The boron conundrum: Bonding in the bowl B30 and B36, fullerene B40 and triple ring B42 clusters

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.

Electron density mapping of boron clusters via convolutional neural networks to augment structure prediction algorithms

Determination and prediction of atomic cluster structures is an important endeavor in the field of nanoclusters and thereby in materials research. To a large extent the fundamental properties of a nanocluster are mainly governed by its molecular structure. Traditionally, structure elucidation is achieved using quantum mechanics (QM) based calculations that are usually tedious and time consuming for large nanoclusters. Various structural prediction algorithms have been reported in the literature (CALYPSO, USPEX). Although they tend to accelerate the structure exploration, they still require the aid of QM based calculations for structure evaluation. This makes the structure prediction process quite a computationally expensive affair. In this paper, we report on the creation of a convolutional neural network model, which can give relatively accurate energies for the ground state of nanoclusters from the promolecule density on the fly and could thereby be utilized for aiding structure prediction algorithms. We tested our model on dataset consisting of pure boron nanoclusters of varying sizes.

A database of low-energy atomically precise nanoclusters

The chemical and structural properties of atomically precise nanoclusters are of great interest in numerous applications, but the structures of the clusters can be computationally expensive to predict. In this work, we present the largest database of cluster structures and properties determined using ab-initio methods to date. We report the methodologies used to discover low-energy clusters as well as the energies, relaxed structures, and physical properties (such as relative stability, HOMO-LUMO gap among others) for 63,015 clusters across 55 elements. We have identified clusters for 593 out of 1595 cluster systems (element-size pairs) explored by literature that have energies lower than those reported in literature by at least 1 meV/atom. We have also identified clusters for 1320 systems for which we were unable to find previous low-energy structures in the literature. Patterns in the data reveal insights into the chemical and structural relationships among the elements at the nanoscale. We describe how the database can be accessed for future studies and the development of nanocluster-based technologies.

Designing a Four-Ring Tubular Boron Motif through Metal Doping

Tubular boron clusters represent a class of extremely unusual geometries that can be regarded as a key indicator for the 2D-to-3D boron structural evolution as well as the embryos for boron nanotubes. While a good number of pure boron or metal-doped boron tubular clusters have been reported so far, most of them are two-ring tubular structures, and their higher-ring analogues are very scarce. We report herein the first example of a four-ring tubular boron motif in the cagelike global minimum of Be₂B₂₄⁺. Global-minimum searches of MB₂₄^q and M₂B₂₄^q (M = alkali/alkaline-earth metals; q = 1+, 0, 1-) reveal that the most stable structure of Be₂B₂₄⁺ is a C_2v-symmetric cage having a four-ring tubular boron moiety, whereas it is a high-lying isomer for those having a two/three-ring tubular boron motif for all other systems. The B₂₄ framework in Be₂B₂₄⁺ can be viewed as consisting of two two-ring B₁₂ tubular structures linked together at one side of the B₆ rings along the high-symmetry axis and two offside B₆ rings capped by two Be atoms. The Be₂-B₂₄ bonding is best described as Be₂²⁺ in an excited triplet state, forming two highly polarized covalent bonds with B₂₄^- in a quartet spin state. The unique ability of beryllium to make strong covalent and electrostatic interactions makes the Be₂B₂₄⁺ cluster stable in such an unusual geometry.

Boron Silicon B2Si3q and B3Si2p Clusters: The Smallest Aromatic Ribbons

The small binary boron silicon clusters B₂Si₃^q with q going from -2 to +2 and B₃Si₂^p with p varying from -3 to +1 were reinvestigated using quantum chemical methods. The thermodynamic stability of these smallest ribbon structures is governed by both Hückel and ribbon models for aromaticity. The more negative the cluster charge, the more ribbon character is shown. In contrast, the more positive the charge state, the more pronounced the Hückel character becomes. The ribbon aromaticity character can also be classified into ribbon aromatic, semiaromatic, antiaromatic, and triplet aromatic when the electron configuration of a ribbon structure is described as [...π²⁽ⁿ⁺¹⁾σ²ⁿ], [...π²ⁿ⁺¹σ²ⁿ], [...π²ⁿσ²ⁿ], and [...π²ⁿ⁺¹σ^2n-1], respectively. Geometry optimizations of the B₂Si₃ lowest-energy structure by some density functional theory (DFT) functionals result in a nonplanar shape because it possesses an antiaromatic ribbon character. However, its π aromaticity assigned by the Hückel rule is stronger in such a way that several other DFT and coupled-cluster theory CCSD(T) calculations show that B₂Si₃ is indeed stable in a planar form (C_s). A new global equilibrium structure for the anion B₂Si₃^2-, which is a ribbon semiaromatic species, was identified. Some benchmark tests were also carried out to evaluate the performance of popular methods for the treatment of binary B-Si clusters. At odds with some previous studies, we found that with reference to the high accuracy CCSD(T)/CBS method, the hybrid TPSSh functional is reliable for a structure search, whereas the hybrid B3LYP functional is more suitable for simulations of some experimental spectroscopic results.

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).

Formation of the quasi-planar B56 boron cluster: topological path from B12 and disk aromaticity

Formation and stability of the B56 boron cluster were investigated using a topological approach and the disk aromaticity model. An extensive global energy minimum search for the B56 system which...

Structure, stability and bonding of the leapfrog B24 0 ,±1,±2

Two new structural motifs of the B₂₄ clusters are constructed by use of the leapfrog transformation. The resulting leapfrog B₂₄ has either a bowl shape with a square vacancy or a quasi-planar 2D close-packed triangular boron sheet. The neutral and ionic forms of the latter are found to be more stable than their homologous leapfrog bowl clusters, with the exception of the dicationic B₂₄ ⁺² . While the leapfrog isomer is less stable than the tubular double ring in the neutral state, it becomes competitive in some ionic states. The nucleus independent chemical shift, electron localization function, ring current maps and the electronic structure of leapfrog B₂₄ clusters reveal them to behave as aromatics.

Quasi-planar B36 boron cluster: a new potential basis for ammonia detection

Detection of NH₃ at a trace level is nowadays of great importance. Here, we investigate the reactivity and sensitivity of a B₃₆ borophene toward NH₃ gas employing DFT calculations. The energetic results point out that the adsorption process strongly depends on the orientation of NH₃ relative to the B₃₆ sheet. An NH₃ molecule preferentially interacts via its N-head with a B atom of the B₃₆ with a change of enthalpy of - 90.5 kJ/mol at room temperature and 1 atm. Mulliken charges analysis results reveal that approximately 0.35 |e| transfers from NH₃ to the B₃₆, leaving partially positive NH₃. We found that the B₃₆ electronic properties are meaningfully sensitive to the NH₃ gas, and it may be a sign of further usage of B₃₆ as a potential NH₃ gas sensor. The density of state analysis shows that the B₃₆ gap is expressively decreased from 1.55 to 1.35 eV, increasing its electrical conductance.

The teetotum cluster Li2FeB14 and its possible use for constructing boron nanowires

Systematic density functional theory (DFT) calculations using the TPSSh functional and the def2-TZVP basis set were carried out to identify the global energy minimum structure of the Li2FeB14 cluster. Keeping the double ring tubular shape of FeB14, capping of two Li atoms leads to a teetotum form at a low spin state, in which the Fe atom is endohedrally covered by two B7 strings, and both Li atoms are attached to Fe along the C7 axis at both sides. Calculated results show that strong electrostatic interactions between 2Li+ and Fe2- arising from Li electron transfer upon doping particularly provide a key driving force for stabilizing this charge-transfer structure. The bonding pattern of the teetotum can be understood from the hollow cylinder model (HCM). TD-DFT calculations demonstrate that this cluster can also be regarded as a useful material for transparent optoelectronic devices. Furthermore, the Li2FeB14 superatom can be used as a building block for making boron-based nanowires with metallic character. Replacement of Li atoms by Mg atoms was also found to lead to nanowires.

The Dynamic State of a Pseudo-Crystalline Structure of B42 Molecules

In this paper, we have developed a mathematical model of the dynamics of molecular structures arising from an approach using B42 molecules. The model is based on equations that determine the motion of the centers of mass of the molecules in question, and equations for the projections of the moments of quantities of motion of these particles on the axes associated with them. The thermal motions of boron atoms within each individual molecule are calculated using a bond-ordered potential. The intermolecular interactions of atoms have a potential that appears to coincide with that of free atoms. However, the interaction parameters differ. The obtained columns of molecular disks for B42 are stable structures. We determine the characteristic vibration amplitudes and rotation frequency of the molecules in question.

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.

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.

Formation of the quasi-planar B50 boron cluster: topological path from B10 and disk aromaticity

The lowest-lying isomer of the B50 boron cluster is confirmed to have a quasi-planar shape with two hexagonal holes. By applying a topological (leap-frog) dual operation followed by boron capping, we demonstrated that such a quasi-planar structure actually comes from the smallest elongated B102-, and its high thermodynamic stability is due to its inherent disk aromaticity arising from its 32 valent π electrons that fully occupy a disk configuration of [(1σ)2(1π)4(1δ)4(2σ)2(1φ)4(2π)4(1γ)4(2δ)4(1η)4]. The aromatic character of the quasi-planar B50 is further supported by a strong diatropic magnetic current flow. The sudden appearance of a quasi-planar B50 again points out that the growth pattern of pure boron clusters is still far from being completely understood.

A theoretical approach to the role of different types of electrons in planar elongated boron clusters

While the stability of planar elongated pure boron clusters is determined by their […σ²⁽ⁿ⁺¹⁾ π₁²⁽ⁿ⁺¹⁾ π₂²ⁿ] electronic configuration, the rectangle model can rationalize the π electronic configuration of rectangle-shaped structures.

Effects of single and double nickel doping on boron clusters: stabilization of tubular structures in BnNim, n = 2–22, m = 1, 2

A systematic investigation on structure, relative stabilities, dissociation behavior and bonding of the singly and doubly Ni doped boron clusters B_nNi_m with n = 2–22 and m = 1–2, was carried out using density functional theory (TPSSh functional) calculations.

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.

Aromatic cage-like B34 and B35+: new axially chiral members of the borospherene family

Shortly after the discovery of all-boron fullerenes D2d B40-/0 (borospherenes), the first axially chiral borospherenes C3/C2 B39- were characterized in experiments in 2015. Based on extensive global minimum searches and first-principles theory calculations, we present herein two new axially chiral members to the borospherene family: the aromatic cage-like C2 B34(1) and C2 B35+(2). Both B34(1) and B35+(2) feature one B21 boron triple chain on the waist and two equivalent heptagons and hexagons on the cage surface, with the latter being obtained by the addition of B+ into the former at the tetracoordinate defect site. Detailed bonding analyses show that they follow the universal bonding pattern of σ + π double delocalization, with 11 delocalized π bonds over a σ skeleton. Extensive molecular dynamics simulations show that these borospherenes are kinetically stable below 1000 K and start to fluctuate at 1200 K and 1100 K, respectively. The IR, Raman, and UV-vis spectra of 1 and 2 are computationally simulated to facilitate their experimental characterization.

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.

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.

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.

N-H bond cleavage of ammonia on graphene-like B36 borophene: DFT studies

Ammonia N-H bond cleavage at metal-free substrates has attracted great attention because of its industrial importance. Here, we investigate the dissociative adsorption of ammonia onto the surface of a B36 borophene sheet by means of density functional theory calculations. We show that the N-H bond may be broken at the edges of B36 even at room temperature, regarding the small energy barrier of 14.1-19.3 kcal mol(-1) at different levels of theory, and more negative Gibbs free energy change. Unlike basis set size, the kind of exchange correlation functional significantly affects the electronic properties of the studied systems. Also, by increasing the percentage of Hartree Fock (HF) exchange of density functionals, the activation and adsorption energies are lowered. A linear relationship between the highest occupied molecular orbital or lowest unoccupied molecular orbital of B36 borophene and the %HF exchange of functionals is predicted. Our work reveals that pure whole boron nanosheets may be promising metal-free materials in N-H bond cleavage, which would raise the potential application of these sheets.

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.

Versatile interactions of boron fullerene B80with gas molecules

Stable all-boron fullerene B₈₀supplements a family of elemental cage molecules.

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.

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).

Comment on "B38: an all-boron fullerene analogue" by J. Lv, Y. Wang, L. Zhu and Y. Ma, Nanoscale, 2014, 6, 11692

In a recent paper (Nanoscale, 2014, 6, 11692), based on the results computed using DFT and MP2 methods, the all-boron fullerene I was reported to be the global minimum of the cluster B38 and was much more stable than the quasi-planar II. In this comment, we have shown that at higher level of theory CCSD(T), both structure I and quasi-planar II are almost degenerate in energy and the B38 can be considered to be of a transition size between 2D and 3D boron clusters. While the MP2 method favours the 3D structure I, the CCSD method tends to overestimate the relative stability of the 2D structure II.

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.

The B32cluster has the most stable bowl structure with a remarkable heptagonal hole

The cluster B₃₂^0/−exhibits an aromatic bowl structure containing one heptagonal hole.

Fullerene-like boron clusters stabilized by an endohedrally doped iron atom: BnFe with n = 14, 16, 18 and 20

Stabilized fullerene and tubular forms can be produced in boron clusters B_nin small sizes fromn∼ 14 to 20 upon doping by transition metal atoms.

A particle on a hollow cylinder: the triple ring tubular cluster B27+

We determined the geometries and chemical bonding phenomena of the B₂₇system in its dicationic, cationic, neutral, anionic and dianionic states using DFT computations using DFT computations. We proposed a hollow cylinder model to interpret the MOs of the triple ring B₂₇⁺.