Structures and electronic properties of B3Sin− (n = 4–10) clusters: A combined ab initio and experimental study

Electronic structure of triangular M3 (M = B, Al, Ga): nonclassical three-center two electron π bond and σ delocalization

The small molecule clusters have received more and more attention due to their widespread applications in chemical insulators, explosives, semiconductors and the high energy density materials industry. The electron deficiency of group IIIA elements endows their clusters with interesting properties. In this work, the electronic structures of M₃ (M = B, Al, Ga) have been investigated by means of a complete active space self-consistent field (CASSCF) method. The nature of the chemical bond has been analyzed using the quantum theory of atoms in molecules (QTAIM) and electron localization function (ELF) analyses. The following conclusions can be drawn: in M₃ (M = B, Al, Ga) clusters, two π electrons are shared by three atoms forming a 3c-2e delocalization π bond. Going from B₃ to Al₃ to Ga₃, more and more electrons move from the bond pair to the outside of the M atom, which leads to a gradual enhancement of the delocalization of σ electrons. Aromaticity and the adaptive natural density partitioning (AdNDP) analyses reveal the existence of the 3c-2e π bond and delocalization of σ electrons in the studied systems.

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.

Transition from exohedral to endohedral geometries of anionic and neutral B4Sin (n = 4-15) clusters: quantum chemical calculations

The growth patterns of anionic and neutral B4Sin (n = 4-15) clusters are investigated by using density functional theory (DFT) calculations combined with particle swarm optimization (CALYPSO) software. The geometries of anionic and neutral B4Sin clusters transform from exohedral to endohedral structures with the increasing cluster sizes. The B4Si14- anion size is critical for forming B4-endohedral structures for anionic clusters, while the B4Si15 neutral size is the threshold size for forming B4-endohedral structures for neutral clusters. Both anionic and neutral B4Sin (n = 4-15) clusters are primarily dominated by prism-based or bipyramid-based geometries. The global minima of anionic and neutral B4Sin clusters adopt different geometrical structures, except for anionic and neutral B4Si10. The binding energies, second-order energy differences, and incremental binding energies of B4Sin- clusters show an odd-even alternation with the growing number of Si atoms. The B atoms in B4Sin-/0 exhibit B-B single bonding and B[double bond, length as m-dash]B double bonding properties. The B atoms are found to carry more negative charges due to charge transfer from Sin frameworks to B atoms. Interestingly, the B4Si4- anion adopts a C2h symmetric bicapped tetragonal bipyramid with σ plus π double bonding characters and has the highest relative stability among the anionic clusters. The bonding interactions in B4Si4- are in the order of B-B > B-Si > Si-Si.

Dynamical fluxionality, multiplicity of structural forms, and electronic properties of the B3Si11 cluster: anion photoelectron spectroscopy and theoretical calculations

The geometrical structures and electronic properties of anionic, neutral, and cationic B₃Si₁₁ clusters were investigated by performing ab initio calculations combined with size-selected anion photoelectron spectroscopy. The experimental photoelectron spectrum of the B₃Si₁₁^- anion is reasonably reproduced by theoretical simulations of two competing isomers. The global minimum of the B₃Si₁₁^- anion is formed by the fusion of a B₃Si₇ bicapped tetragonal antiprism to a B₃Si₄ pentagonal bipyramid by sharing a B₃ triangle, while that of neutral B₃Si₁₁ has a B₃-endohedral sandwich structure composed of a Si₅ five-membered ring and a Si₆ six-membered ring, and that of the B₃Si₁₁⁺ cation adopts a Si₁₁ tricapped tetragonal antiprism with three face-capping B atoms. It is interesting that a Si₅ five-membered ring and a Si₆ six-membered ring are stabilized by three B atoms in B₃Si₁₁. The three B atoms tend to bond with each other to form a B₃ triangle with stronger B-B bonds than B-Si bonds. Moreover, neutral B₃Si₁₁ exhibits σ + π double delocalized bonding patterns. Anionic, neutral, and cationic B₃Si₁₁ clusters have multiplicity of structural forms and their low-lying isomers show dynamical fluxionality. The bond lengths, bond orders, MO, constant electronic charge density surfaces, and PDOS analyses showed that the three B atoms in B₃Si₁₁ have strong bonding interactions.

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.

Medium-sized [Formula: see text] (n = 14-20) clusters: a combined study of photoelectron spectroscopy and DFT calculations

Size-selected anionic silicon clusters, [Formula: see text] (n  =  14-20), have been investigated by photoelectron spectroscopy and density functional theory (DFT) calculations. Low-energy structures of the clusters are globally searched for by using a genetic algorithm based on DFT calculations. The electronic density of states and vertical detachment energies have been simulated by using ten DFT functionals and compared to the experimental results. We systematically evaluated the DFT functionals for the calculation of the energetics of silicon clusters. CCSD(T) single-point energies based on MP2 optimized geometries for selected isomers of [Formula: see text] are also used as benchmark for the energy sequence. The HSE06 functional with aug-cc-pVDZ basis set is found to show the best performance. Our global minimum search corroborates that most of the lowest-energy structures of [Formula: see text] (n  =  14-20) clusters can be derived from assembling tricapped trigonal prisms in various ways. For most sizes previous structures are confirmed, whereas for [Formula: see text] a new structure has been found.

B3@Si12+: strong stabilizing effects of a triatomic cyclic boron unit on tubular silicon clusters

Remarkably strong effects of the aromatic B₃ cycle in stabilizing tubular silicon clusters were observed for the first time. The doped cluster B₃@Si₁₂⁺ presents a novel structural motif for silicon clusters in which a B₃ cycle is encapsulated into a (6 × 2) Si₁₂ prism giving rise to a high symmetry stable tubular structure (D_3h). A large amount of electron density is transferred to the boron cycle, and the B₃^δ- unit not only retains a delocalized bonding pattern within the Si₁₂ prism but also enables a two-fold aromaticity for the resulting silicon double ring. This double ring can be used as a building block to make longer nanotubes.

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.