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.

B63: The Most Stable Bilayer Structure with Dual Aromaticity

The emergence of a bilayer B48 cluster, which has been both theoretically predicted and experimentally observed, as well as the recent experimental synthesis of bilayer borophene sheets on Ag and Cu surfaces, has generated tremendous curiosity in the bilayer structures of boron clusters. However, the connection between bilayer boron cluster and bilayer borophene remains unknown. By combining a genetic algorithm and density functional theory calculations, a global search for the low-energy structures of the B63 cluster was conducted, revealing that the Cs bilayer structure with three interlayer B-B bonds is the most stable bilayer structure. This structure was further examined in terms of its structural stability, chemical bonding, and aromaticity. Interestingly, the interlayer bonds induce strong electronegativity and robust aromaticity. Furthermore, the dual aromaticity stems from diatropic currents originating from virtual translational transitions for both σ and π electrons. This unprecedent bilayer boron cluster is anticipated to enrich the concept of dual aromaticity and serve as a potential precursor for bilayer borophene.

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.

Perfect Core-Shell Octahedral B@B38 + , Be@B38 , and Zn@B38 with an Octa-Coordinate Center as Superatoms Following the Octet Rule

Planar, tubular, cage-like, and bilayer boron clusters B_n ^+/0/- (n=3∼48) have been observed in joint experimental and theoretical investigations in the past two decades. Based on extensive global searches augmented with first-principles theory calculations, we predict herein the smallest perfect core-shell octahedral borospherene O_h B@B₃₈ ⁺ (1) and its endohedral metallo-borospherene analogs O_h Be@B₃₈ (2), and O_h Zn@B₃₈ (3) which, with an octa-coordinate B, Be or Zn atom located exactly at the center, turn out to be the well-defined global minima of the systems highly stable both thermodynamically and dynamically. B@B₃₈ ⁺ (1) represents the first boron-containing molecule reported to date which contains an octa-coordinate B center covalently coordinated by eight face-capping boron atoms at the corners of a perfect cube in the first coordination sphere. Detailed natural bonding orbital (NBO) and adaptive natural density partitioning (AdNDP) bonding analyses indicate that these high-symmetry core-shell complexes X@B₃₈ ^+/0/- (X=B, Be, Zn) as super-noble gas atoms follow the octet rule in coordination bonding patterns (1S² 1P⁶ ), with one delocalized 9c-2e S-type coordination bond and three delocalized 39c-2e P-type coordination bonds formed between the octa-coordinate X center and its octahedral O_h B₃₈ ligand to effectively stabilize the systems. Their IR, Raman, and UV-Vis spectra are computationally simulated to facilitate their spectroscopic characterizations.

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

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

B96: a complete core-shell structure with high symmetry

A complete core-shell and highly symmetric B₉₆ was designed. The core-shell B₉₆ of T_h symmetry is energetically favorable compared to the bilayer motif and the core-shell structure can be well maintained during first-principles molecular dynamics simulations at high temperatures (up to 1000 K). Moreover, it exhibits a superatomic electronic configuration and spherical aromaticity. Our theoretical work not only confirmed that the core-shell structural pattern is more energetically favorable for large-sized boron clusters, but also provided a strategy to design large boron clusters with a core-shell structure of high symmetry.

Relative Stability of Boron Planar Clusters in Diatomic Molecular Model

In the recently introduced phenomenological diatomic molecular model imagining the clusters as certain constructions of pair interatomic chemical bonds, there are estimated specific (per atom) binding energies of small all-boron planar clusters B_n, n = 1–15, in neutral single-anionic and single-cationic charge states. The theoretically obtained hierarchy of their relative stability/formation probability correlates not only with results of previous calculations, but also with available experimental mass-spectra of boron planar clusters generated in process of evaporation/ablation of boron-rich materials. Some overestimation in binding energies that are characteristic of the diatomic approach could be related to differences in approximations made during previous calculations, as well as measurement errors of these energies. According to the diatomic molecular model, equilibrium binding energies per B atom and B–B bond lengths are expected within ranges 0.37–6.26 eV and 1.58–1.65 Å, respectively.

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...

B48-: a bilayer boron cluster

Size-selected negatively-charged boron clusters (B_n^-) have been found to be planar or quasi-planar in a wide size range. Even though cage structures emerged as the global minimum at B₃₉^-, the global minimum of B₄₀^- was in fact planar. Only in the neutral form did the B₄₀ borospherene become the global minimum. How the structures of larger boron clusters evolve is of immense interest. Here we report the observation of a bilayer B₄₈^- cluster using photoelectron spectroscopy and first-principles calculations. The photoelectron spectra of B₄₈^- exhibit two well-resolved features at low binding energies, which are used as electronic signatures to compare with theoretical calculations. Global minimum searches and theoretical calculations indicate that both the B₄₈^- anion and the B₄₈ neutral possess a bilayer-type structure with D_2h symmetry. The simulated spectrum of the D_2h B₄₈^- agrees well with the experimental spectral features, confirming the bilayer global minimum structure. The bilayer B₄₈^-/0 clusters are found to be highly stable with strong interlayer covalent bonding, revealing a new structural type for size-selected boron clusters. The current study shows the structural diversity of boron nanoclusters and provides experimental evidence for the viability of bilayer borophenes.

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.

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.