which are expected to lead to interesting magnetic properties and potential applications in molecular devices. The calculated spectra indicate that MB24 (M = Sc, V, and Mn) has meaningful characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these single-atom transition metal-doped boron clusters. Our work enriches the database of geometrical structures of doped boron clusters and can provide an insight into new doped boron clusters.

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

Lowest-energy structures, the distribution of isomers, and their molecular properties depend significantly on geometry and temperature. Total energy computations using DFT methodology are typically carried out at a temperature of zero K; thereby, entropic contributions to the total energy are neglected, even though functional materials work at finite temperatures. In the present study, the probability of the occurrence of one particular Be4B8 isomer at temperature T is estimated by employing Gibbs free energy computed within the framework of quantum statistical mechanics and nanothermodynamics. To identify a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surfaces is carried out using a multi-level multistep global genetic algorithm search coupled with DFT. In addition, we discuss the energetic ordering of structures computed at the DFT level against single-point energy calculations at the CCSD(T) level of theory. The total VCD/IR spectra as a function of temperature are computed using each isomer's probability of occurrence in a Boltzmann-weighted superposition of each isomer's spectrum. Additionally, we present chemical bonding analysis using the adaptive natural density partitioning method in the chiral putative global minimum. The transition state structures and the enantiomer-enantiomer and enantiomer-achiral activation energies as a function of temperature evidence that a change from an endergonic to an exergonic type of reaction occurs at a temperature of 739 K.

Prediction of unexpected B n P n structures: promising materials for non-linear optical devices and photocatalytic activities

In the present work, a modern method of crystal structure prediction, namely USPEX conjugated with density functional theory (DFT) calculations, was used to predict the new stable structures of B _n P _n (n = 12, 24) clusters. Since B₁₂N₁₂ and B₂₄N₂₄ fullerenes have been synthesized experimentally, it motivated us to explore the structural prediction of B₁₂P₁₂ and B₂₄P₂₄ clusters. All new structures were predicted to be energetically favorable with negative binding energy in the range from -4.7 to -4.8 eV per atom, suggesting good experimental feasibility for the synthesis of these structures. Our search for the most stable structure of B _n P _n clusters led us to classify the predicted structures into two completely distinct structures such as α-B _n P _n and β-B _n P _n phases. In α-B _n P _n , each phosphorus atom is doped into a boron atom, whereas B atoms form a B _n unit. On the other hand, each boron atom in the β-phase was bonded to a phosphorus atom to make a fullerene-like cage structure. Besides, theoretical simulations determined that α-B _n P _n structures, especially α-B₂₄P₂₄, show superior oxidation resistance and also, both α-B _n P _n and β-B _n P _n exhibit better thermal stability; the upper limit temperature that structures can tolerance is 900 K. The electronic properties of new compounds illustrate a higher degree of absorption in the UV and visible-region with the absorption coefficient larger than 10⁵ cm^-1, which suggests a wide range of opportunities for advanced optoelectronic applications. The β-B _n P _n phase has suitable band alignments in the visible-light excitation region, which will produce enhanced photocatalytic activities. On the other hand, α-B _n P _n structures with modest band gap exhibit large second hyperpolarizability, which are anticipated to have excellent potential as second-order non-linear optical (NLO) materials.

TM4B180/− (TM = Hf, Ta, W, Re, Os): new structure construction with TM doped B wheel units

The lowest energy structure of Ta₄B₁₈ shows a conflicting aromaticity and is assembled from four planar molecular Ta@B₉ units.

Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be6B11- Flux-Ional Cluster

The starting point to understanding cluster properties is the putative global minimum and all the nearby local energy minima; however, locating them is computationally expensive and difficult. The relative populations and spectroscopic properties that are a function of temperature can be approximately computed by employing statistical thermodynamics. Here, we investigate entropy-driven isomers distribution on Be₆B₁₁⁻ clusters and the effect of temperature on their infrared spectroscopy and relative populations. We identify the vibration modes possessed by the cluster that significantly contribute to the zero-point energy. A couple of steps are considered for computing the temperature-dependent relative population: First, using a genetic algorithm coupled to density functional theory, we performed an extensive and systematic exploration of the potential/free energy surface of Be₆B₁₁⁻ clusters to locate the putative global minimum and elucidate the low-energy structures. Second, the relative populations’ temperature effects are determined by considering the thermodynamic properties and Boltzmann factors. The temperature-dependent relative populations show that the entropies and temperature are essential for determining the global minimum. We compute the temperature-dependent total infrared spectra employing the Boltzmann factor weighted sums of each isomer’s infrared spectrum and find that at finite temperature, the total infrared spectrum is composed of an admixture of infrared spectra that corresponds to the spectra of the lowest-energy structure and its isomers located at higher energies. The methodology and results describe the thermal effects in the relative population and the infrared spectra.

New theoretical insights into high-coordination-number complexes in actinides-centered borane

The coordination number of a given element affects its behavior, and consequently, there is great interest in understanding the related chemistry, which could greatly promote the extension and development of new materials, but remains challenging. Herein, we report a new record high coordination number (CN) for actinides established in the cage-like An(BH)24 (An = Th to Cm) via using relativistic quantum chemistry methods. Analysis of U(BH)n (n = 1 to 24) confirmed these series of systems as being geometric minima, with the BH acting as a ligand located in the first shell around the uranium. In contrast, global searches revealed a low CN half-cage structure for UB24, which could be extended to the series of AnB24 materials and which prevails over the competing structural isomers, such as cages. The intrinsic geometric difference for AnB24 and An(BH)24 mainly arise from the B sp3 hybridization in borane inducing strong interactions between An 5f6d7s hybrid orbitals and B 2pz orbitals in An(BH)24 compared to that of AnB24. This fundamental trend presents a valuable insight for future experimental endeavors searching for isolable complexes with high-coordination actinide and provides details of a new structural motif of boron clusters and nanostructures.

Structural effects of alkali-metals on the B12 skeleton

After an exhaustive exploration of the potential energy surface of B₁₂E^- and B₁₂E₂ (E = Li-Cs) systems, it was found that for the anionic series, a cage-type and a quasi-planar structure (very similar to the naked B₁₂ cluster) compete to be the putative global minimum. For neutral systems, competition arises between the quasi-planar cluster and a double-ring with the alkali-metals on the highest-symmetry axis. The chemical bonding analyses show that for the entire series, the interaction, predominantly electrostatic, is essentially indistinguishable regardless of the alkali-metal and insufficient for determining the isomeric preference. The isomerization energy decomposition analysis (IEDA) reveals that in the anions, the structural change in the lighter complexes is possible because of the relatively low energy required for the boron skeleton deformation, as opposed to the case of heavy metals. In the case of the neutral systems, the factor determining one isomer over the other corresponds to that of the energy deformation of the alkali-metal dimer.

Inverse sandwich complexes of B7M2−, B8M2, and B9M2+ (M = Zr, Hf): the nonclassical M–M bonds embedded in monocyclic boron rings

Three delocalized σ orbitals of the boron rings are perpendicularly mixed with one negligible σ and two π bonds of the M₂ (M = Zr, Hf) motifs, giving rise to less pronounced and nonclassical bonding interactions between two short-contact M atoms.

Structural evolution and electronic properties of medium-sized boron clusters doped with scandium

Doping of boron-based materials with transition metal atoms allows one to tune or modify the properties and structure of the materials. In this work, an extensive search for the global minima on potential energy surfaces of ScB _n and ScB[Formula: see text] clusters has been performed using the CALYPSO method. The structural evolution of scandium doped boron clusters of this range is found to proceed in three steps; namely, the formation of half-sandwich type structures is followed by the formation of drum-like structures with the Sc atom located at the center and terminates with the cage-like structures. It is also found that highly symmetrical geometric structures are more common for the smaller size range of [Formula: see text]. The neutral ScB₁₃ cluster is identified as magic on the basis of an analysis of relative stabilities in the ScB _n series. Our analysis of chemical bonding has shown that the stability of this cluster is mainly due to the formation of several delocalized [Formula: see text]-bonding molecular orbitals composed of Sc 3d and B 2s atomic orbitals. These bonds appear to be responsible for the enhanced stability of ScB₁₃ with respect to other Sc-doped boron clusters.

Formation of the M2B18q Teetotum Boron Clusters with 4d and 5d Transition Metals M = Rh, Pd, Ir, and Pt

In the present theoretical study using DFT computations, we successfully designed a series of boron clusters possessing a teetotum shape stabilized upon metal doping. The resulting M₂B₁₈ teetotum geometry emerges as a general structural motif for the B₁₈ boron cluster doped by either two 4d and 5d transition metal atoms. Doping of two different metal atoms also conserves the teetotum motif such as in the mixed RhPdB₁₈⁺ and IrPtB₁₈⁺ clusters. A bonding analysis points out that each dimeric metal unit enjoys several stabilizing orbital interactions with an idealized B₁₈ tubular moiety and thereby establish a bimetallic configuration of [σ(σ_5s-B₁₈)]² [π(π_4d-B₁₈)]⁴ [σ(σ_4d-B₁₈)]² [δ(δ_4d-B₁₈)]⁴ [σ*(σ_4d-B₁₈)]² [π*_4d]⁴ [σ(σ*_4d-B₁₈)]² [δ*_4d]⁴ for 4d metals and of [σ(σ_6s-B₁₈)]² [π(π_5d-B₁₈)]⁴ [σ(σ_5d-B₁₈)]² [δ(δ_5d-B₁₈)]⁴ [σ*(σ_5d-B₁₈)]² [π*_5d]⁴ [σ(σ*_5d-B₁₈)]² [δ*_5d]⁴ for 5d metal atoms for 24 electrons. All the M₂B₁₈^q teetotum structures considered behave as aromatic compounds whose character is indicated by the strongly diatropic current density.

Li2B24: the simplest combination for a three-ring boron tube

Herein we introduce a strategy employing lithium atoms as a scaffold to stabilize an embryo for boron tubes. The systematical exploration of the potential energy surface via evolutionary algorithms allowed us to find that Li2B24 adopts a tubular structure formed by three stacked rings of eight borons each with two lithium atoms capping the tube. The lithium atoms are essential for stabilization because of the strong electrostatic interaction between the Li cations and the boron framework, and concomitantly, they compensate for the energy cost of distorting a quasi-planar or double ring B24 cluster.

Probing the structures and bonding of size-selected boron and doped-boron clusters

Because of their interesting structures and bonding and potentials as motifs for new nanomaterials, size-selected boron clusters have received tremendous interest in recent years. In particular, boron cluster anions (Bn-) have allowed systematic joint photoelectron spectroscopy and theoretical studies, revealing predominantly two-dimensional structures. The discovery of the planar B36 cluster with a central hexagonal vacancy provided the first experimental evidence of the viability of 2D borons, giving rise to the concept of borophene. The finding of the B40 cage cluster unveiled the existence of fullerene-like boron clusters (borospherenes). Metal-doping can significantly extend the structural and bonding repertoire of boron clusters. Main-group metals interact with boron through s/p orbitals, resulting in either half-sandwich-type structures or substitutional structures. Transition metals are more versatile in bonding with boron, forming a variety of structures including half-sandwich structures, metal-centered boron rings, and metal-centered boron drums. Transition metal atoms have also been found to be able to be doped into the plane of 2D boron clusters, suggesting the possibility of metalloborophenes. Early studies of di-metal-doped boron clusters focused on gold, revealing ladder-like boron structures with terminal gold atoms. Recent observations of highly symmetric Ta2B6- and Ln2Bn- (n = 7-9) clusters have established a family of inverse sandwich structures with monocyclic boron rings stabilized by two metal atoms. The study of size-selected boron and doped-boron clusters is a burgeoning field of research. Further investigations will continue to reveal more interesting structures and novel chemical bonding, paving the foundation for new boron-based chemical compounds and nanomaterials.

Structural and electronic properties of MB22− (M = Na, K) clusters: tubular boron versus quasi-planar boron forms

Electron deficiency of boron atom has led to the abundant chemical properties of boron clusters, such as intriguing structures, unique multi-center bonding and electronic properties, as well as the structural evolution from planar to three-dimensional forms.

Structure evolution of chromium-doped boron clusters: toward the formation of endohedral boron cages

The electron-deficient nature of boron endows isolated boron clusters with a variety of interesting structural and bonding properties that can be further enriched through metal doping. In the current work, we report the structural and electronic properties of a series of chromium-doped boron clusters. The global minimum structures for CrB_n clusters with an even number of n ranging from 8 to 22 are proposed through extensive first-principles swarm-intelligence structure searches. Half-sandwich structures are found to be preferred for CrB₈, CrB₁₀, CrB₁₂ and CrB₁₄ clusters and to transform to a drum-like structure at CrB₁₆ cluster. Endohedral cage structures with the Cr atom located at the center are energetically most favorable for CrB₂₀ and CrB₂₂ clusters. Notably, the endohedral CrB₂₀ cage has a high symmetry of D_2d and a large HOMO–LUMO gap of 4.38 eV, whose stability is attributed to geometric fit and formation of an 18-electron closed-shell configuration. The current results advance our understanding of the structure and bonding of metal-doped boron clusters.

The effect of chromium doping on the structure evolution of small-sized boron clusters.

B10M2 (M = Rh, Ir): finally a stable boron-based icosahedral cluster

The putative global minimum of clusters with formula B₁₀M₂ (M = Rh, Ir) corresponds to icosahedral structures formed by two alternately stacked B₅ rings with the metals located at the top and bottom vertices.

Stable global tubular boron clusters in Na2B18 and Na2B18−

The optimal electrostatic interactions arising from the doping effect play a crucial role in stabilizing the tubular structure against the planar and quasi-planar preferences of the negatively charged boron clusters.

Insights into the effects produced by doping of medium-sized boron clusters with ruthenium

Modification of properties of boron nanoparticles by doping with transition metals presents a challenging problem because the number of isomers of both doped and un-doped nanoparticles rapidly increases with the nanoparticle size. Here, we perform a study of neutral and anionic Ru-doped boron clusters RuBn (n = 9-20) using the unbiased CALYPSO structural search method in combination with density functional theory calculations. Our results show that the neutral RuB9 cluster possesses a perfect planar wheel-like geometrical structure, whereas the RuBn clusters prefer structures of the half-sandwich type in the range of 10 ≤ n ≤ 14, drum-like type in the range of 15 ≤ n ≤ 18 and cage-like structures for larger n values. The geometrical structures of the lowest total energy states of the RuBn- anions are similar to those of the corresponding neutrals, except for RuB10-, RuB11-, RuB14-, RuB15- and RuB20-. The neutral RuB12 and RuB14 clusters are found to exhibit enhanced stability with respect to the rest of the RuBn clusters due to the delocalized bonding between the Ru atom and the boron host.

Evidence for the Superatom-Superatom Bonding from Bond Energies

Metal clusters with specific number of valence electrons are described as superatoms. Super valence bond (SVB) model points out that superatoms could form the superatomic molecules through SVBs by sharing nucleus and electrons. The existence of superatom-superatom bonding was verified by the shape of their orbitals in former studies. In this paper, another important evidence-bond energy is studied as the criterion for the SVBs using the density functional theory method. In order to get the reliable values of bond energies, the series of Zn-Cu and Mg-Li superatomic molecules composed of two tetrahedral superatoms which do not share their nucleus are designed. Considering the number of the valence electrons in one tetrahedral superatomic unit, (Zn₄)₂/(Mg₄)₂, (Zn₃Cu)₂/(Mg₃Li)₂, (Zn₂Cu₂)₂/(Mg₂Li₂)₂, and (ZnCu₃)₂/(MgLi₃)₂ clusters are 8e-8e, 7e-7e, 6e-6e, and 5e-5e binary superatomic molecules with super nonbond, single bond, double bond, and triple bond, respectively, which are verified by chemical bonding analysis depending on the SVB model. Further calculations reveal that the bond energies increase and the bond lengths decrease along with the bond orders in Zn-Cu and Mg-Li systems which is in accordance with the classical nonbond, single bond, double bond, and triple bond in C-H systems. Thus, these values of bond energies confirm the existence of the SVBs. Moreover, electron localization function analysis is also carried on to describe the similarity between the superatomic bonds and atomic bonds in simple molecules directly. This study reveals the new evidence for the existence of the superatom-superatom bonding depending on the bond energies, which gives the new insight for the further investigation of the superatomic clusters.

Boron Teetotum: Metallic [Ti(B6C xN y)] q and Bimetallic [Ti2(B6C xN y)] q Nine-Membered Heterocycles with x + y = 3 and -1 ≤ q ≤ 3

We investigated the geometry, stability, and aromaticity of a series of singly and doubly titanium-doped boron clusters. Ti dopants bring in planar cyclic form with a nine-membered boron ring B₉^- and B₉^3- and C and N isoelectronic derivatives where perfectly planar B₆N₃, B₆CN₂, B₆C₂N, and B₆C₃ heterorings are coordinated with one and two Ti atoms. The presence of both C and N atoms induces bimetallic heterocycles while Ti₂B₉^q clusters are not stable in cyclic form. Doubly Ti doped clusters have the shape of a teetotum toy. High thermodynamic stability of these bimetallic boron heterocycles, that are global equilibrium structures of corresponding systems, can be understood as the result of a stabilizing overlap between bonding and antibonding MOs of Ti₂ with different eigenstates of B₆C _xN _y cycles. Both C and N elements, which are more electronegative than the B atom, also enjoy the formation of planar nine-membered ring via classical 2c-2e bonding, rather than occupancy of high coordination position. A double aromaticity feature which comprises both σ and π aromaticity is supported by magnetic responses of electron density within a planar cycle. Such an aromatic character is also in line with the classical electron count for both sets of delocalized σ and π electron systems.

Lithium doped tubular structure in LiB20 and LiB20-: a viable global minimum

We present a strategy by which the stability of tubular boron clusters can be significantly enhanced by doping the B20 cluster with a lithium atom. High-level quantum chemical calculations showed that the lowest energy structures of LiB20 and LiB20- are tubular structures with D10d symmetry, in which the lithium atom is located at the center of the tubular structure. Chemical bonding analysis revealed that the high-symmetry tubular boron clusters are characterized as charge transfer complexes (Li+B20- and Li+B202-), resulting in double aromaticity with delocalized π + σ bonding and strong electrostatic interactions between cationic Li+ and tubular boron motifs with twenty Li-B interactions. The unique bonding pattern of the LiB20 and LiB20- species provides a key driving force to stabilize tubular structures over quasi-planar structures, suggesting that electrostatic interactions resulting from alkali metals might unveil a new clue to the structural evolution of boron clusters.

Cage-like Ta@B complexes (n = 23-28, q = -1-+ 3) in 18-electron configurations with the highest coordination number of twenty-eight

Inspired by recent observations of the highest coordination numbers of CN = 10 in planar wheel-type complexes in D10h Ta@B10- and CN = 20 in double-ring tubular species in D10d Ta@B20- and theoretical prediction of the smallest endohedral metalloborospherene D2 Ta@B22- (1) with CN = 22, we present herein the possibility of larger endohedral metalloborospherenes C2 Ta@B23 (2), C2 Ta@B24+ (3), C2v Ta@B24- (4), C1 Ta@B25 (5), D2d Ta@B26+ (6), C2 Ta@B272+ (7), and C2 Ta@B283+ (8) based on extensive first-principles theory investigations. These cage-like Ta@Bqn complexes with B6 pentagonal or B7 hexagonal pyramids on their surface turn out to be the global minima of the systems with CN = 23, 24, 24, 25, 26, 27, and 28, respectively, unveiling the highest coordination number of CN = 28 in spherical environments known in chemistry. Detailed bonding analyses show that 1-8 as superatoms conform to the 18-electron configuration with a universal σ + π double delocalization bonding pattern. They are effectively stabilized via spd-π coordination interactions between the Ta center and ηn-Bn ligand which match both geometrically and electronically. Such complexes may serve as embryos of novel metal-boride nanomaterials.

Scandium carbides/cyanides in the boron cage: computational prediction of X@B80 (X = Sc2C2, Sc3C2, Sc3CN and Sc3C2CN)

As the first study on metal carbide/cyanide boron clusterfullerenes, the geometries, energies, stabilities and electronic properties of four novel scandium cluster-containing B80 buckyball derivatives, namely Sc2C2@B80, Sc3C2@B80, Sc3CN@B80 and Sc3C2CN@B80, were investigated by means of density functional theory computations. The rather favorable binding energies, which are very close to those of the experimentally abundant carbon fullerene analogues, suggest a considerable possibility to realize these doped boron clusterfullerenes. Their intracluster and cluster-cage bonding natures were thoroughly revealed by various theoretical approaches. In contrast to carbon clusterfullerenes, in which the encaged non-metal atoms mainly play a stabilizing role in the metal clusters, the encapsulated carbon and nitrogen atoms inside the B80 cage covalently bond to the boron framework, resulting in strong cluster-cage interactions. Furthermore, infrared spectra and (11)B nuclear magnetic resonance spectra were simulated and fingerprint peaks were proposed to assist future experimental characterization.

Accelerating CALYPSO structure prediction by data-driven learning of a potential energy surface

CALYPSO structure prediction is significantly accelerated by on-the-fly learning of a potential energy surface.

Ultrastable actinide endohedral borospherenes

DFT-PBE0 calculations on AnB_n (An = U, Th; n = 36, 38, and 40) reveal the feasibility of actinide-doped borospherenes.

Effects of manganese doping on the structure evolution of small-sized boron clusters

Atomic doping of clusters is known as an effective approach to stabilize or modify the structures and properties of resulting doped clusters. We herein report the effect of manganese (Mn) doping on the structure evolution of small-sized boron (B) clusters. The global minimum structures of both neutral and charged Mn doped B cluster [Formula: see text] (n  =  10-20 and Q  =  0, ±1) have been proposed through extensive first-principles swarm-intelligence based structure searches. It is found that Mn doping has significantly modified the grow behaviors of B clusters, leading to two novel structural transitions from planar to tubular and then to cage-like B structures in both neutral and charged species. Half-sandwich-type structures are most favorable for small [Formula: see text] (n  ⩽  13) clusters and gradually transform to Mn-centered double-ring tubular structures at [Formula: see text] clusters with superior thermodynamic stabilities compared with their neighbors. Most strikingly, endohedral cages become the ground-state structures for larger [Formula: see text] (n  ⩾  19) clusters, among which [Formula: see text] adopts a highly symmetric structure with superior thermodynamic stability and a large HOMO-LUMO gap of 4.53 eV. The unique stability of the endohedral [Formula: see text] cage is attributed to the geometric fit and formation of 18-electron closed-shell configuration. The results significantly advance our understanding about the structure and bonding of B-based clusters and strongly suggest transition-metal doping as a viable route to synthesize intriguing B-based nanomaterials.

Structural transition in metal-centered boron clusters: from tubular molecular rotors Ta@B21and Ta@B22+to cage-like endohedral metalloborospherene Ta@B22−

Extensive first-principles theory investigations unveil a tubular-to-cage-like structural transition in metal-centered boron clusters at (±)-D₂Ta@B₂₂⁻, the smallest axially chiral endohedral metalloborospherenes.

Observation of a metal-centered B2-Ta@B18−tubular molecular rotor and a perfect Ta@B20−boron drum with the record coordination number of twenty

A B₂-Ta@B₁₈⁻tubular molecular rotor and a Ta@B₂₀⁻boron drum with the record coordination number of twenty were observedviaa joint experimental and theoretical investigation.