Induced Currents and Electron Counting in Aromatic Boron Wheels: B82- and B9-

The Quest for Stable Borozene Core in Main-Group Capped Inverse Sandwich Complexes, [(HE)2B6H6]2- (E=B, Al, Ga, In, and Tl)

The ubiquitous chemistry of benzene led us to explore ways to stabilise analogous borozene, by capping them with appropriate groups. The mismatch in overlap of ring-cap fragment molecular orbitals in [(HB)2B6H6]2- is overcome by replacing the two BH caps with higher congeners of boron. We calculated the relative energies of all the polyhedral structural candidates for [(HE)2B6H6]2- (E=Al-Tl) and found hexagonal bipyramid (HBP) to be more stable with Al-H caps. A global minimum search also gives HBP as the most stable structure for [Al2B6H8]2-. The capped B6H6 ring in [(HAl)2B6H6]2- has aromaticity comparable to that of benzene.

QSym2: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

Symmetry provides a powerful machinery to classify, interpret, and understand quantum-mechanical theories and results. However, most contemporary quantum chemistry packages lack the ability to handle degeneracy and symmetry breaking effects, especially in non-Abelian groups, and they are not able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym2 that makes use of group and representation theories to provide symmetry analysis for a wide range of quantum-chemical calculations is introduced. With its ability to generate character tables symbolically on-the-fly and by making use of a generic symmetry-orbit-based representation analysis method formulated in this work, QSym2 is able to address all of these shortcomings. To illustrate these capabilities of QSym2, four sets of case studies are examined in detail in this article: (i) high-symmetry C84H64, C60, and B9- to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral Fe(CN)63- to demonstrate the analysis of symmetry-broken determinants and MOs; (iii) linear hydrogen fluoride in a magnetic field to demonstrate the analysis of magnetic symmetry; and (iv) equilateral H3+ to demonstrate the analysis of density symmetries.

Aromaticity of Singlet and Triplet Boron Disk-like Clusters: A Test for Electron Counting Aromaticity Rules

Boron clusters are polyhedral boron-containing structures that have unique features and properties. The disk-like boron clusters are among the most fascinating boron cluster forms. These clusters have a molecular orbital (MO) distribution similar to the one derived from the simple particle-on-a-disk model. In this model, the MOs come in pairs except for m = 0. Disk-like boron clusters in their singlet ground state are aromatic when they reach a closed-shell structure. One could expect that disk-like aromatic boron clusters in the singlet state, when acquiring or releasing two electrons, may also be aromatic in the lowest-lying triplet state. We use magnetically induced current densities and bond current strengths to analyze the aromatic character of a series of disk-like boron clusters. Our results show that, with the exception of triplet ³B₁₉^-, the disk-like boron clusters follow Hückel and Baird's rules if one considers the different MOs grouped by their symmetry. We also found that if the lowest-lying triplet state in disk-like boron clusters is aromatic, this triplet state is the ground state for this species.

The unique sandwich K6Be2B6H6 cluster with a real borozene B6H6 core

Theoretical evidence is reported for a boron-based K₆Be₂B₆H₆ sandwich cluster, showing a perfectly D _6h B₆H₆ ring, being capped by two tetrahedral K₃Be ligands. Due to the comfortable charge transfer, the sandwich is viable in [K₃Be]³⁺[B₆H₆]^6-[BeK₃]³⁺ ionic complex in nature. The [B₆H₆]^6- core with 6π aromaticity vividly imitates the benzene (C₆H₆), occurring as a real borozene. In contrast, the tetrahedral [K₃Be]³⁺ ligand is 2σ three-dimensional aromatic, acting as the simple superatom. Thus, this complex possesses a collectively three-fold 2σ/6π/2σ aromaticity. The interlaminar interaction is governed by the robust electrostatic attraction. The unique chemical bonding gives rise to interesting dynamic fluxionality.

Computational investigation of two-dimensional borides with planar octacoordinated main group elements

In this communication, by means of first principles calculations, we searched stable two-dimensional borides with octacoordinated main group elements, and we found that only AlB4 monolayer is stable in the planar octacoordinate motif through our stability screenings, which can be used for electrocatalyzing the hydrogen evolution reaction.

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.

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.

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).

How can carbon favor planar multi-coordination in boron-based clusters? Global structures of CBxEy2−(E = Al, Ga, x + y = 4)

CB₂E₂Mg (E = Al, Ga) designed in the present study represents the first successful design of a boron-based planar penta-coordinate carbon (ppC) structures as the global minima.

Understanding boron through size-selected clusters: structure, chemical bonding, and fluxionality

Boron is an interesting element with unusual polymorphism. While three-dimensional (3D) structural motifs are prevalent in bulk boron, atomic boron clusters are found to have planar or quasi-planar structures, stabilized by localized two-center-two-electron (2c-2e) σ bonds on the periphery and delocalized multicenter-two-electron (nc-2e) bonds in both σ and π frameworks. Electron delocalization is a result of boron's electron deficiency and leads to fluxional behavior, which has been observed in B13(+) and B19(-). A unique capability of the in-plane rotation of the inner atoms against the periphery of the cluster in a chosen direction by employing circularly polarized infrared radiation has been suggested. Such fluxional behaviors in boron clusters are interesting and have been proposed as molecular Wankel motors. The concepts of aromaticity and antiaromaticity have been extended beyond organic chemistry to planar boron clusters. The validity of these concepts in understanding the electronic structures of boron clusters is evident in the striking similarities of the π-systems of planar boron clusters to those of polycyclic aromatic hydrocarbons, such as benzene, naphthalene, coronene, anthracene, or phenanthrene. Chemical bonding models developed for boron clusters not only allowed the rationalization of the stability of boron clusters but also lead to the design of novel metal-centered boron wheels with a record-setting planar coordination number of 10. The unprecedented highly coordinated borometallic molecular wheels provide insights into the interactions between transition metals and boron and expand the frontier of boron chemistry. Another interesting feature discovered through cluster studies is boron transmutation. Even though it is well-known that B(-), formed by adding one electron to boron, is isoelectronic to carbon, cluster studies have considerably expanded the possibilities of new structures and new materials using the B(-)/C analogy. It is believed that the electronic transmutation concept will be effective and valuable in aiding the design of new boride materials with predictable properties. The study of boron clusters with intermediate properties between those of individual atoms and bulk solids has given rise to a unique opportunity to broaden the frontier of boron chemistry. Understanding boron clusters has spurred experimentalists and theoreticians to find new boron-based nanomaterials, such as boron fullerenes, nanotubes, two-dimensional boron, and new compounds containing boron clusters as building blocks. Here, a brief and timely overview is presented addressing the recent progress made on boron clusters and the approaches used in the authors' laboratories to determine the structure, stability, and chemical bonding of size-selected boron clusters by joint photoelectron spectroscopy and theoretical studies. Specifically, key findings on all-boron hydrocarbon analogues, metal-centered boron wheels, and electronic transmutation in boron clusters are summarized.

Quantum rules for planar boron nanoclusters

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