Boron-based binary Be6B102- cluster: three-layered aromatic sandwich, electronic transmutation, and dynamic structural fluxionality

CBe4H6: a molecular rotor with a built-in on-off switch

It is highly challenging to control (stop and resume as needed) molecular rotors because their intramolecular rotations are electronically enabled by delocalized σ bonding, and the desired control needs to be able to destroy and restore such σ bonding, which usually means difficult chemical manipulation (substitution or doping atom). In this work, we report CBe4H6, a molecular rotor that can be controlled independently of chemical manipulation. This molecule exhibited the uninterrupted free rotation of Be and H atoms around the central carbon in first-principles molecular dynamics simulations at high temperatures (600 and 1000 K), but the rotation cannot be witnessed in the simulation at room temperature (298 K). Specifically, when a C-H bond in the CBe4H6 molecule adopts the equatorial configuration at 298 K, it destroys the central delocalized σ bonding and blocks the intramolecular rotation (the rotor is turned "OFF"); when it can adopt the axial configuration at 600 and 1000 K, the central delocalized σ bonding can be restored and the intramolecular rotation can be resumed (the rotor is turned "ON"). Neutral CBe4H6 is thermodynamically favorable and electronically stable, as reflected by a wide HOMO-LUMO gap of 7.99 eV, a high vertical detachment energy of 9.79 eV, and a positive electron affinity of 0.24 eV, so it may be stable enough for the synthesis, not only in the gas phase, but also in the condensed phase.

Boron-based ternary MgTa2B6 cluster: a turning nanoclock with dynamic structural fluxionality

Boron-based complex clusters are a fertile ground for the exploration of exotic chemical bonding and dynamic structural fluxionality. Here we report on the computational design of a ternary MgTa2B6 cluster via global structural searches and quantum chemical calculations. The cluster turns out to be a new member of the molecular rotor family, closely mimicking a turning clock at the subnanoscale. It is composed of a hexagonal B6 ring with a capping Ta atom at the top and bottom, whereas the Mg atom is linked to one Ta site as a radial Ta-Mg dimer. These components serve as the dial, axis, and hand of a nanoclock, respectively. Chemical bonding analyses reveal that the inverse sandwich Ta2B6 motif in the cluster features 6π/6σ double aromaticity, whose electron counting conforms to the (4n + 2) Hückel rule. The Ta-Mg dimer has a Lewis-type σ bond, and the Mg site has negligible bonding with B6 ring. The ternary cluster can be formulated as an [Mg]0[Ta2B6]0 complex. Molecular dynamics simulations suggest that the cluster is structurally fluxional analogous to a nanoclock, even at a low temperature of 100 K. The Ta-Mg hand turns almost freely around the Ta2 axis and along the B6 dial. The tiny intramolecular rotation barrier is less than 0.3 kcal mol-1, being dictated by the bonding nature of double 6π/6σ aromaticity. The present system offers a new type of molecular rotor in physical chemistry.

Chemical bonding and dynamic structural fluxionality of a boron-based Al2B8 binary cluster: the robustness of a doubly 6π/6σ aromatic [B8]2- molecular wheel

Despite the isovalency between Al and B elements, Al-doping in boron clusters can deviate substantially from an isoelectronic substitution process. We report herein on a unique sandwich di-Al-doped boron cluster, Al₂B₈, using global structural searches and quantum chemical calculations. The cluster features a perfectly planar B₈ molecular wheel, with two isolated Al atoms symmetrically floating above and below it. The two Al atoms are offset from the center of the molecular wheel, resulting in a C _2v symmetry for the cluster. The Al₂B₈ cluster is shown to be dynamically fluxional even at far below room temperature (100 K), in which a vertical Al₂ rod slides or rotates freely within a circular rail on the B₈ plate, although there is no direct Al-Al interaction. The energy barrier for intramolecular rotation is only 0.01 kcal mol^-1 at the single-point CCSD(T) level. Chemical bonding analysis shows that the cluster is a charge-transfer complex and can be formulated as [Al]⁺[B₈]^2-[Al]⁺. The [B₈]^2- molecular wheel in sandwich cluster has magic 6π/6σ double aromaticity, which underlies the dynamic fluxionality, despite strong electrostatic interactions between the [Al]⁺, [B₈]^2-, and [Al]⁺ layers.

A plier-shaped binary molecular wheel B7Mg4+ cluster: hybrid in-plane heptacoordination, double π/σ aromaticity, and electronic transmutation

A plier-shaped charge-transfer [Mg2]2+[Mg2B7]− complex cluster exhibits double 6π/6σ aromaticity, whose hybrid molecular wheel structure is rationalized using the concept of electronic transmutation.

B3Al4+: A Three-Dimensional Molecular Reuleaux Triangle

We systematically explore the potential energy surface of the B3Al4+ combination of atoms. The putative global minimum corresponds to a structure formed by an Al4 square facing a B3 triangle. Interestingly, the dynamical behavior can be described as a Reuleaux molecular triangle since it involves the rotation of the B3 triangle at the top of the Al4 square. The molecular dynamics simulations, corroborating with the very small rotational barriers of the B3 triangle, show its nearly free rotation on the Al4 ring, confirming the fluxional character of the cluster. Moreover, while the chemical bonding analysis suggests that the multicenter interaction between the two fragments determines its fluxionality, the magnetic response analysis reveals this cluster as a true and fully three-dimensional aromatic system.

Electronic structure, stability, and aromaticity of M2B6 (M = Mg, Ca, Sr, and Ba): an interplay between spin pairing and electron delocalization

It has been shown in previous studies that the Be₂B₆ complex exhibits a triplet ground state with double aromaticity. In this work, the stability, electronic structure, and aromaticity of the homologous series M₂B₆ (M = Mg, Ca, Sr and Ba) were examined and compared to those of Be₂B₆. At the CCSD(T)/def2-TZVP//B3LYP/def2-TZVP level of theory, the target molecules were found to be more stable in the singlet than in the triplet spin state. Magnetically induced current densities and multicentre delocalization index (MCI) were employed to assess the aromatic character of the studied complexes. Both employed methods agree that M₂B₆ (M = Mg, Ca, Sr and Ba) are π aromatic and σ nonaromatic in the singlet ground state, and double aromatic in the triplet state. It was demonstrated that the electron counting rules of aromaticity cannot be used to correctly predict the aromaticity and relative stability of the examined molecules in different spin states.

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

Lowest-energy structures, the distribution of isomers, and their molecular properties depend significantly on geometry and temperature. Total energy computations using DFT methodology are typically carried out at a temperature of zero K; thereby, entropic contributions to the total energy are neglected, even though functional materials work at finite temperatures. In the present study, the probability of the occurrence of one particular Be4B8 isomer at temperature T is estimated by employing Gibbs free energy computed within the framework of quantum statistical mechanics and nanothermodynamics. To identify a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surfaces is carried out using a multi-level multistep global genetic algorithm search coupled with DFT. In addition, we discuss the energetic ordering of structures computed at the DFT level against single-point energy calculations at the CCSD(T) level of theory. The total VCD/IR spectra as a function of temperature are computed using each isomer's probability of occurrence in a Boltzmann-weighted superposition of each isomer's spectrum. Additionally, we present chemical bonding analysis using the adaptive natural density partitioning method in the chiral putative global minimum. The transition state structures and the enantiomer-enantiomer and enantiomer-achiral activation energies as a function of temperature evidence that a change from an endergonic to an exergonic type of reaction occurs at a temperature of 739 K.

Concentric Inner 2π/6σ and Outer 10π/14σ Aromaticity Underlies the Dynamic Structural Fluxionality of Planar B19- Wankel Motor Cluster

Planar C_2v B₁₉^- global-minimum (GM) cluster is known as a molecular Wankel motor, featuring unique chemical bonding and structural fluxionality. While the geometry, bonding, and molecular dynamics of the cluster are documented in the literature, it remains warranted to fully understand its bonding nature and unravel the mechanism behind the structural dynamics. We shall offer herein an updated bonding model on the bases of canonical molecular orbital (CMO) analysis and adaptive natural density partitioning (AdNDP), further aided by natural bond orbital (NBO) analysis and orbital composition calculations. The computational data indicate that the B₁₉^- cluster has inner 2π/6σ and outer 10π/14σ concentric 4-fold π/σ aromaticity. Being spatially isolated from each other, the inner B₆ disk supports 2π and 6σ subsystems, whereas the outer B₁₈ double-ring ribbon has 10π and 14σ subsystems. All 4-fold π/σ subsystems are intrinsically delocalized and conform to the (4n + 2) Hückel rule for aromaticity. The change of Wiberg bond index (WBI) from GM to transition-state (TS) for radial B-B links is minimal and uniform, which offers a semiquantitative measure of structural dynamics and underlies the low energy barrier.

Boron-based Be2B5+/0/− alloy clusters: inverse sandwiches with pentagonal boron ring and reduction-induced structural transformation to molecular wheel structure

Boron-based Be₂B₅^+/0/− alloy clusters feature inverse sandwich versus molecular wheel structures, which sensitively depend on their charge states and show distinct π/σ aromaticity.

Anchoring a bow-shaped boron single chain in binary Be6B7- cluster: hybrid octagonal ring, multifold π/σ aromaticity, and dual electronic transmutation

Elemental boron clusters do not form linear chain or monocyclic ring structures, which is in contrast to carbon. Based on computer global searches and quantum chemical calculations, we report on the viability of a curved boron single chain in binary Be6B7- cluster. The boron motif assumes a bow shape, being anchored on a Be6 prism. Such a motif, which appears to be highly strained in its free-standing form, is exotic in boron-based clusters and nanostructures. Chemically, the cluster is analogous to a "clam-and-pearl-chain" system at the nanoscale (about 1 nm in size), in which a Be6 clam moderately opens its mouth, except that a B7 pearl chain is too large to be encapsulated inside. The picture differs from a three-layered sandwich. This cluster features a hybrid Be2B7 monocyclic ring, which is octagonal in nature and supports double 10π/6σ aromaticity. The number of π bonds substantially surpasses that in bare boron clusters of similar sizes. Two Be3 rings in the prism are also σ aromatic, albeit with effective 1σ/1σ electron-counting only. The unique multifold 1σ/10π/6σ/1σ aromaticity governs the geometry of the Be6B7- cluster, which can also be rationalized using the concept of dual electronic transmutation.

Are all planar and quasi-planar boron clusters aromatic? Counter examples of island or global π antiaromaticity from chemical bonding analysis

Boron is an electron-deficient element. The flatland of planar or quasi-planar (2D) boron clusters is believed to possess aromaticity for all members, which remains a fundamental issue in debate in boron chemistry. Using a selected set of D_2h B₆^2-, C_2h B₂₈^2-, and C_2v B₂₉^- clusters as counter examples, we shall present computational evidence for global or island π antiaromaticity in 2D boron clusters. The latter two are flattened for the purpose of clarity, which model their quasi-planar C₂ or C_s monoanion clusters observed in prior gas-phase experiments. Chemical bonding in the clusters is elucidated collectively on the basis of canonical molecular orbital (CMO) analysis, adaptive natural density partitioning (AdNDP), electron localization functions (ELFs), and localized molecular orbital (LMO) analysis. These results are complementary to each other and yet highly coherent. As a quantitative indicator, nucleus-independent chemical shifts (NICSs) are calculated at selected specific points in the clusters, which help differentiate between π aromaticity and antiaromaticity. Intriguingly, triangular sites in the same boron cluster can be aromatic, antiaromatic, or nonaromatic, despite the fact that they are physically indistinguishable. The phenomenon is understood in analogy to hydrocarbons and polycyclic aromatic hydrocarbons (PAHs). Even perfect sheet-like boron clusters are convertible to the PAH analogous systems. This work provides compelling examples for global and island π antiaromaticity in the 2D boron clusters.

Structure and bonding of molecular stirrers with formula B7M2- and B8M2 (M = Zn, Cd, Hg)

In this work, we systematically explored clusters with formula B₇M₂^- and B₈M₂ (M = Zn, Cd, Hg). The putative global minima are formed by an M₂ dimer and a disk-shaped boron wheel. Moreover, the chemical bonding analysis revealed that charge transfer from the metal atoms to the boron motifs resulted in (B₇)^3-(M₂)²⁺ and (B₈)^2-(M₂)²⁺ complexes with double (σ + π) aromatic boron wheels and a single bond for the metallic dimer. Above all, the computed rotational barriers of the M-M fragment with respect to the boron disk and molecular dynamics simulations indicate a virtually barrierless spin, resembling a magnetic stirrer on a baseplate.

Boron-Based Chiral Helix Be6 B10 2- and Be6 B11 - Clusters: Structures, Chemical Bonding, and Formation Mechanism

Boron forms a rich variety of low-dimensional nanosystems, including the newly discovered helix Be₆ B₁₀ ^2- (1) and Be₆ B₁₁ ^- (2) clusters. We report herein on the elucidation of chemical bonding in clusters 1/2, using the modern quantum chemistry tools of canonical molecular orbital analyses and adaptive natural density partitioning (AdNDP). It is shown that clusters 1/2 contain a chiral helix Be₂ B₁₀ Be₂ or Be₂ B₁₁ Be₂ skeleton with a total of 11 and 12 segments, respectively, which effectively curve into "helical pseudo rings" and chemically consist of two "quasicircles" as defined by their anchoring Be centers. The helix skeleton is connected via Lewis-type B-B and Be-B-Be σ bonds, being further stabilized by island π/σ bonds and a loose π bond at the junction. The Be₆ component in 1/2 assumes a distorted prism shape only physically, and it is fragmented into four parts: two terminal Be₂ dimers and two isolated Be centers. A Be₂ dimer at the far end manages to bend over and cap a quasicircle from one side of B plane. Consequently, each quasicircle of a helical pseudo ring is capped from opposite sides by two Be₂ /Be units, facilitating intramolecular charge-transfers of 5 electrons from Be to B. Overall, the folding of B helix involves as many as 10 electrons. The enormous electrostatics offers the ultimate driving forces for B helix formation.

Inverse sandwich complexes of B7M2−, B8M2, and B9M2+ (M = Zr, Hf): the nonclassical M–M bonds embedded in monocyclic boron rings

Three delocalized σ orbitals of the boron rings are perpendicularly mixed with one negligible σ and two π bonds of the M₂ (M = Zr, Hf) motifs, giving rise to less pronounced and nonclassical bonding interactions between two short-contact M atoms.

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.

The structure and chemical bonding in inverse sandwich B6Ca2 and B8Ca2 clusters: conflicting aromaticity vs. double aromaticity

Boron-based B₆Ca₂ and B₈Ca₂ clusters adopt unique inverse sandwich architectures, which are stabilized by interesting conflicting aromaticity and double aromaticity, respectively.

Fluxional Boron Clusters: From Theory to Reality

Isolated boron clusters exhibit many intriguing properties, which have only recently been unfolding with the hand-in-hand advancement of state-of-the-art experimental and theoretical methods for the analyses of their electronic structure, chemical reactivity, and nuclear dynamics. A fascinating property that a number of these clusters display is fluxionality, a dynamical phenomenon associated with the delocalized nature of the chemical bonding and related to the continuous exchange between interatomic neighbors. The electron-deficient nature of boron is the driving force behind its extraordinary ability to form multicenter bonds, and this in turn leads to fluxional behavior only when an appropriate combination of topology and bonding is present. The first instance of fluxionality in boron clusters, the quasi-planar anion B₁₉^-, was reported in 2010. The rotational barrier of the inner B₆ unit spinning within the peripheral B₁₃ ring can be overcome even at low temperature, mimicking the characteristic motion of a rotary internal combustion engine, and hence, B₁₉^- was entitled a boron-based molecular Wankel engine. Shortly after that, it was found that other quasi-planar boron clusters, like B₁₃⁺ and B₁₈^2-, also exhibit an almost barrier-free rotation of internal planar moieties. The case of the B₁₃⁺ cation is special because, on the one hand, it was chosen to examine the way to initiate, control, and direct the internal rotation using circularly polarized laser radiation, and on the other hand, the experimental manifestation of fluxionality was first established for this system through infrared experiments. Nevertheless, fluxional behavior is not limited to planar or pure boron clusters. Larger boron clusters, such as the fullerene-analogue borospherenes B₄₀ and B₃₉^-, are also predicted to show pronounced dynamical behavior that is related to the interconversion between six- and seven-membered rings. Be₆B₁₁^-, a triple-layer cluster, is another particularly interesting system since it exhibits multifold fluxionality consisting of the revolution of the outer boron ring around the Be₆ core and the spinning of the two Be₃ rings with respect to each other. The essential criteria for dynamical behavior in boron clusters are (1) the absence of a localized two-center, two-electron (2c-2e) bond between two molecular regions that tend to rotate with respect to each other, (2) the absence of steric hindrances for rotation and reorganization, and (3) retention of the delocalized electronic structure throughout the rotation/reorganization process. The fulfillment of the above three conditions ensures that low energy barriers will be associated with the rotation or reorganization of molecular moieties. The first two points can be illustrated from the facts that a single localized C-B σ bond in CB₁₈ raises the rotational barrier by 27.0 kcal·mol^-1 and the expansion of the outer ring by a single boron atom in moving from B₁₂⁺ to B₁₃⁺ lowers the rotational barrier by 7.5 kcal·mol^-1. Alternatively, it is also possible to make a rigid boron cluster fluxional through doping, where the geometric and electronic changes caused by a suitable dopant, as in MB₁₂^- (M = Co, Rh, Ir) and B₁₀Ca, reduce the corresponding rotational barriers enough to achieve fluxionality. At present, there are 13 pure boron clusters (B₁₁^-/0/+, B₁₃^+/0/-, B₁₅^+/0/-, B₁₈^2-, B₁₉^-, and B₂₀^-/2-) and eight metal-doped boron clusters (B₁₀Ca, NiB₁₁^-, [B₂-Ta@B₁₈]^-, Be₆B₁₁^-, Be₆B₁₀^2-, and MB₁₈^- (M = K, Rb, Cs)) that have sufficiently small rotational barriers (less than ∼1.5 kcal·mol^-1) to exhibit fluxional behavior at low temperature. Some of the other reported boron clusters show more sizable barriers, and their dynamical behavior is manifested only at elevated temperatures. The research on such systems is driven by the notion that it ultimately will pave the way for the development of light-harvesting boron-based nanomotors/machines and robots, a reality that may not be that far away!

Structures, Stabilities, and Spectral Properties of Endohedral Borospherenes M@B40 0/- (M = H2, HF, and H2O)

The discovery of borospherene B₄₀ leads to a new beginning for the study of boron chemistry and may lead to new boron-based nanomaterials. Based on density functional theory, the structures, electronic properties, infrared and Raman spectra, photoelectron spectra, and electronic absorption spectra of endohedral borospherenes M@B₄₀ ^0/- (M = H₂, HF, and H₂O) are investigated. It is found that H₂, HF, and H₂O monomers can form stable endohedral borospherenes M@B₄₀ ^0/- (M = H₂, HF, and H₂O). In addition, the calculated results indicate that the doped molecule at the off-center location can relax to the center location within the cage and the symcenter of the doped molecule is almost located in the center of the cage. Unlike endohedral metalloborospherene Ca@B₄₀, which is a charge-transfer complex between Ca²⁺ and B₄₀ ^2-, natural population analyses and chemical bonding analyses reveal that there is no significant charge transfer of the doped molecule. The calculated spectra indicate that doping of a molecule (H₂, HF, or H₂O) in borospherene B₄₀ can change the photoelectron spectra and doping of a polar molecule (HF or H₂O) in borospherene B₄₀ can change the spectral properties. For instance, the addition of a molecule can increase infrared and Raman-active modes and cause a red shift or blue shift of electronic spectra. These spectral features can be compared with future experimental values of endohedral borospherenes M@B₄₀ ^0/- (M = H₂, HF, and H₂O).

Starting a subnanoscale tank tread: dynamic fluxionality of boron-based B10Ca alloy cluster

Alloying an elongated B₁₀ cluster with Ca is shown to give rise to a dynamically fluxional B₁₀Ca cluster, the latter behaving like a tank tread at the subnanoscale. Computer global search identifies the B₁₀Ca C ₂ (¹A) global-minimum structure, which is chiral in nature and retains the quasi-planar moiety of bare B₁₀ cluster with Ca capped at one side, forming a half-sandwich. The rotation barrier of B₁₀Ca cluster is reduced with respect to B₁₀ by one order of magnitude, down to 1 kcal mol^-1 at the PBE0/6-311+G* level, which demonstrates structural fluxionality at 600 K and beyond via molecular dynamics simulations. Structurewise, the Ca alloying in B₁₀Ca cluster generates rhombic defect holes, preactivating the species and making it flexible against deformation. Chemical bonding analyses indicate that the B₁₀Ca cluster is a charge-transfer [B₁₀]^2-[Ca]²⁺ complex, being doubly π/σ aromatic with the 6π and 10σ electron-counting. Such a pattern offers ideal π/σ delocalization and facilitates fluxionality. In contrast, bare B₁₀ cluster has conflicting aromaticity with 6π and 8σ electrons, which is nonfluxional with a barrier of 12 kcal mol^-1. Double π/σ aromaticity versus conflicting aromaticity is a key mechanism that distinguishes between fluxional B₁₀Ca and nonfluxional B₁₀ clusters, offering a compelling example that the concept of aromaticity (and double aromaticity) can be exploited to design dynamically fluxional nanosystems.

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.

Be2B6 and Be2B7+: two double aromatic inverse sandwich complexes with spin-triplet ground state

Be₂B₆ and Be₂B₇⁺ clusters adopt interesting inverse sandwich structures with double σ/π aromaticity, and the former possesses the smallest monocyclic boron ring motif.