The Boron conundrum: the case of cationic clusters B n + with n = 2–20

A reinvestigation of the boron cluster B15+/0/-: a benchmark of density functionals and consideration of aromaticity models

This study presents a thorough reinvestigation of the B15+/0/- isomers, first employing coupled-cluster theory CCSD(T) calculations to validate the performance of different DFT functionals. The B15+ cation has two planar lowest-lying isomers, while the first 3D isomer is less stable than the global minimum by ∼10 kcal mol-1. The PBE functional, within this benchmark survey, has proved to be reliable in predicting relative energies for boron isomers. Other functionals such as the TPSSh, PBE0 and HSE06 result in good energy ordering of isomers but warrant reconsideration when distinguishing between 2D and 3D forms. Caution is needed for structures having high spin contamination, as it may lead to significant errors. The anomalously lower stability of the B15- anion with respect to its neighbours, in terms of electron detachment energy, was explained through a competition between both rectangle and disk models for its geometry. This elucidates its stability with 12 electrons in rectangle model and instability with 10 electrons in disk-shaped structure, emphasizing the value of employing such geometric models. The proximity of the σ* LUMO to the π HOMO also contributes to the weakening of the B15- stability.

Planar Elongated B12 Structure in M3B12 Clusters (M = Cu-Au)

Here, it is shown that the M₃B₁₂ (M = Cu-Au) clusters' global minima consist of an elongated planar B₁₂ fragment connected by an in-plane linear M₃ fragment. This result is striking since this B₁₂ planar structure is not favored in the bare cluster, nor when one or two metals are added. The minimum energy structures were revealed by screening the potential energy surface using genetic algorithms and density functional theory calculations. Chemical bonding analysis shows that the strong electrostatic interactions with the metal compensate for the high energy spent in the M₃ and B₁₂ fragment distortion. Furthermore, metals participate in the delocalized π-bonds, which infers an aromatic character to these species.

Quasi-planar Co atom-doped boron cluster: CoB192

PURPOSE AND METHODS

A global search for the lowest energy structure of CoB₁₉^2- clusters was conducted.  RESULTS: Its ground state is a quasi-planar structure with the Co atom surrounded by a B₈ ring. The central Co atom has an oxidation state of +1 with d⁸ electron configuration. The wave function analysis showed that the Co-B interaction is not a covalent bond. The bonding strength of peripheral B-B bonds is stronger than that of inner ones. The inner B₈ ring bonds with outer boron atoms via σ- and π-type bonds.

CONCLUSION

CoB₁₉^2- shows remarkable aromatic character.

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.

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.

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...

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.

Tuning of Structure Evolution and Electronic Properties through Palladium-Doped Boron Clusters: PdB16 as a Motif for Boron-Based Nanotubes

Transition metal-doped electronic deficiency boron clusters have led to a vast variety of electronic bonding properties in chemistry and materials science. We have determined the ground state structures of PdB_n^0/- (n = 10-20) clusters by performing CALYPSO search and density functional theory (DFT) optimization. The identified lowest energy structures for both neutral and anionic Pd-doped boron clusters follow the structure evolution from two dimensional (2D) planar configurations to 3D distorted Pd-centered drum-like or tubular structures. Photoelectron spectra are simulated by time-dependent DFT theoretical calculations, which is a powerful method to validate our obtained ground-state structures. More interestingly, two "magic" number clusters, PdB₁₂ and PdB₁₆, are found with enhanced stability in the middle size regime studied. Subsequently, molecular orbital and adaptive natural density partitioning analyses reveal that the high stability of the PdB₁₆ cluster originates from doubly σ π aromatic and bonding interactions of d-type atomic orbitals of the Pd atom with tubular B₁₆ units. The tubular C_8v PdB₁₆ cluster, with robust relative stability, is an ideal embryo for forming finite and infinite nanotube nanomaterials.

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 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.

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.

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.

A computational study on the endohedral alkali metal and ion B40 nanocluster

Recent exploration of the boron fullerenes has raised exciting new prospects for boron applications. Here, the endohedral X/X⁺@B₄₀ complexes (X = Li, Na, and K) were explored by means of density functional theory calculations. By increasing the atomic number, the interaction of alkali metals with the B₄₀ nanocage is unusually weakened. It was concluded that by increasing the alkali metals' size, their electrons repel those of the cage, and the interaction weakens. The interaction of X with B₄₀ is more favorable than that of X⁺. For example, the calculated ΔG of interaction at 298 K and 1 atm is about -108.3 and + 18.4 kJ mol^-1 for X and X⁺, respectively. Compared to the X⁺ cations, the X atoms considerably enhance the boron cluster electrical conductivity, by reducing the gap. We found that the B₄₀ nanocluster is not large enough to freely embed large atoms, such as Na and K. Also, the electron emission from the surface of B₄₀ cluster is increased and reduced by X and X⁺ encapsulations, respectively.

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.

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.

Dynamical behavior of boron clusters

Several of the lowest energy structures of small and medium sized boron clusters are two-dimensional systems made up of a pair of concentric rings. In some cases, the barriers to the rotation of one of those rings relative to the other are remarkably low. We find that a combination of electronic and geometrical factors, including apparently the relative sizes and symmetries of the inner and outer rings, are decisive for the diminished barriers to in-plane rotation in these two dimensional clusters. A sufficiently large outer ring is important; for instance, expansion of the outer ring by a single atom may reduce the barrier significantly. A crucial factor for an apparent rotation is that the σ-skeleton of the individual rings remains essentially intact during the rotation. Finally, the transition state for the rotation of the inner ring comprises the transformation of a square into a diamond, which may be linked to a mechanism suggested decades ago for the isomerization of carboranes and boranes.

Electronic structure of the boron fullerene B14 and its silicon derivatives B13Si(+), B13Si(-) and B12Si2: a rationalization using a cylinder model

Geometric and electronic structures of the boron cluster B14 and its silicon derivatives B13Si(+), B13Si(-), and B12Si2 were determined using DFT calculations (TPSSh/6-311+G(d)). The B12Si2 fullerene, which is formed by substituting two B atoms at two apex positions of the B14 fullerene by two Si atoms, was also found as the global minimum structure. We demonstrated that the electronic structure and orbital configuration of these small fullerenes can be predicted by the wavefunctions of a particle on a cylinder. The early appearance of high angular node MOs in B14 and B12Si2 can be understood by this simple model. Replacement of one B atom at a top position of B14 by one Si atom, followed by the addition or removal of one electron does not lead to a global minimum fullerene structure for the anion B13Si(-) and cation B13Si(+). The early appearance of the 5σ1 orbital in B13Si(+) causes a lower stability for the fullerene-type structure.

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.

Noble gas supported B3+ cluster: formation of strong covalent noble gas–boron bonds

Ar to Rn atoms formed exceptionally strong bonds with B₃⁺, where the Ng (HOMO) → B₃Ng₂⁺ (LUMO) σ-donation is the key term to stabilize the complexes.

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.

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.

Structures and bonding of auropolyboroenes [Au2(B4)xB3]−, [Au2(B4)xB2]2− and [Au2(B4)xB]+ (x = 2, 3): comparison with dihydride polyboroenes

Equilibrium structures of auropolyboroenes [Au₂(B₄)_xB₃]⁻, [Au₂(B₄)_xB₂]²⁻ and [Au₂(B₄)_xB]⁺ (x = 2, 3) are obtained from density functional theory-based calculations.

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.

Design of novel tetra-hetero[8]circulenes: a theoretical study of electronic structure and charge transport characteristics

Tetra-hetero[8]circulenes were theoretically designed and emerged as good candidates for ambipolar organic semiconductors.

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 disk-aromatic bowl cluster B30: toward formation of boron buckyballs

The B₃₀ cluster is a bowl-shape structure, rather than a double-ring tubular form and exhibits disk-aromatic features similar to those of B₁₉⁻ and B₂₀²⁻. It suggests a consistent route for the formation of boron buckyballs such as B₈₀ and B₉₂ from multiple B₃₀ units.

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⁺.

Quantum rules for planar boron nanoclusters

The nodal structure of boron sheets follows the pattern of cylindrical bessel function.