A family of superconducting boron crystals made of stacked bilayer borophenes

Monolayer borophenes tend to be easily oxidized, while thicker borophenes have stronger antioxidation properties. Herein, we proposed four novel metallic boron crystals by stacking the experimentally synthesized borophenes, and one of the crystals has been reported in our previous experiments. Bilayer units tend to act as blocks for crystals as determined by bonding analyses. Their kinetic, thermodynamic and mechanical stabilities are confirmed by our calculated phonon spectra, molecular dynamics and elastic constants. Our proposed allotropes are more stable than the boron α-Ga phase below 1000 K at ambient pressure. Some of them become more stable than the α-rh or γ-B₂₈ phases at appropriate external pressure. More importantly, our calculations show that three of the proposed crystals are phonon-mediated superconductors with critical temperatures of about 5-10 K, higher than those of most superconducting elemental solids, in contrast to typical boron crystals with significant band gaps. Our study indicates a novel preparation method for metallic and superconducting boron crystals dispensing with high pressure.

Boron Silicon B2Si3q and B3Si2p Clusters: The Smallest Aromatic Ribbons

The small binary boron silicon clusters B₂Si₃^q with q going from -2 to +2 and B₃Si₂^p with p varying from -3 to +1 were reinvestigated using quantum chemical methods. The thermodynamic stability of these smallest ribbon structures is governed by both Hückel and ribbon models for aromaticity. The more negative the cluster charge, the more ribbon character is shown. In contrast, the more positive the charge state, the more pronounced the Hückel character becomes. The ribbon aromaticity character can also be classified into ribbon aromatic, semiaromatic, antiaromatic, and triplet aromatic when the electron configuration of a ribbon structure is described as [...π²⁽ⁿ⁺¹⁾σ²ⁿ], [...π²ⁿ⁺¹σ²ⁿ], [...π²ⁿσ²ⁿ], and [...π²ⁿ⁺¹σ^2n-1], respectively. Geometry optimizations of the B₂Si₃ lowest-energy structure by some density functional theory (DFT) functionals result in a nonplanar shape because it possesses an antiaromatic ribbon character. However, its π aromaticity assigned by the Hückel rule is stronger in such a way that several other DFT and coupled-cluster theory CCSD(T) calculations show that B₂Si₃ is indeed stable in a planar form (C_s). A new global equilibrium structure for the anion B₂Si₃^2-, which is a ribbon semiaromatic species, was identified. Some benchmark tests were also carried out to evaluate the performance of popular methods for the treatment of binary B-Si clusters. At odds with some previous studies, we found that with reference to the high accuracy CCSD(T)/CBS method, the hybrid TPSSh functional is reliable for a structure search, whereas the hybrid B3LYP functional is more suitable for simulations of some experimental spectroscopic results.

A flat carborane with multiple aromaticity beyond Wade-Mingos' rules

It is widely known that the skeletal structure of clusters reflects the number of skeletal bonding electron pairs involved, which is called the polyhedral skeletal electron pair theory (PSEPT) or Wade and Mingos rules. While recent computational studies propose that the increase of skeletal electrons of polyhedral clusters leads to the flat structure beyond the PSEPT, little experimental evidence has been demonstrated. Herein, we report the synthesis of a C2B4R4 carborane 2 featuring a flat ribbon-like structure. The C2B4 core of 2 bearing 16 skeletal electrons in the singlet-ground state defies both the [4n + 2] Hückel's rule and Baird's rule. Nevertheless, the delocalization of those electrons simultaneously induces two independent π- and two independent σ-aromatic ring currents, rendering quadruple aromaticity.

Electronic Properties of Linear and Cyclic Boron Nanoribbons from Thermally-Assisted-Occupation Density Functional Theory

It remains rather difficult for traditional computational methods to reliably predict the properties of nanosystems, especially for those possessing pronounced radical character. Accordingly, in this work, we adopt the recently formulated thermally-assisted-occupation density functional theory (TAO-DFT) to study two-atom-wide linear boron nanoribbons l-BNR[2,n] and two-atom-wide cyclic boron nanoribbons c-BNR[2,n], which exhibit polyradical character when the n value (i.e., the number of boron atoms along the length of l-BNR[2,n] or the circumference of c-BNR[2,n]) is considerably large. We calculate various electronic properties associated with l-BNR[2,n] and c-BNR[2,n], with n ranging from 6 to 100. Our results show that l-BNR[2,n] and c-BNR[2,n] have singlet ground states for all the n values examined. The electronic properties of c-BNR[2,n] exhibit more pronounced oscillatory patterns than those of l-BNR[2,n] when n is small, and converge to the respective properties of l-BNR[2,n] when n is sufficiently large. The larger the n values, the stronger the static correlation effects that originate from the polyradical nature of these ribbons. Besides, the active orbitals are found to be delocalized along the length of l-BNR[2,n] or the circumference of c-BNR[2,n]. The analysis of the size-dependent electronic properties indicates that l-BNR[2,n] and c-BNR[2,n] can be promising for nanoelectronic devices.

Overlap of Radial Dangling Orbitals Controls the Relative Stabilities of Polyhedral B nH n- x Isomers ( n = 5-12, x = 0 to n - 1)

The removal of H atoms from polyhedral boranes results in the formation of dangling radial orbitals with one electron each. If there is a requirement of electrons for skeletal bonding to meet the Wade's rule, these are provided from the exohedral orbitals. Additional electrons occupy a linear combination of the dangling orbitals. Stabilization of these molecular orbitals depends on their overlap. The lateral (sideways) overlap of dangling orbitals decreases with the decreasing cluster size from 12 to 5 boron atoms as the orbitals become more and more splayed out. Thus, as the number of dangling orbitals increases, the destabilization of their combinations increases at a higher rate for smaller polyhedral boranes, leading to flat structures with the removal of a fewer number of hydrogens. Though exohedral orbitals form better overlap in larger polyhedral clusters, the increase of electrons with the removal of H atoms results in occupancy of antibonding skeletal orbitals (beyond Wade's rules) and leads to flat structures. The reverse happens when hydrogens are added to a flat cluster. Substitution of BH by Si does not change structural patterns.

A theoretical approach to the role of different types of electrons in planar elongated boron clusters

While the stability of planar elongated pure boron clusters is determined by their […σ²⁽ⁿ⁺¹⁾ π₁²⁽ⁿ⁺¹⁾ π₂²ⁿ] electronic configuration, the rectangle model can rationalize the π electronic configuration of rectangle-shaped structures.

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.

Silicon doped boron clusters: how to make stable ribbons?

A doping of small boron clusters with silicon atoms leads to the formation of stable boron nanoribbon structures. We present an analysis on the geometric and electronic structure, using MOs and electron localization function (ELF) maps, of boron ribbons represented by the dianions B₁₀Si₂^2- and B₁₂Si₂^2-. The effect of Si dopants and the origin of the underlying electron count [π²⁽ⁿ⁺¹⁾σ²ⁿ] are analyzed. Interaction between both systems of delocalized π and σ electrons creating alternant B-B bonds along the perimeter of a ribbon induces its high thermodynamic stability. The enhanced stability is related to the self-locked phenomenon.

B12Fn0/- (n = 1-6) series: when do boron double chain nanoribbons become global minima?

We present an extensive density-functional and wave function theory study of partially fluorinated B₁₂F_n^0/- (n = 1-6) series, which show that the global minima of B₁₂F_n^0/- (n = 2-6) are characterized to encompass a central boron double chain (BDC) nanoribbon and form stable BF₂ groups at the corresponding BDC corner when n ≥ 3, but the B₁₂F^0/- system maintains the structural feature of the well-known quasi-planar C_3v B₁₂. When we put the spotlight on B₁₂F₆^0/- species, our single-point CCSD(T) results unveil that albeit with the 3D icosahedral isomers not being their global minima, C₂ B₁₂F₆ (6.1, ¹A) and C₁ B₁₂F₆^- (12.1, ²A) as typical low-lying isomers are 0.60 and 1.95 eV more stable than their 2D planar counterparts D_3h B₁₂F₆ (6.7, ¹A') and C_2v B₁₂F₆^- (12.7, ²A₂), respectively, alike to B₁₂H₆^0/- species in our previous work. Detailed bonding analyses suggest that B₁₂F_n^0/- (n = 2-5) possess ribbon aromaticity with σ plus π double conjugation along the BDC nanoribbon on account of their total number of σ and π delocalized electrons conforming the common electron configuration (π²⁽ⁿ⁺¹⁾σ²ⁿ). Furthermore, the simulated PES spectra of the global minima of B₁₂F_n^- (n = 1-6) monoanions may facilitate their experimental characterization in the foreseeable future. Our work provides new examples for ribbon aromaticity and powerful support for the F/H/Au/BO analogy.

Cage-like B39+clusters with the bonding pattern of σ + π double delocalization: new members of the borospherene family

The recently observed cage-like borospherenesD_2dB₄₀^−/0andC₃/C₂B₃₉⁻have attracted considerable attention in chemistry and materials science.

Structural transition in metal-centered boron clusters: from tubular molecular rotors Ta@B21and Ta@B22+to cage-like endohedral metalloborospherene Ta@B22−

Extensive first-principles theory investigations unveil a tubular-to-cage-like structural transition in metal-centered boron clusters at (±)-D₂Ta@B₂₂⁻, the smallest axially chiral endohedral metalloborospherenes.

Structural transition upon hydrogenation of B20 at different charge states: from tubular to disk-like, and to cage-like

Extensive first-principles theoretical investigations indicate that neutral B20 undergoes a dramatic structural transition upon partial hydrogenation, from the tubular D2d B20 (), to the disk-like C2v B20H2 (), and then to the cage-like C2 B20H4 (). Both the singly charged C2v B20(-) () and C2 B20H2(-) () favor 2D disk-like planar structures with a filled hexagon (B7) at the center, while C2 B20H4(-) () follows its neutral counterpart with a 3D cage-like geometry. All the doubly charged C2v B20(2-) (), C2 B20H2(2-) (), and C1 B20H4(2-) () turn out to prefer planar or quasi-planar 2D structures over 3D geometries, with the most stable B20H4(2-) () possessing a unique hexagon hole (B6) at the center. Detailed CMO and AdNDP analyses reveal that both the perfect planar B20(2-) () and B20H2 () possess concentric dual π aromaticity, with two π-electrons delocalized over the filled hexagon B7 at the center and ten π-electrons delocalized between the filled B7 and the B13 outer ring, each separately conforming to 4n + 2 Hückel's rule. They are therefore the boron analogues of coronene (D6h C24H12). The quasi-planar C2 B20H2(2-) () and C1 B20H4(2-) () also appear to be π aromatic with one π system following the 4n + 2 rule. The B20H4(2-) () structure with a hexagon hole may serve as the embryo for monolayer boron α sheet. Both the cage-like C2 B20H4 () and C2 B20H4(-) () appear to be 3D aromatic with the large negative NICS values of -51.5 and -55.5 ppm, respectively. The structural changes from to reflect a competition between 2D and 3D aromaticities in these clusters, depending on the extent of hydrogenation and electronic charge states. The PES spectra of B20H2(-) () and B20H4(-) () are predicted to facilitate their future experimental characterizations and production.

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.

Planar B3S2H3−and B3S2H3clusters with a five-membered B3S2ring: boron–sulfur hydride analogues of cyclopentadiene

Boron–sulfur hydride clusters,C_2vB₃S₂H₃⁻and B₃S₂H₃, possess a five-membered B₃S₂ring as the core, which is analogous to cyclopentadiene in terms of π bonding.

Planar wheel-type M©BnHn2−/−/0 clusters (M = Cr, Mn and Fe for dianion, anion and neutral, respectively; n = 6 and 7)

A new “electronic” strategy that adds two electrons into the d_z2 orbital of the central M atom to form a lone pair, in contrast to Hoffmann’s “electronic” strategy to turn the bowl-type MB_nH_n^0/+ (M = Cr and Mn; n = 6 and 7) clusters into planar wheel-type clusters.

Unconventional charge distribution in the planar wheel-type M©B6H6−/0/+ (M = Mn, Fe and Co): central M with negative charges and peripheral boron ring with positive charges

Unconventional charge distribution exists in the planar wheel-type M©B₆H₆^−/0/+ (M = Mn, Fe and Co).

Ternary B2X2H2(X = O and S) rhombic clusters and their potential use as inorganic ligands in sandwich-type (B2X2H2)2Ni complexes

Boron-based ternary B₂O₂H₂and B₂S₂H₂clusters possess a rhombic, heteroatomic ring with 4π electrons in a nonbonding/bonding combination, differing from cyclobutadiene.

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes

Example of concerted electronic (right) and nuclear (left) fluxes: isomerization of B₄.

The B35 cluster with a double-hexagonal vacancy: a new and more flexible structural motif for borophene

Elemental boron is electron-deficient and cannot form graphene-like structures. Instead, triangular boron lattices with hexagonal vacancies have been predicted to be stable. A recent experimental and computational study showed that the B36 cluster has a planar C6v structure with a central hexagonal hole, providing the first experimental evidence for the viability of atom-thin boron sheets with hexagonal vacancies, dubbed borophene. Here we report a boron cluster with a double-hexagonal vacancy as a new and more flexible structural motif for borophene. Photoelectron spectrum of B35(-) displays a simple pattern with certain similarity to that of B36(-). Global minimum searches find that both B35(-) and B35 possess planar hexagonal structures, similar to that of B36, except a missing interior B atom that creates a double-hexagonal vacancy. The closed-shell B35(-) is found to exhibit triple π aromaticity with 11 delocalized π bonds, analogous to benzo(g,h,i)perylene (C22H12). The B35 cluster can be used to build atom-thin boron sheets with various hexagonal hole densities, providing further experimental evidence for the viability of borophene.

Boronyl chemistry: the BO group as a new ligand in gas-phase clusters and synthetic compounds

Boronyl (BO) is a monovalent σ radical with a robust B≡O triple bond. Although BO/BO(-) are isovalent to CN/CN(-) and CO, the chemistry of boronyl has remained relatively unknown until recently, whereas CN/CN(-) and CO are well-known inorganic ligands. Further analogy may be established for BO versus H or Au ligands, which are all monovalent σ radicals. This Account intends to provide an overview of research activities over the past few years that are relevant to the development of boronyl chemistry, in particular, in size-selected gaseous clusters containing BO. The systems covered herein include transition metal boronyl clusters, carbon boronyl clusters, boron oxide clusters and boron boronyl complexes, the boronyl boroxine, and the first synthetic Pt-BO bulk compound. In these boronyl clusters and compounds, the BO groups show remarkable structural and chemical integrity as a ligand. Among transition metal boronyls, gold monoboronyl clusters Aun(BO)(-) and Aun(BO) (n = 1-3) have been characterized, and they are shown to possess electronic and structural properties similar to the corresponding Au(n+1)(-) and Au(n+1) bare clusters, demonstrating the BO/Au analogy. The Au-B bonding in the Au-BO clusters is highly covalent. A recent advance in boronyl chemistry is the successful synthesis and isolation of the first boronyl compound, trans-[(Cy3P)2BrPt(BO)]. This unique Pt-BO compound and other potential transition metal boronyl compounds may find applications in catalysis and as chemical building blocks. Carbon boronyl clusters versus boron carbonyl clusters is a topic of interest in designing new aromatic complexes. Experimental and theoretical data obtained to date show that carbon boronyl clusters are generally far more stable than their boron carbonyl counterparts, highlighting the potency of boronyl as a ligand in aromatic compounds. Notably, in light of the BO/H analogy, the perfectly hexagonal (CBO)6 cluster is a carbon boronyl analogue of benzene. The BO groups also dominate the structures and bonding of boron oxide clusters and boron boronyl complexes, in which BO groups occupy terminal, bridging, or face-capping positions. The bridging η(2)-BO groups feature three-center two-electron bonds, akin to the BHB τ bonds in boranes. A close isolobal analogy is thus established between boron oxide clusters and boranes, offering vast opportunities for the rational design of novel boron oxide clusters and compounds. Boron boronyl clusters may also serve as molecular models for mechanistic understanding of the combustion of boron and boranes. An effort to tune the B versus O composition in boron oxide clusters leads to the discovery of boronyl boroxine, D3h B3O3(BO)3, an analogue of boroxine and borazine and a new member of the "inorganic benzene" family. Furthermore, a unique concept of π and σ double conjugation is proposed for the first time to elucidate the structures and bonding in the double-chain nanoribbon boron diboronyl clusters, which appear to be inorganic analogues of polyenes, cumulenes, and polyynes. This Account concludes with a brief outlook for the future directions in this emerging and expanding research field.

Pi and sigma double conjugations in boronyl polyboroene nanoribbons: B(n)(BO)2- and B(n)(BO)2 (n = 5-12)

A series of boron dioxide clusters, B(x)O2(-) (x = 7-14), have been produced and investigated using photoelectron spectroscopy and quantum chemical calculations. The dioxide clusters are shown to possess elongated ladder-like structures with two terminal boronyl (BO) groups, forming an extensive series of boron nanoribbons, B(n)(BO)2(-) (n = 5-12). The electron affinities of B(n)(BO)2 exhibit a 4n periodicity, indicating that the rhombic B4 unit is the fundamental building block in the nanoribbons. Both π and σ conjugations are found to be important in the unique bonding patterns of the boron nanoribbons. The π conjugation in these clusters is analogous to the polyenes (aka polyboroenes), while the σ conjugation plays an equally important role in rendering the stability of the nanoribbons. The concept of σ conjugation established here has no analogues in hydrocarbons. Calculations suggest the viability of even larger boronyl polyboroenes, B16(BO)2 and B20(BO)2, extending the boron nanoribbons to ~1.5 nm in length or possibly even longer. The nanoribbons form a new class of nanowires and may serve as precursors for a variety of boron nanostructures.

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.

Photoelectron spectroscopy of boron-gold alloy clusters and boron boronyl clusters: B3Au(n)(-) and B3(BO)n(-) (n = 1, 2)

Photoelectron spectroscopy and density-functional theory are combined to study the structures and chemical bonding in boron-gold alloy clusters and boron boronyl clusters: B3Au(n)(-) and B3(BO)n(-) (n = 1, 2). Vibrationally resolved photoelectron spectra are obtained for all four species and the B-Au and B-BO clusters exhibit similar spectral patterns, with the latter species having higher electron binding energies. The electron affinities of B3Au, B3Au2, B3(BO), and B3(BO)2 are determined to be 2.29 ± 0.02, 3.17 ± 0.03, 2.71 ± 0.02, and 4.44 ± 0.02 eV, respectively. The anion and neutral clusters turn out to be isostructural and isovalent to the B3H(n)(-)∕B3H(n) (n = 1, 2) species, which are similar in bonding owing to the fact that Au, BO, and H are monovalent σ ligands. All B3Au(n)(-) and B3(BO)n(-) (n = 1, 2) clusters are aromatic with 2π electrons. The current results provide new examples for the Au∕H and BO∕H isolobal analogy and enrich the chemistry of boronyl and gold.