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.

A topological path to the formation of a quasi-planar B70 boron cluster and its dianion

In view of the competing assignments regarding the most stable isomer of the B70 boron cluster including the quasi-planar and bilayer structures, we reinvestigated the structural motifs of B70 using a genetic algorithm for structure search (MEGA) in conjunction with density functional theory computations using the PBE functional. The quasi-planar structure was also constructed using the topological leapfrog algorithm. The latter search aimed to give us unique insight into its formation and the growth pattern of boron clusters. Also, the di-anionic state of B70 was explored. Our extensive search suggested a competition between the quasi-planar, tubular and bilayer isomers for the ground state of B70 in both neutral and dianionic states. While the bilayer form is more stable in the neutral state, the quasi-planar counterpart becomes more stable in the dianionic B702-. The stability arises due to the fact that the B702- dianion possesses 50 π electrons that satisfy the disk aromaticity model rule. These results tend to extend the stabilization of the quasi-planar structure upon negative charge addition previously found in small size boron clusters to larger sizes.

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).

Spatial and electronic structures of BeB8 and MgB8. How far the analogy goes?

Doping of boron clusters with Be and its heavier alkaline-earth congener, Mg usually leads to complexes of different geometry and electronic structure. In this work we showed that both neutral BeB 8 and MgB 8 exhibit a singlet ground state umbrella-like form. In addition, the stability, electronic structure, and aromaticity of the target molecules were compared. The magnetically induced current densities showed that BeB 8 and MgB 8 are double aromatic systems: π and σ electrons induce strong diatropic currents. The current densities induced in the studied complexes are of very similar intensity, but with a different spatial distribution. The found differences between the current density patterns in BeB 8 and MgB 8 arise from the very nature of the bonding interactions between the M atom and B 8 fragment, as demonstrated through the energy decomposition analysis (EDA).

Structures and Properties of CoB19 +/0/- Clusters

A global search for the lowest energy structure of Co atom-doped boron clusters (CoB19 +, CoB19, and CoB19 - clusters) was conducted. The lowest energy structures of them are remarkably different from those of B20 and CoB18 - clusters. CoB19 + clusters have a bowl-shaped geometry, where the Co atom is at the bottom of the bowl and is coordinated with eight B atoms. The CoB19 cluster presents seven- and eight-membered B rings. The CoB19 - cluster can be viewed as a structure that evolves from a Co-doped boron plane. The coordination number of CoB19 and CoB19 - clusters are 16 and 14, respectively. Several low-lying isomers have quasi-planar structures for the CoB19 - cluster. Some properties including charge transformation and distribution, HOMO-LUMO gaps, molecular orbital distribution, and stability of neutral CoB19 are discussed. CoB19 + and CoB19 - exhibit magnetism with a net moment of 1.0 and 0.94 μB because of odd number of electrons.

Structures, Electronic, and Spectral Properties of Doped Boron Clusters MB12 0/- (M = Li, Na, and K)

Structures and electronic properties of alkali metal atom-doped boron clusters MB12 0/- (M = Li, Na, K) are determined using the CALYPSO method for the global minimum search followed by density functional theory. It is found that the global minima obtained for the neutral clusters correspond to the half-sandwich structure and those of the monoanionic clusters correspond to the boat-shaped structure. The neutral MB12 (M = Li, Na, K) can be considered as a member of the half-sandwich doped B12 clusters, and the geometrical pattern of anion MB12 - (M = Li, Na, K) is a new structure that is different from other doped B12 clusters. Natural population and chemical bonding analyses reveal that the alkali metal atom-doped boron clusters MB12 - are characterized as charge transfer complexes, M+B12 2-, resulting in symmetrically distributed chemical bonds and electrostatic interactions between cationic M+ and boron atoms. The calculated spectra indicate that MB12 0/- (M = Li, Na, K) has meaningful spectral features that can be compared with future experimental data. Our work enriches the varieties of geometrical structures of doped boron clusters and can provide much insight into boron nanomaterials.

Structures, stabilities and aromatic properties of endohedrally transition metal doped boron clusters M@B22, M = Sc and Ti: a theoretical study

A genetic search algorithm in conjunction with density functional theory calculations was used to determine the lowest-energy minima of the pure B22 cluster and thereby to evaluate the capacity of its isomers to form endohedrally doped cages with two transition metal atoms M (M = Sc and Ti). An important charge transfer from metal atoms M to the boron cage takes place, stabilizing the endohedral compounds, as predicted with the genetic algorithm implemented. High-level coupled-cluster theory CCSD(T) calculations were carried out to confirm that the structures found are the lowest-energy isomers. For a deeper understanding of the doping effects and related charge transfer, the best structural motif of the B22 isomers was also determined when the bare cages are in anionic states, such as B222- and B224-. It was found that B22 has an appropriate size, geometric shape and electronic state to host the chosen metal atoms and, consequently, to form stable endohedrally doped compounds Ti@B22 (C2v, 4-Ti) and Sc@B22 (C2v, 5-Sc). The chemical bonding was analyzed in order to understand the molecular orbitals that these novel systems form. The cage aromaticity was evaluated by means of the nuclear independent chemical shift (NICS(0)iso) indices, the isochemical shielding surface (ICSSzz), the anisotropy of the current induced density (ACID) maps, and the magnetic ring current Gauge-Including Magnetically Induced Current (GIMIC) method, indicating that aromaticity plays a crucial role in the stabilization of endohedrally doped boron clusters. Finally, the thermodynamic stability of the latter, using parameters derived from density functional theory (DFT), was evaluated. Ab initio molecular dynamics (AIMD) simulations were performed to elucidate the stability, at high temperature, of the most stable endohedrally doped boron clusters 4-Ti and 5-Sc.

Analysis of the structures, stabilities and electronic properties of MB16− (M = V, Cr, Mn, Fe, Co, Ni) clusters and assemblies

Stacking of lowest-energy structures of Fe₂B₂₄⁻ and Co₂B₂₄⁻ dimers.

Competition between tubular, planar and cage geometries: a complete picture of structural evolution of Bn (n = 31–50) clusters

Stimulated by the early theoretical prediction of B₈₀ fullerene and the experimental finding of the B₄₀ cage, the structures of medium-sized boron clusters have attracted intensive research interest during the last decade, but a complete picture of their size-dependent structural evolution remains a puzzle.

Singlet and triplet states of the sandwich-type Be2B6 and Be2B7+ clusters. A test for the electron counting rules of aromaticity

The studied complexes exhibit double aromaticity in their triplet states in line with the predictions of Hückel and Baird's rules.

Sea-shell-like B31+ and B32: two new axially chiral members of the borospherene family

Since the discovery of the cage-like borospherenes D_2d B₄₀^−/0 and the first axially chiral borospherenes C₃/C₂ B₃₉⁻, a series of fullerene-like boron clusters in different charge states have been reported in theory. Based on extensive global minimum searches and first-principles theory calculations, we present herein two new axially chiral members C₂ B₃₁⁺ (I) and C₂ B₃₂ (VI) to the borospherene family. B₃₁⁺ (I) features two equivalent heptagons on the top and one octagon at the bottom on the cage surface, while B₃₂ (VI) possesses two equivalent heptagons on top and two equivalent heptagons at the bottom. Detailed bonding analyses show that both sea-shell-like B₃₁⁺ (I) and B₃₂ (VI) follow the universal σ + π double delocalization bonding pattern of the borospherene family, with ten delocalized π bonds over a σ skeleton, rendering spherical aromaticity to the systems. Extensive molecular dynamics simulations show that these novel borospherenes are kinetically stable below 1000 K. The IR, Raman, and UV-vis spectra of B₃₁⁺ (I) and B₃₂ (VI) are computationally simulated to facilitate their future experimental characterizations.

Two new axially chiral sea-shell-like boron clusters C₂ B₃₁⁺ (a) and C₂ B₃₂ (b) are presented at first-principles theory level to the borospherene family.

Structures, Stabilities, and Spectral Properties of Endohedral Borospherenes M@B40 0/- (M = H2, HF, and H2O)

The discovery of borospherene B₄₀ leads to a new beginning for the study of boron chemistry and may lead to new boron-based nanomaterials. Based on density functional theory, the structures, electronic properties, infrared and Raman spectra, photoelectron spectra, and electronic absorption spectra of endohedral borospherenes M@B₄₀ ^0/- (M = H₂, HF, and H₂O) are investigated. It is found that H₂, HF, and H₂O monomers can form stable endohedral borospherenes M@B₄₀ ^0/- (M = H₂, HF, and H₂O). In addition, the calculated results indicate that the doped molecule at the off-center location can relax to the center location within the cage and the symcenter of the doped molecule is almost located in the center of the cage. Unlike endohedral metalloborospherene Ca@B₄₀, which is a charge-transfer complex between Ca²⁺ and B₄₀ ^2-, natural population analyses and chemical bonding analyses reveal that there is no significant charge transfer of the doped molecule. The calculated spectra indicate that doping of a molecule (H₂, HF, or H₂O) in borospherene B₄₀ can change the photoelectron spectra and doping of a polar molecule (HF or H₂O) in borospherene B₄₀ can change the spectral properties. For instance, the addition of a molecule can increase infrared and Raman-active modes and cause a red shift or blue shift of electronic spectra. These spectral features can be compared with future experimental values of endohedral borospherenes M@B₄₀ ^0/- (M = H₂, HF, and H₂O).

Magnetically induced current density in triple-layered beryllium–boron clusters

Magnetically induced current densities reveal the double aromatic character of the examined Be–B 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.

Formation of a bi-rhodium boron tube Rh2B18 and its great CO2 capture ability

The geometries, bonding and abilities for CO₂ capture of the doubly rhodium-doped boron cluster Rh₂B₁₈ are presented.

Planarization of B20 clusters by Si and C atom substitution

An optimization strategy combining a global semi-empirical quantum mechanical search and all-electron density functional theory was adopted to determine the lowest energy structures of B₁₉Si and B₁₉C clusters. The planarization of a B₂₀ cluster by Si and C atom substitution was observed. The structural transition was from the double-ring tubular B₂₀ to an almost perfect planar B₁₉Si and a quasi-planar bowl B₁₉C. B₁₉Si possessed a geometry with a central B atom surrounded by a six-membered ring and a 13-atom outer ring. B₁₉C adopted a geometry with a B₅C six-membered hole. Both Si and C atoms occupied peripheral positions. The observed planarization may be attributed to sp² hybridization, changes in the peripheral bonding, and structural mechanics. Some properties, including the HOMO-LUMO gaps, on-site charge on Si and C atoms, and deformed charge distribution, were discussed.

Boron clusters with 46, 48, and 50 atoms: competition among the core-shell, bilayer and quasi-planar structures

Using a genetic algorithm combined with density functional theory calculations, we perform a global search for the lowest-energy structures of B_n clusters with n = 46, 48, 50. Competition among different structural motifs including a hollow cage, core-shell, bilayer, and quasi-planar, is investigated. For B₄₆, a core-shell B₄@B₄₂ structure resembling the larger B_n clusters with n ≥ 68 is found to compete with a quasi-planar structure with a central hexagonal hole. A quasi-planar configuration with two connected hexagonal holes is most favorable for B₅₀. More interestingly, an unprecedented bilayer structure is unveiled at B₄₈, which can be extended to a two-dimensional bilayer phase exhibiting appreciable stability. Our results suggest alternatives to the cage motif as lower-energy B_n cluster structures with n > 50.

Structures, stabilities and spectral properties of metalloborospherenes MB0/−40 (M = Cu, Ag, and Au)

Metalloborospherenes MB0/−40 (M = Cu, Ag, and Au) are predicted. Relative energies of these metalloborospherenes suggest that Cu, Ag and Au atoms favor the exohedral configuration.

Aromatic cage-like B46: existence of the largest decagonal holes in stable atomic clusters

The boron cluster B₄₆has a cage-like structure containing two hexagonal, two heptagonal and two decagonal holes. This finding presents a new family of cage-like boron clusters containing large B_Nholes withN= 6–10.

Aromatic character of planar boron-based clusters revisited by ring current calculations

The planarity of small boron-based clusters is the result of an interplay between geometry, electron delocalization, covalent bonding and stability.

Aromatic cages B0/+42: unprecedented existence of octagonal holes in boron clusters

The cluster B₄₂⁺exhibits an aromatic cage-like structure containing remarkable octagonal holes.

Stability and bonding of the multiply coordinated bimetallic boron cycles: B8M22−, B7NM2and B6C2M2with M = Sc and Ti

A theoretical investigation of the geometry, stability and aromaticity of boron clusters doped by two Sc and Ti atoms was carried out using DFT calculations.

A new chiral boron cluster B44 containing nonagonal holes

The B44 cluster has a cage-like structure containing two hexagonal, two heptagonal and two nonagonal holes. The presence of nonagonal holes is a new and remarkable finding since they have never been reported before in clusters. The present work does not only identify the new chiral members, but also provide more insight into the growth motif of large-sized boron clusters.

B28: the smallest all-boron cage from an ab initio global search

Our ab initio global searches reveal the lowest-energy cage for B28, which is built from two B12 units and prevails over the competing structural isomers such as planar, bowl, and tube. This smallest boron cage extends the scope of all-boron fullerene and provides a new structural motif of boron clusters and nanostructures.

Effects of bimetallic doping on small cyclic and tubular boron clusters: B7M2 and B14M2 structures with M = Fe, Co

Using density functional theory with the TPSSh functional and the 6-311+G(d) basis set, we extensively searched for the global minima of two metallic atoms doped boron clusters B6M2, B7M2, B12M2 and B14M2 with transition metal element M being Co and Fe. Structural identifications reveal that B7Co2, B7Fe2 and B7CoFe clusters have global minima in a B-cyclic motif, in which a perfectly planar B7 is coordinated with two metallic atoms placed along the C7 axis. The B6 cluster is too small to form a cycle with the presence of two metals. Similarly, the B12 cluster is not large enough to stabilize the metallic dimer within a double ring 2 × B6 tube. The doped B14M2 clusters including B14Co2, B14Fe2 and B14CoFe have a double ring 2 × B7 tubular shape in which one metal atom is encapsulated by the B14 tube and the other is located at an exposed position. Dissociation energies demonstrate that while bimetallic cyclic cluster B7M2 prefers a fragmentation channel that generates the B7 global minimum plus metallic dimer, the tubular structure B14M2 tends to dissociate giving a bimetallic cyclic structure B7M2 and a B@B6 cluster. The enhanced stability of the bimetallic doped boron clusters considered can be understood from the stabilizing interactions between the anti-bonding MOs of metal-metal dimers and the levels of a disk aromatic configuration (for bimetallic cyclic structures), or the eigenstates of the B14 tubular form (in case of bimetallic tubular structure).

How can carbon favor planar multi-coordination in boron-based clusters? Global structures of CBxEy2−(E = Al, Ga, x + y = 4)

CB₂E₂Mg (E = Al, Ga) designed in the present study represents the first successful design of a boron-based planar penta-coordinate carbon (ppC) structures as the global minima.

Electronic structure and photoelectron spectra of Bnwith n = 26–29: an overview of structural characteristics and growth mechanism of boron clusters

In this report, the electronic structure and photoelectron spectra of boron clusters B_26–29were theoretically investigated and an overview of the growth mechanism of boron clusters was shown.