Ab initio MO study of neutral and cationic boron clusters

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.

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.

Exploring the structure and electronic properties of germanium doped boron clusters using density functional theory based global optimization method

Density functional theory calculations to investigate the effect of single and double germanium atom doping on the geometric structure and electronic properties of boron clusters with 10 to 20 atoms.

Step-Edge Epitaxy for Borophene Growth on Insulators

Borophene─a monatomic layer of boron atoms─stands out among two-dimensional (2D) materials, with its versatile properties tantalizing for physics exploration and next-generation devices. Yet its phases are all synthesized on and stay bound to metal substrates, hampering both characterization and use. Borophene growth on an inert insulator would allow postsynthesis exfoliation, but the weak adhesion to such a substrate results in a high 2D nucleation barrier, preventing clean borophene growth. This challenge can be circumvented in a strategy devised and demonstrated here with ab initio calculations. Naturally present 1D-defects, the step-edges on an h-BN substrate surface, enable boron epitaxial assembly, reduce the nucleation dimensionality, and lower the barrier by an order of magnitude (to 1.1 eV or less), yielding a v_1/9 phase. Weak borophene adhesion to the insulator makes it readily accessible for comprehensive property tests or transfer into the device setting.

Electronic Structure and Electron Delocalization in Bare and Dressed Boron Pentamer Clusters

The electronic structures of the lowest energy spin-states of the cationic, neutral and anionic bare boron pentamer clusters have been investigated by means of high level multiconfigurational type calculations, in view of the large static and dynamical electron correlation effects for these species. We found that B 5 + resembles a singlet spin-state perfect pentagon, which bears no intra-annular chemical bonding interactions, as shown by our analysis of the electron delocalization carried out in terms of the normalized Giambiagi ring-current index, and the total and adjacent atom-pair delocalization indices. However, its lowest-energy triplet and quintet spin-state isomers have C2v symmetry, with large intra-annular chemical bonding interactions. This geometrical feature extends to both the neutral and the anionic species. Namely, the lowest-energy isomers of boron pentamer neutral and anionic clusters have peripheral and intra-annular sizable bonding interactions reflected in the delocalization of both π- and σ-type valence natural orbitals over the whole molecular plane, which impart large structural stability. In accordance to our calculations, the lowest energy triplet spin-state isomer of the anionic boron pentamer cluster has C2 symmetry, and consequently, it should show optical activity. Finally, we have studied the change of the geometrical structure of the boron pentamer clusters from planar to compact three-dimensional structures caused by the bonding of ligands to the boron atoms. Our explicit all-electron calculations have been rationalized in terms of the shell-closure of the delocalized valence orbitals of the clusters as predicted by the jellium model extended to nonspherical confinement potentials, circumscribing the role of the ligand to modulate the total number of valence electrons assigned to the core cluster.

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.

Planar B38- and B37- clusters with a double-hexagonal vacancy: molecular motifs for borophenes

Boron clusters have been found to exhibit a variety of interesting electronic, structural, and bonding properties. Of particular interest are the recent discoveries of the 2D hexagonal B₃₆^-/0 which led to the concept of borophenes and the 3D fullerene-like B₄₀^-/0 which marked the onset of borospherene chemistry. Here, we present a joint photoelectron spectroscopic and first-principles study of B₃₇^- and B₃₈^-, which are in the transition size range between the 2D borophene-type clusters and the 3D borospherenes. These two clusters are found to possess highly stable 2D global-minimum structures consisting of a double-hexagonal vacancy. Detailed bonding analyses reveal that both B₃₇^- and B₃₈^- are all-boron analogues of coronene (C₂₄H₁₂) with a unique delocalized π system, featuring dual π aromaticity. These clusters with double hexagonal vacancies can be viewed as molecular motifs for the χ3-borophene which is the most stable form of borophenes recently synthesized on an Ag(111) substrate.

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.

Next generation of the self-consistent and environment-dependent Hamiltonian: Applications to various boron allotropes from zero- to three-dimensional structures

An upgrade of the previous self-consistent and environment-dependent linear combination of atomic orbitals Hamiltonian (referred as SCED-LCAO) has been developed. This improved version of the semi-empirical SCED-LCAO Hamiltonian, in addition to the inclusion of self-consistent determination of charge redistribution, multi-center interactions, and modeling of electron-electron correlation, has taken into account the effect excited on the orbitals due to the atomic aggregation. This important upgrade has been subjected to a stringent test, the construction of the SCED-LCAO Hamiltonian for boron. It was shown that the Hamiltonian for boron has successfully characterized the electron deficiency of boron and captured the complex chemical bonding in various boron allotropes, including the planar and quasi-planar, the convex, the ring, the icosahedral, and the fullerene-like clusters, the two-dimensional monolayer sheets, and the bulk alpha boron, demonstrating its transferability, robustness, reliability, and predictive power. The molecular dynamics simulation scheme based on the Hamiltonian has been applied to explore the existence and the energetics of ∼230 compact boron clusters BN with N in the range from ∼100 to 768, including the random, the rhombohedral, and the spherical icosahedral structures. It was found that, energetically, clusters containing whole icosahedral B12 units are more stable for boron clusters of larger size (N > 200). The ease with which the simulations both at 0 K and finite temperatures were completed is a demonstration of the efficiency of the SCED-LCAO Hamiltonian.

An insight into the structures, stabilities, and bond character of B(n)Pt (n=1∼6) clusters

We perform a systematical investigation on the geometry, thermodynamic/kinetic stability, and bonding nature of low-lying isomers of BnPt (n=1-6) at the CCSD(T)/[6-311+G(d)/LanL2DZ]//B3LYP/[6-311+G(d)/LanL2DZ] level. The most stable isomers of BnPt (n=1-6) adopt planar or quasi-planar structure. BnPt (n=2-5) clusters can be generated by capping a Pt atom on the B-B edge of pure boron clusters. However, For B6Pt with non-planar structure, a single doped Pt atom significantly affects the shape of the host boron cluster. The dopant of the Pt atom can improve the stability of pure boron clusters. The valence molecular orbital (VMO), electron localization function (ELF), and Mayer bond order (MBO) are applied to gain insight into the bonding nature of BnPt (n=2-6) isomers. The aromaticity for some isomers of BnPt (n=2-6) is analyzed and discussed in terms of VMO, ELF, adaptive natural density partitioning (AdNDP), and nucleus-independent chemical shift (NICS) analyses. Results obtained from the energy and cluster decomposition analyses demonstrate that B2Pt and B4Pt exhibits as highly stable. Importantly, some isomers of BnPt (n=2-5) are stable both thermodynamically and kinetically, which are observable in future experiment.

Probing the structures and chemical bonding of boron-boronyl clusters using photoelectron spectroscopy and computational chemistry: B4(BO)(n)- (n = 1-3)

The electronic and structural properties of a series of boron oxide clusters, B(5)O(-), B(6)O(2)(-), and B(7)O(3)(-), are studied using photoelectron spectroscopy and density functional calculations. Vibrationally resolved photoelectron spectra are obtained, yielding electron affinities of 3.45, 3.54, and 4.94 eV for the corresponding neutrals, B(5)O, B(6)O(2), and B(7)O(3), respectively. Structural optimizations show that these oxide clusters can be formulated as B(4)(BO)(n)(-) (n = 1-3), which involve boronyls coordinated to a planar rhombic B(4) cluster. Chemical bonding analyses indicate that the B(4)(BO)(n)(-) clusters are all aromatic species with two π electrons.

Structure and stability of small boron and boron oxide clusters

To rationally design and explore a potential energy source based on the highly exothermic oxidation of boron, density functional theory (DFT) was used to characterize small boron clusters with 0-3 oxygen atoms and a total of up to ten atoms. The structures, vibrational frequencies, and stabilities were calculated for each of these clusters. A quantum molecular dynamics procedure was used to locate the global minimum for each species, which proved to be crucial given the unintuitive structure of many of the most stable isomers. Additionally, due to the plane-wave, periodic DFT code used in this study a straightforward comparison of these clusters to the bulk boron and B2O3 structures was possible despite the great structural and energetic differences between the two forms. Through evaluation of previous computational and experimental work, the relevant low-energy structures of all but one of the pure boron clusters can be assigned with great certainty. Nearly all of the boron oxide clusters are described here for the first time, but there are strong indications that the DFT procedure chosen is particularly well suited for the task. Insight into the trends in boron and boron oxide cluster stabilities, as well as the ultimate limits of growth for each, are also provided. The work reported herein provides crucial information towards understanding the oxidation of boron at a molecular level.