Dynamic Structural Fluxionality in a Planar Tetracoordinate Carbon Cluster Stabilized by Boron Ligands

The design of boron-based molecular rotors stems from boron-carbon binary clusters containing multiple planar hypercoordinate carbons (phCs, such as C2B8). However, the design of boron-coordinated phCs is challenging due to boron's tendency to occupy hypercoordinate centers more than carbon. Although this challenge has been addressed, the designed clusters of interest have not exhibited dynamic fluxionality similar to that of the initial C2B8. To address this issue, we report a σ/π doubly aromatic CB2H5 + cluster, the first global minimum containing a boron-coordinated planar tetracoordinate carbon atom with dynamic fluxionality. Dynamics simulations show that two ligand H atoms exhibit alternate rotation, resulting in an intriguing dynamic fluxionality in this cluster. Electronic structure analysis reveals the flexible bonding positions of the ligand H atoms because they do not participate in π delocalized bonding nor bond to any other non-carbon atom, highlighting this rotational fluxionality. Unprecedentedly, the fluxional process involves not only the usual conversion of the number of bonding atoms, but also the type of bonding (3c π bonds ↔4c σ bonds), which is an uncommon fluxional mechanism. The cluster represents an effort to apply phC species to molecular machines.

A reinvestigation of the boron cluster B15+/0/-: a benchmark of density functionals and consideration of aromaticity models

This study presents a thorough reinvestigation of the B15+/0/- isomers, first employing coupled-cluster theory CCSD(T) calculations to validate the performance of different DFT functionals. The B15+ cation has two planar lowest-lying isomers, while the first 3D isomer is less stable than the global minimum by ∼10 kcal mol-1. The PBE functional, within this benchmark survey, has proved to be reliable in predicting relative energies for boron isomers. Other functionals such as the TPSSh, PBE0 and HSE06 result in good energy ordering of isomers but warrant reconsideration when distinguishing between 2D and 3D forms. Caution is needed for structures having high spin contamination, as it may lead to significant errors. The anomalously lower stability of the B15- anion with respect to its neighbours, in terms of electron detachment energy, was explained through a competition between both rectangle and disk models for its geometry. This elucidates its stability with 12 electrons in rectangle model and instability with 10 electrons in disk-shaped structure, emphasizing the value of employing such geometric models. The proximity of the σ* LUMO to the π HOMO also contributes to the weakening of the B15- stability.

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.

[(OB)2-M©B7O7-BO]- (M = Mn, Tc, Re): Chemically Stable and Triply Aromatic Ballet Rotors

Single-molecule nanorotors are generally constructed based on boron atoms to obtain structural fluxionality via possessing the delocalized multicenter bonds. However, the electron-deficient boron atoms are commonly exposed in these nanorotors, which leads to extremely high chemical reactivity, which blocks the synthesis in the condensed phase. In this work, we computationally designed a series of transition-metal-doped boron oxide clusters MB10O10- (in structural configuration of [(OB)2-M©B7O7-BO]-, M = Mn, Tc, Re, © means "centered" in a planar or quasi-planar hypercoordinate environment), which can be vividly named as "ballet rotors" to label their anthropomorphic dynamic rotational behaviors. The rotational fluxionality in ballet rotors originates from the completely delocalized nature of the bonding within their MB10 core moieties. Remarkably, compared with single-molecule nanorotors having bare boron atoms and the narrow HOMO-LUMO gaps (≤4.00 eV) as well as low vertical detachment energies (VDEs, ≤4.46 eV for anions), the ballet rotors possess significantly improved chemical stability, as evidenced sterically by the absence of exposed boron atoms and electronically by much wider HOMO-LUMO gaps (5.66-5.98 eV) as well as obviously higher VDEs between 5.36 and 5.47 eV. Specifically, the ballet rotors are mainly stabilized by the delicately placed peripheral oxygen atoms, which can compensate for all electron-deficient boron atoms via O → B π back bonds and sterically protect them. Simultaneously, they are additionally stabilized by aromatic stabilization effect from possessing the novel S + P + D triple aromaticity. We expect that the proposal of chemically stable ballet rotors in this work can arouse the rational design of nanorotors for experimental realization in the condensed phase.

Isovalent electronic systems B+13 and BeB12: structural interchange of GM and TS

Fluxional Wankel motor molecules have received considerable attention in recent years in both chemistry and nanoscience. Based on extensive first-principles theory calculations, we present herein the smallest neutral quasi-planar alkaline-earth metal-doped Wankel motor complex Cs BeB12 (BeB2@B10), which is isovalent with C2v B+13 (B3@B10+). The global minimum (GM) Cs BeB12 (1) and transition state (TS) Cs BeB12 (2) correspond to the C2v TS (4) and C2v GM (3) of B+13, respectively. Molecular dynamics simulations show that, with ten equivalent GMs and ten equivalent TSs intervals, the B10 outer ring in BeB12 (1/2) overcomes the rotational energy barrier to rotate almost freely around the BeB2 triangular core above 800 K in a rotation angle of 36° in each step. Detailed bonding analyses indicate that, in addition to the ten localized periphery B-B bonds, both Cs BeB12 (1) and Cs BeB12 (2) possess three delocalized bonding systems over the molecular framework satisfying the (4n+2) Hückel rule, making the neutral complex 2σ + π triply aromatic in nature and highly stable in thermodynamics.

Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based Na5B7 Sandwich Cluster

Doping alkali metals into boron clusters can effectively compensate for the intrinsic electron deficiency of boron and lead to interesting boron-based binary clusters, owing to the small electronegativity of the former elements. We report on the computational design of a three-layered sandwich cluster, Na5B7, on the basis of global-minimum (GM) searches and electronic structure calculations. It is shown that the Na5B7 cluster can be described as a charge-transfer complex: [Na4]2+[B7]3-[Na]+. In this sandwich cluster, the [B7]3- core assumes a molecular wheel in shape and features in-plane hexagonal coordination. The magic 6π/6σ double aromaticity underlies the stability of the [B7]3- molecular wheel, following the (4n + 2) Hückel rule. The tetrahedral Na4 ligand in the sandwich has a [Na4]2+ charge-state, which is the simplest example of three-dimensional aromaticity, spherical aromaticity, or superatom. Its 2σ electron counting renders σ aromaticity for the ligand. Overall, the sandwich cluster has three-fold 6π/6σ/2σ aromaticity. Molecular dynamics simulation shows that the sandwich cluster is dynamically fluxional even at room temperature, with a negligible energy barrier for intramolecular twisting between the B7 wheel and the Na4 ligand. The Na5B7 cluster offers a new example for dynamic structural fluxionality in molecular systems.

Two-layer molecular rotors: A zinc dimer rotating over planar hypercoordinate motifs

Multi-layer molecular rotors represent a class of unique combination of topology and bonding, featuring a barrier-free rotation of one layer with respect to other layers. This emerging fluxional behavior has been found in a few doped boron clusters. Herein, we strongly enrich this intriguing family followed by an effective design strategy, summarized as essential factors: i) considerable electrostatic interactions originated from a strong charge transfer between layers; ii) the absence of strong covalent bonds between layers; and iii) fully delocalized σ/π electrons from at least one layer. We found that planar hypercoordinate motifs consisting of monocyclic boron rings and metals with σ + π dual aromaticity can be regarded as one promising layer, which can support the suspended X₂ (X = Zn, Cd, Hg) dimers. By detailed investigations of thermodynamic and kinetic stabilities of 60 species, eventually, MB₇ X₂ ^- and MB₈ X₂ (X = Zn, Cd; M = Be, Ru, Os; Be works only for Zn-based cases) clusters were verified to be the global-minimum two-layer molecular rotors. Especially, their electronic structure analyses vividly confirm the practicability of the electronic structure requirements mentioned above for designing multi-layer molecular rotors.

Be3B11- cluster: a dynamically fluxional beryllo-borospherene

The beryllium-doped Be₃B₁₁^- cluster has two nearly isoenergetic isomers, adopting the smallest trihedral spherical geometries with a boron single-chain skeleton. The B₁₁ skeleton in the global minimum (C_2v, ¹A₁) comprises three conjoined boron rings (one B₈/two B₇) on the waist, sharing two B₃ equilateral triangles at the top and bottom, respectively. However, the local minimum (C_s, ¹A') has one deformed B₄ pyramid at the top. The drastic structural transformation of B₁₁ skeletons from perfectly planar B₁₁ clusters mainly profited from robust electrostatic interaction between Be atoms and B₁₁ skeletons. The dynamic simulations suggest that two species can interconvert via a novel mechanism, that is "triangle-pyramid-triangle", which facilitates the free migration of boron atoms in the B₁₁ skeleton, thereby showing the fascinating dynamic fluxionality. The chemical bonding analyses reveal that the B₁₁ skeleton is covered by two types of delocalized π bonds in an orthogonal direction, which leads to its spherical aromaticity.

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.

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.

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.

Metallocene: multi-layered molecular rotors

The electronic and structural prerequisites for a multi-layered molecular rotor have been demonstrated herein in terms of nine 18-valence-electron metallocene sandwich complexes. First, the lack of strong covalent bonds between layers is a key issue to obtain a barrier-free rotation of one layer relative to other layers, where the considerable energetic but unidirectional (such as electrostatic interactions) interactions are needed between layers to keep the structural integrity against fragment separation and structural distortion in a rotation process. Second, one or more layers should possess continuous and delocalized π electron clouds to provide a driving force for the barrier-free rotation. More importantly, besides a negligible rotation barrier, the reasonable rotational period associated with the ultra-soft rotation mode is a critical point for the observability of dynamical behavior in multi-layered molecular rotors.

Possible effects of fluxionality of a cavitand on its catalytic activity through confinement

The discovery of fullerenes was a huge milestone in the scientific community, and with it came the urge to discover and analyze various small and large atomic and molecular clusters having a cavity. These cavitands of varied shapes and sizes have wide applications in the encapsulation of rare gas atoms to induce bond formation between them, storage of hydrogen and hydrocarbons to be used as alternative sources of fuel, catalyzation of otherwise slow reactions without using a catalyst, activation of small gas molecules, etc. Various cavitands like fullerenes, [ExBox]4+, cucurbit[n]urils, borospherenes, octa acid, etc. have been used for this purpose. Some clusters including cavitands exhibit fluxional behaviour. Systems in a confined environment often manifest interesting variations in their properties and behaviour, compared to their unconfined counterparts, facilitating the aforementioned applications. In this perspective article, we explore the possibility of making use of this extra degree of freedom, viz., the fluxionality, in changing the catalytic activity of the cavitand.

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.

Vibrational band-structures caused by internal rotations of the boron Wankel rotor B11. RSC Adv 2021;11:3613-3621. [PMID: 35424268 PMCID: PMC8694174 DOI: 10.1039/d0ra08821h]

Nuclear quantum effects are often neglected for systems without hydrogen atoms. However some planar boron rotors turn out to exhibit remarkable nuclear quantum effects. Recent experiment on infrared spectroscopy of B₁₃⁺ shows unexpected spectral broadening which still awaits physical explanation. Here we present quantitative investigations of the vibrational energy levels of B₁₁⁻ up to full dimension. A harmonic-bath averaged Hamiltonian suitable for planar boron rotors is constructed and used to predict typical types of vibrational states of B₁₁⁻. Band structures caused by internal rotations are found for all the investigated vibrational states. The experimental phenomenon of spectral broadening is thus due to the band structures of the corresponding vibrational levels. The detailed information of the relevant vibrational states reported in the present work may provide valuable references for future investigations of high resolution spectroscopy of B₁₁⁻.

The band structures of the vibrational energy levels of B₁₁⁻ lead to corresponding spectral broadening. The vibrational band-structures of planar boron rotors are caused by internal rotations.

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.

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.

Intriguing structural, bonding and reactivity features in some beryllium containing complexes

We highlighted our contributions to Be chemistry which include bond-stretch isomerism in Be₃²⁻ species, Be complexes bound with noble gas, CO, and N₂, Be based nanorotors, and intriguing bonding situations in some Be complexes.

Probing the structure and electronic properties of beryllium doped boron clusters: A planar BeB16- cluster motif for metallo-borophene

Beryllium-doped boron clusters display essential similarities to borophene (boron sheet) with a molecular structure characterized by remarkable properties, such as anisotropy, metallicity and high conductivity. Here we have determined low-energy structures of BeBn0/- (n = 10-20) clusters by utilizing CALYPSO searching program and DFT optimization. The results indicated that most ground states of clusters prefer plane or quasi-plane structures by doped Be atom. A novel unexpected fascinating planar BeB16- cluster with C2v symmetry is uncovered which possesses robust relative stability. Furthermore, planar BeB16- offers a possibility to construct metallo-borophene nano-materials. Molecular orbital and chemical bonding analysis reveal the peculiarities of BeB16- cluster brings forth the aromaticity and the strong interaction of B-B σ-bonds in boron network.

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.

Nuclear spin blockade of laser ignition of intramolecular rotation in the model boron rotor B 13 + 11

The boron rotor B 13 + 11 consists of a tri-atomic inner "wheel" that may rotate in its pseudo-rotating ten-atomic outer "bearing"-this concerted motion is called "contorsion." B 13 + 11 in its ground state has zero contorsional angular momentum. Starting from this initial state, it is a challenge to ignite contorsion by a laser pulse. We discover, however, that this is impossible, i.e., one cannot design any laser pulse that induces a transition from the ground to excited states with non-zero contorsional angular momentum. The reason is that the ground state is characterized by a specific combination of irreducible representations (IRREPs) of its contorsional and nuclear spin wavefunctions. Laser pulses conserve these IRREPs because hypothetical changes of the IRREPs would require nuclear spin flips that cannot be realized during the interaction with the laser pulse. We show that all excited target states of B 13 + 11 with non-zero contorsional angular momentum have different IRREPs that are inaccessible by laser pulses. Conservation of nuclear spins thus prohibits laser-induced transitions from the non-rotating ground to rotating target states. We discover various additional constraints imposed by conservation of nuclear spins, e.g., laser pulses can change clockwise to counter-clockwise contorsions or vice versa, but they cannot stop them. The results are derived in the frame of a simple model.

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

Boron-based nanoclusters have unique structures, bonding, and dynamic properties, which originate from boron's electron-deficiency. We demonstrate here that pouring in extra electrons can alter such systems fundamentally. A coaxial triple-layered Be6B102- sandwich cluster is designed via global structural searches and quantum chemical calculations. It is well defined as the global minimum, which consists of a slightly elongated B10 monocyclic ring and two Be3 rings, the latter forming a Be6 trigonal-prism albeit without interlayer Be-Be bonding. The B10 ring shows structural and chemical integrity with respect to the Be3 rings, and yet it differs markedly from the free B10 cluster and closely resembles the C10 cluster. The present data testify to the idea of electronic transmutation, in which a B- is equivalent to C and a B10 cluster, upon charge-transfer, is converted to and stabilized as a monocyclic ring analogous to C10. Chemical bonding analyses reveal that the B10 ring in the Be6B102- cluster has 10π and 10σ delocalization and each Be3 ring is held together by 2σ electrons, collectively rendering four-fold π/σ aromaticity. The bonding pattern is in line with the formula of [Be3]4+[B10]10-[Be3]4+, suggesting a highly charged electron-transfer complex. Furthermore, the Be6B102- cluster is dynamically fluxional with dual modes of revolution (orbiting) and rotation (twisting), being structurally robust at least up to a temperature of 1500 K.

Boron Nanowheels with Axles Containing Noble Gas Atoms: Viable Noble Gas Bound M©B10- Clusters (M=Nb, Ta)

The viability of noble gas axled boron nanowheels Ng_n M©B₁₀^- (Ng=Ar-Rn; M=Nb, Ta; n=1, 2) is explored by ab initio computations. In the resulting Ng₂ -M complexes, the Ng-M-Ng nanorod passes through the center of the B₁₀^- ring, providing them with an inverse sandwich-like structure. While in the singly Ng bound analogue, the Ng binding enthalpy H_b at 298 K ranges from 2.5 to 10.6 kcal mol^-1 , in doubly Ng bound cases it becomes very low for the Ng₂ M©B₁₀^- →Ng+NgM©B₁₀^- dissociation channel, except for the case of Rn, for which the corresponding H_b values are 3.4 (Nb) and 4.0 kcal mol^-1 (Ta). For a given Ng, Ta has slightly higher Ng-binding ability than Nb. The corresponding free-energy changes indicate that these systems, particularly the Xe and Rn complexes, are good candidates for experimental realization in a low-temperature matrix. The Ng-M bonds were found to be covalent in nature, as reflected in their large Wiberg bond indices, formation of a 2c-2e σ orbital between Ng and M centers in natural bond orbital and adaptive natural density partitioning (AdNDP) analyses, and the short Ng-M distances. Energy decomposition analysis and a study on the natural orbitals for chemical valence show that the Ng-M contact is supported mainly by the orbital and electrostatic interactions, with almost equal contributions. Although both the Ng→M σ donation and Ng←M π backdonation play roles in the origin of orbital interaction, the former is significantly dominant over the latter. Further, AdNDP analysis indicates that the doubly aromatic character (both σ and π) in MB₁₀^- clusters is not perturbed by the interaction with Ng atoms.

Au26: a case of fluxionality/co-existence

BOMD simulations are performed on experimentally identified conformations of the fluxional Au26 cluster at finite temperature. Comprehensive analysis of structural, electronic and thermal properties indicates that the highest energy tubular cage conformation (till 500 K) outperforms the ground state conformation (till 400 K) in terms of thermal stability.

Coaxial Triple-Layered versus Helical Be6 B11- Clusters: Dual Structural Fluxionality and Multifold Aromaticity

Two low-lying structures are unveiled for the Be₆ B₁₁^- nanocluster system that are virtually isoenergetic. The first, triple-layered cluster has a peripheral B₁₁ ring as central layer, being sandwiched by two Be₃ rings in a coaxial fashion, albeit with no discernible interlayer Be-Be bonding. The B₁₁ ring revolves like a flexible chain even at room temperature, gliding freely around the Be₆ prism. At elevated temperatures (1000 K), the Be₆ core itself also rotates; that is, two Be₃ rings undergo relative rotation or twisting with respect to each other. Bonding analyses suggest four-fold (π and σ) aromaticity, offering a dilute and fluxional electron cloud that lubricates the dynamics. The second, helix-type cluster contains a B₁₁ helical skeleton encompassing a distorted Be₆ prism. It is chiral and is the first nanosystem with a boron helix. Molecular dynamics also shows that at high temperature the helix cluster readily converts into the triple-layered one.

Why nanoscale tank treads move? Structures, chemical bonding, and molecular dynamics of a doped boron cluster B10C

Planar boron clusters form dynamic rotors, either as molecular Wankel motors or subnanoscale tank treads, the latter being exemplified by an elongated B₁₁^- cluster. For an in-depth mechanistic understanding of the rotors, we investigate herein a doped boron cluster, B₁₀C, in which a C atom isovalently substitutes B^- in the B₁₁^- tank tread. Two critical structures are achieved: the C_s (¹A') global minimum (GM) with C positioned in the peripheral ring and the C_2v (¹A₁) local minimum (LM) with C in the diatomic core. In the GM the C atom completely halts the rotation of B₁₀C, whereas in the LM the dynamic fluxionality remains. The energy barriers for in-plane rotation differ markedly: 12.93/18.31 kcal mol^-1 for GM versus 1.84 kcal mol^-1 for LM at the single-point CCSD(T) level. The GM rotates via two transition states (TS), compared to one for the LM. Chemical bonding in the structures is elucidated via canonical molecular orbital (CMO) analysis, adaptive natural density partitioning (AdNDP), electron localization functions (ELFs), and Wiberg bond indices (WBI). Electron delocalization is shown to be essential for structural fluxionality. In particular, the variation of WBI from the GM or LM geometries to their TS structures correlates positively with the energy barrier, which offers a quasi-quantitative measure of the barrier height and hence controls the dynamics. This finding may be extended to all molecular rotors. It also helps rationalize why a strongly covalently bound system can behave dynamically in a manner similar to a weakly bound one; it is the latter that is generally anticipated to be structurally fluxional.

A Spinning Umbrella: Carbon Monoxide and Dinitrogen Bound MB12- Clusters (M = Co, Rh, Ir)

Strong binding of carbon monoxide (CO) and dinitrogen (N₂) by MB₁₂^- (M = Co, Rh, Ir) clusters results in a spinning umbrella-like structure. For OCMB₁₂^- and NNMB₁₂^- complexes, the bond dissociation energy values range within 50.3-67.7 kcal/mol and 25.9-35.7 kcal/mol, respectively, with the maximum value obtained in Ir followed by that in Co and Rh analogues. COMB₁₂^- complex is significantly less stable than the corresponding C-side bonded isomer. The associated dissociation processes for OCMB₁₂^- and NNMB₁₂^- into CO or N₂ and MB₁₂^- are highly endergonic in nature at 298 K, implying their high thermochemical stability with respect to dissociation. In OCMB₁₂^- and NNMB₁₂^- complexes, the C-O and N-N bonds are found to be elongated by 0.022-0.035 Å along with a large red-shift in the corresponding stretching frequencies, highlighting the occurrence of bond activation therein toward further reactivity due to complexation. The obtained red-shift is explained by the dominance of L←M π-back-donation (L = CO, OC, NN) over L→M σ-donation. The binding of L enhances the energy barrier for the rotation of the inner B₃ unit within the outer B₉ ring by 0.4-1.8 kcal/mol, which can be explained by a reduction in the distance of the longest bond between inner B₃ and outer B₉ rings upon complexation. A good correlation is found between the change in rotational barrier relative to that in MB₁₂^- and the energy associated with the L→M σ-donation. Born-Oppenheimer molecular dynamics simulations further support that the M-L bonds in the studied systems are kinetically stable enough to retain the original forms during the internal rotation of inner B₃ unit.

A universal mechanism of the planar boron rotors B11-, B13+, B15+, and B19-: inner wheels rotating in pseudo-rotating outer bearings

Planar boron clusters B₁₁^-, B₁₃⁺, B₁₅⁺, and B₁₉^- have been introduced recently as molecular Wankel motors or tank treads. Here we present a universal mechanism for these dynamically fluxional clusters; that is, they are molecular rotors with inner wheels that rotate almost freely in pseudo-rotating outer bearings, analogous to rotating molecules trapped in pseudo-rotating cages. This mechanism has significant quantum mechanical consequences: the global-minimum structures of the clusters have C_2v symmetry, whereas the wheels rotating in pseudo-rotating bearings generate rosette-type shapes with D_9h, D_10h, D_11h, and D_13h symmetries. The related rotational/pseudo-rotational energies appear with characteristic band structures, effecting the dynamics.

Wheel-like, elongated, circular, and linear geometries in boron-based CnB7−n(n = 0–7) clusters: structural transitions and aromaticity

Boron–carbon mixed clusters C_nB_7−n(n= 0–7) assume wheel-like, elongated, circular, and linear geometries, dictated by (π and σ) aromaticity and antiaromaticity.

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.

Concentric dual π aromaticity in bowl-like B30cluster: an all-boron analogue of corannulene

The bowl-like B₃₀cluster is an all-boron analogue of corannulene, featuring concentric dual π aromaticity with 6π and 14π electrons for the inner and the outer boron ribbons, respectively.