All-boron aromatic clusters as potential new inorganic ligands and building blocks in chemistry

The unique sandwich K6Be2B6H6 cluster with a real borozene B6H6 core

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

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.

Boron-lead multiple bonds in the PbB2O- and PbB3O2- clusters

Despite its electron deficiency, boron can form multiple bonds with a variety of elements. However, multiple bonds between boron and main-group metal elements are relatively rare. Here we report the observation of boron-lead multiple bonds in PbB₂O^- and PbB₃O₂^-, which are produced and characterized in a cluster beam. PbB₂O^- is found to have an open-shell linear structure, in which the bond order of B☱Pb is 2.5, while the closed-shell [Pb≡B-B≡O]^2- contains a B≡Pb triple bond. PbB₃O₂^- is shown to have a Y-shaped structure with a terminal B = Pb double bond coordinated by two boronyl ligands. Comparison between [Pb≡B-B≡O]^2-/[Pb=B(B≡O)₂]^- and the isoelectronic [Pb≡B-C≡O]^-/[Pb=B(C≡O)₂]⁺ carbonyl counterparts further reveals transition-metal-like behaviors for the central B atoms. Additional theoretical studies show that Ge and Sn can form similar boron species as Pb, suggesting the possibilities to synthesize new compounds containing multiple boron bonds with heavy group-14 elements.

AuB8-: an Au-borozene complex

Photoelectron spectroscopy and quantum chemistry studies are used to investigate the structure and bonding of AuB₈^-. Global minimum sturctural searches show that AuB₈^- possesses a chair-like structure, which can be viewed as Au⁺ bonded to the edge of the doubly-aromatic B₈^2- borozene, Au⁺[η²-B₈^2-]. Chemical bonding analyses reveal that the AuB₈^- is a novel borozene complex with unique Au-borozene bonding.

Relative Stability of Boron Planar Clusters in Diatomic Molecular Model

In the recently introduced phenomenological diatomic molecular model imagining the clusters as certain constructions of pair interatomic chemical bonds, there are estimated specific (per atom) binding energies of small all-boron planar clusters B_n, n = 1–15, in neutral single-anionic and single-cationic charge states. The theoretically obtained hierarchy of their relative stability/formation probability correlates not only with results of previous calculations, but also with available experimental mass-spectra of boron planar clusters generated in process of evaporation/ablation of boron-rich materials. Some overestimation in binding energies that are characteristic of the diatomic approach could be related to differences in approximations made during previous calculations, as well as measurement errors of these energies. According to the diatomic molecular model, equilibrium binding energies per B atom and B–B bond lengths are expected within ranges 0.37–6.26 eV and 1.58–1.65 Å, respectively.

Electron correlation effects in boron clusters BQn (for Q = -1, 0, 1 and n ≤ 13) based on quantum Monte Carlo simulations

We present all-electron quantum Monte Carlo simulations on the anionic, neutral, and cationic boron clusters BQn with up to 13 atoms (Q = -1, 0, +1 and n ≤ 13). Accurate total energies of these clusters are obtained and an excellent agreement is reached with available experimental results for adiabatic and vertical detachment energies. We also perform very accurate Hartree-Fock calculations in the complete-basis-set limit where electron correlation is absent. In combination with the FN-DMC and HF-CBS results, we quantify the correlation effects and present the first attempt for a systematic investigation on the electron correlation effects in boron clusters. The obtained results show that, in general, electron correlation may contribute significantly to both the atomic and electronic structures of the boron clusters, manifested in the quantities such as the average binding energies of the clusters, atomic dissociation energies, detachment energies, and ionization potentials. For instance, the calculations indicate that the electron correlation maintains the bound state of cationic cluster B₂⁺ and it also contributes 99% of the detachment energy of the anionic cluster B₅^-.

A perfect match between borophene and aluminium in the AlB3 heterostructure with covalent Al-B bonds, multiple Dirac points and a high Fermi velocity

By performing a swarm-intelligent global structure search combined with first-principles calculations, a stable two-dimensional (2D) AlB₃ heterostructure with directed, covalent Al–B bonds forms due to a nearly perfect lattice match between 2D borophene and the Al(111) surface. The AlB₃ heterosheet with the P6mm space group is composed of a planar Al(111) layer and a corrugated borophene layer, where the in-plane coordinates of Al covalently link with the corrugated B atoms. The resulting structure shows a similar interlayer interaction energy to that of the Al(111) surface layer to the bulk and high mechanical and thermal stability, possesses multiple Dirac points in the Brillouin zone with a remarkably high Fermi velocity of 1.09 × 10⁶ m s⁻¹, which is comparable to that of graphene. Detailed analysis of the electronic structure employing the electron localisation function and topological analysis of the electron density confirm the covalent Al–B bond with high electron localisation between the Al and B centres and with only little interatomic charge transfer. The combination of borophene with metal monolayers in 2D heterostructures opens the door to a rich chemistry with potentially unprecedented properties.

By performing a swarm-intelligent global structure search combined with first-principles calculations, a stable 2D AlB₃ heterostructure with directed, covalent Al–B bonds forms due to a nearly perfect lattice match between 2D borophene and the Al(111) surface.

Probing the Nature of the Transition-Metal-Boron Bonds and Novel Aromaticity in Small Metal-Doped Boron Clusters Using Photoelectron Spectroscopy

Photoelectron spectroscopy combined with quantum chemistry has been a powerful approach to elucidate the structures and bonding of size-selected boron clusters (B_n^-), revealing a prevalent planar world that laid the foundation for borophenes. Investigations of metal-doped boron clusters not only lead to novel structures but also provide important information about the metal-boron bonds that are critical to understanding the properties of boride materials. The current review focuses on recent advances in transition-metal-doped boron clusters, including the discoveries of metal-boron multiple bonds and metal-doped novel aromatic boron clusters. The study of the RhB^- and RhB₂O^- clusters led to the discovery of the first quadruple bond between boron and a transition-metal atom, whereas a metal-boron triple bond was found in ReB₂O^- and IrB₂O^-. The ReB₄^- cluster was shown to be the first metallaborocycle with Möbius aromaticity, and the planar ReB₆^- cluster was found to exhibit aromaticity analogous to metallabenzenes. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

Synthesis and structural properties of a 2D Zn(II) dodecahydroxy-closo-dodecaborate coordination polymer

In this work, we discuss the synthesis and characterization of a 2D coordination polymer composed of a dianionic perhydroxylated boron cluster, [B12(OH)12]2-, coordinated to Zn(II)—the first example of a transition...

Ground and Electronically Excited States of Main-Group-Metal-Doped B20 Double Rings

Ab initio coupled-cluster, electron propagator, and Møller-Plesset second-order perturbation theory calculations are utilized to analyze the low-lying electronic states of several metal-doped B₂₀. In the ground state, the presently focused AB₂₀/EB₂₀ (A = Li, Na, and K; E = Mg and Ca) consist of charge-separated A⁺B₂₀^-/E²⁺B₂₀^2- frameworks. The excited electronic states of AB₂₀ and EB₂₀⁺ were analyzed by computing the vertical electron attachment energies (VEAEs) of AB₂₀⁺ and EB₂₀²⁺. In several excited states, the radical electron is predominantly localized on the B₂₀ frames, which are counterparts of the low-lying states of bare B₂₀^-. A variety of basis sets were tested on obtaining VEAEs, and the aug-cc-pVDZ/_A,E d-aug-cc-pVDZ/_B combination provided the best accuracy-efficiency compromise on them. Furthermore, this work analyzes the Rydberg-like excited states of AB₂₀ and EB₂₀⁺ and will serve as a guide for future studies on similar metal-doped boron systems.

Predicting bilayer B50, B52, B56, and B58: structural evolution in bilayer B48-B72 clusters

The successive experimental observations of planar, cage-like, seashell-like, and bilayer B_n^-/0 clusters in the size range between n = 3-48 well demonstrate the structural diversity and rich chemistry of boron nanoclusters. Based on extensive global minimum search and density functional theory calculations, we predict herein the bilayer C₁ B₅₀ (I), C_2h B₅₂ (II), C₁ B₅₆ (IV), and C_2v B₅₈ (V) as the global minima of the systems to fill in the missing gap in the bilayer B_2n series between B₄₈-B₇₂. These highly stable species all contain a B₃₈ bilayer hexagonal prism at the center, with 2, 2, 3, and 3 effective interlayer B-B σ-bonds formed between inward-buckled atoms on the top and bottom layers, respectively. Our bilayer C₁ B₅₀ (I) and C₁ B₅₆ (IV) prove to be obviously more stable than the previously reported quasi-planar C_2v B₅₀ and C_2v B₅₆ with two adjacent B₆ hexagonal holes. Detailed bonding analyses indicate that these bilayer clusters follow the universal bonding pattern of σ + π double delocalization, making them three-dimensionally aromatic in nature. The bilayer B_2n species in the size range between B₄₈-B₇₂ evolve gradually on the waist around the B₃₈ or elongated B₄₆ bilayer hexagonal prism at the center.

Is Aromaticity a Driving Force in Catalytic Cycles? A Case from the Cycloisomerization of Enynes Catalyzed by All-Metal Aromatic Pd3+ Clusters and Carboxylic Acids

The work details a mechanistic study based on density functional theory modeling on the cycloisomerization of polyunsaturated substrates catalyzed by all-metal aromatic tripalladium complexes and carboxylic acids. These clusters are an emerging class of catalysts for a variety of relevant transformations, including C-C forming processes that occur under mild conditions and display synthetic features complementary to those of established mononuclear complexes. This study is the first computational one devoted to the comprehension of the series of elementary steps involved in a synthetic transformation catalyzed by an all-metal aromatic complex. Present results confirm previous experimental hints on the striking mechanistic differences exerted by these clusters with respect to the usual cyclization pathways of related substrates. Moreover, the catalytic cycle involving present all-metal aromatic clusters closely parallels the mechanism of the aromatic substitution of regular arenes.

Monovalent lanthanide(I) in borozene complexes

Lanthanide (Ln) elements are generally found in the oxidation state +II or +III, and a few examples of +IV and +V compounds have also been reported. In contrast, monovalent Ln(+I) complexes remain scarce. Here we combine photoelectron spectroscopy and theoretical calculations to study Ln-doped octa-boron clusters (LnB₈⁻, Ln = La, Pr, Tb, Tm, Yb) with the rare +I oxidation state. The global minimum of the LnB₈⁻ species changes from C_s to C_7v symmetry accompanied by an oxidation-state change from +III to +I from the early to late lanthanides. All the C_7v-LnB₈⁻ clusters can be viewed as a monovalent Ln(I) coordinated by a η⁸-B₈²⁻ doubly aromatic ligand. The B₇³⁻, B₈²⁻, and B₉⁻ series of aromatic boron clusters are analogous to the classical aromatic hydrocarbon molecules, C₅H₅⁻, C₆H₆, and C₇H₇⁺, respectively, with similar trends of size and charge state and they are named collectively as “borozenes”. Lanthanides with variable oxidation states and magnetic properties may be formed with different borozenes.

The most common oxidation state for lanthanides is +3. Here the authors use photoelectron spectroscopy and theoretical calculations to study half-sandwich complexes where a lanthanide center in the oxidation state +1 is bound to an aromatic wheel-like B₈^2- ligand.

Theoretical Design of Novel Boron-Based Nanowires via Inverse Sandwich Clusters

Borophene has important application value, boron nanomaterials doped with transition metal have wondrous structures and chemical bonding. However, little attention was paid to the boron nanowires (NWs). Inspired by the novel metal boron clusters Ln₂B_n⁻ (Ln = La, Pr, Tb, n = 7–9) adopting inverse sandwich configuration, we examined Sc₂B₈ and Y₂B₈ clusters in such novel structure and found that they are the global minima and show good stability. Thus, based on the novel structural moiety and first-principles calculations, we connected the inverse sandwich clusters into one-dimensional (1D) nanowires by sharing B−B bridges between adjacent clusters, and the 1D-Sc₄B₂₄ and 1D-Y₂B₁₂ were reached after structural relaxation. The two nanowires were identified to be stable in thermodynamical, dynamical and thermal aspects. Both nanowires are nonmagnetic, the 1D-Sc₄B₂₄ NW is a direct-bandgap semiconductor, while the 1D-Y₂B₁₂ NW shows metallic feature. Our theoretical results revealed that the inverse sandwich structure is the most energy-favored configuration for transition metal borides Sc₂B₈ and Y₂B₈, and the inverse sandwich motif can be extended to 1D nanowires, providing useful guidance for designing novel boron-based nanowires with diverse electronic properties.

OsB9 -: An Aromatic Osmium-Centered Monocyclic Boron Ring

Transition-metal-centered monocyclic boron wheels are important candidates in the family of planar hypercoordinate species that show intriguing structure, stability and bonding situation. Through the detailed potential energy surface explorations of MB₉⁻ (M = Fe, Ru, Os) clusters, we introduce herein OsB₉⁻ to be a new member in the transition-metal-centered borometallic molecular wheel gallery. Previously, FeB₉⁻ and RuB₉⁻ clusters were detected by photoelectron spectroscopy and the structures were reported to have singlet D_9h symmetry. Our present results show that the global minimum for FeB₉⁻ has a molecular wheel-like structure in triplet spin state with C_s symmetry, whereas its heavier homologues are singlet molecular wheels with D_9h symmetry. Chemical bonding analyses show that RuB₉⁻ and OsB₉⁻ display a similar type of electronic structure, where the dual σ + π aromaticity, originated from three delocalized σ bonds and three delocalized π bonds, accounts for highly stable borometallic molecular wheels.

Analysis of Local and Global Aromaticity in Si3C5 and Si4C8 Clusters. Aromatic Species Containing Planar Tetracoordinate Carbon

The minimum energy structures of the Si3C5 and Si4C8 clusters are planar and contain planar tetracoordinate carbons (ptCs). These species have been classified, qualitatively, as global (π) and local (σ) aromatics according to the adaptive natural density partitioning (AdNDP) method, which is an orbital localization method. This work evaluates these species’ aromaticity, focusing on confirming and quantifying their global and local aromatic character. For this purpose, we use an orbital localization method based on the partitioning of the molecular space according to the topology of the electronic localization function (LOC-ELF). In addition, the magnetically induced current density is analyzed. The LOC-ELF-based analysis coincides with the AdNDP study (double aromaticity, global, and local). Moreover, the current density analysis detects global and local ring currents. The strength of the global and local current circuit is significant, involving 4n + 2 π- and σ-electrons, respectively. The latter implicates the Si-ptC-Si fragment, which would be related to the 3c-2e σ-bond detected by the orbital localization methods in this fragment.

Effects of strain and electric fields on the electronic transport properties of single-layer β12-borophene nanoribbons

Motivated by recent experimental and theoretical research on a monolayer of boron atoms, borophene, the transmission probability and current-voltage characteristics of β₁₂-borophene nanoribbons (BNRs) with zigzag and armchair edges have been calculated using the five-band tight-binding calculation, the Green's function approach, and the Landauer-Büttiker formalism. We focus on the effects of the geometrical parameters, perpendicular electric field, and external strain on the electronic transport properties of β₁₂-BNRs by considering the effects of the substrate. Our calculations show that the transmission coefficient and current of the system decrease by increasing the channel length, whereas increasing ribbon width leads to an increment in the transmission probability as well as the I-V characteristic of β₁₂-BNRs. Besides, the application of tensile strain causes a decrement in the current of the inversion symmetric model of the armchair β₁₂-BNR, whereas the current increases in the presence of compressive strain. We also observed a dip in the transmission spectrum of the biased β₁₂-BNR along the armchair direction which shows a metal-to-n-doped semiconductor phase transition in the device when applying a strong enough electric field. Moreover, the current of the inversion symmetric model of the β₁₂-BNR with zigzag and armchair edges increases with the application of a perpendicular electric field, while in the case of the homogeneous model, the application of an electric field enhances the current of the β₁₂-BNR only in the zigzag direction. These results provide insights for future experimental research and show that β₁₂-BNRs are potential candidates for next-generation electronic devices.

Photoelectron Spectroscopy of Size-Selected Bismuth-Boron Clusters: BiBn- (n = 6-8)

Because of its low toxicity, bismuth is considered to be a "green metal" and has received increasing attention in chemistry and materials science. To understand the chemical bonding of bismuth, here we report a joint experimental and theoretical study on a series of bismuth-doped boron clusters, BiB_n^- (n = 6-8). Well-resolved photoelectron spectra are obtained and are used to understand the structures and bonding of BiB_n^- in conjunction with theoretical calculations. Global minimum searches find that all three BiB_n^- clusters have planar structures with the Bi atom bonded to the edge of the planar B_n moiety via two Bi-B σ bonds as well as π bonding by the 6p_z orbital. BiB₆^- is found to consist of a double-chain B₆ with a terminal Bi atom. Both BiB₇^- and BiB₈^- are composed of a Bi atom bonded to the planar global minima of the B₇^- and B₈^- clusters. Chemical bonding analyses reveal that BiB₆^- is doubly antiaromatic, whereas BiB₇^- and BiB₈^- are doubly aromatic. In the neutral BiB_n (n = 6-8) clusters, except BiB₆ which has a planar structure similar to the anion, the global minima of both BiB₇ and BiB₈ are found to be half-sandwich-type structures due to the high stability of the doubly aromatic B₇^3- and B₈^2- molecular wheel ligands.

Periodoannulenes: A Generalized Annulene-within-an-Annulene Paradigm for Combined σ and π Ring Currents

Periodoannulene molecules and ions C_xI_x^q in planar geometry offer examples of systems with the potential for outer σ and inner π ring-current double aromaticity, given a sufficient overlap of tangential p_σ-orbital manifolds on the large atoms of the outer cycle. Previous theoretical work indicated concentric diatropic currents in the dication C₆I₆²⁺. Ab initio ipsocentric calculations support an account in terms of frontier-orbital selection rules for current contributions in C₆I₆²⁺ (and radical C₆I₆⁺, implicated in recent experimental work on the oxidation of periodobenzene). A σ/π analogue of the annulene-within-an-annulene model is applied here to periodo systems based on cyclooctatetraene. Model species C₈I₈^q with charges q = 0, +1, +2, +4, -2 and structures constrained to a planar D_4h symmetry exhibit maps with all combinations of σ/π con- and counter-rotation, comprising global σ ring currents on the iodine perimeter and central π ring currents on the carbocycle. All can be rationalized by the separate application of the tropicity selection rules to the two subsystems, whether in singlet or triplet states.

Electronic Structure of Superoxidized Radical Cationic Dodecaborate-Based Clusters

The expanding field of boron clusters has attracted continuous theoretical efforts to understand their diverse structures and unique bonding. We recently discovered a new reversible redox event of B₁₂(O-3-methylbutyl)₁₂ in which the superoxidized radical cationic form [B₁₂(O-3-methylbutyl)₁₂]^•+ was identified and isolated for the first time. Herein, comprehensive (TD-)DFT studies in tandem with electrochemical experiments were employed to demonstrate the generality of the reported behavior across perfunctionalized B₁₂(OR)₁₂ clusters (R = aryl or alkyl). While the spin density of radical cationic clusters is delocalized in the core region, the oxidation brings about notable gains of positive partial charges on the supporting groups whose electronics can readily tune the redox potential of the 0/•+ couple. The underlying changes of frontier orbitals were elucidated, and the resulting [B₁₂(OR)₁₂]^•+ species manifest a general diagnostic absorption as a consequence of mixed local/charge-transfer excitations.

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

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

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.

Strong Binding of Noble Gases to [B12X11]-: A Theoretical Study

We systematically explore the stability and properties of [B₁₂X₁₁NG]^- adducts resulting from the binding of noble gas atoms to anionic [B₁₂X₁₁]^- clusters in the gas phase of mass spectrometers. [B₁₂X₁₁]^- can be obtained by stripping one X^- off the icosahedral closo-dodecaborate dianion [B₁₂X₁₂]^2-. We study the binding of the noble gas atoms He, Ne, Ar, Kr, and Xe to [B₁₂X₁₁]^- with substituents X = F, Cl, Br, I, and CN. While He cannot be captured by these clusters and Ne only binds at low temperatures, the complexes with the heavier noble gas atoms Ar, Kr, and Xe show appreciable complexation energies and exceed 1 eV at room temperature in the case of [B₁₂(CN)₁₁Xe]^-. The predicted B-NG equilibrium distance in the complexes with Ar, Kr, and Xe is only 0.10-0.25 Å longer than the sum of the covalent radii of the two corresponding atoms, and a significant charge transfer from the noble gas atom to the icosahedral B₁₂ cage is observed.

Double σ-Aromaticity in a Planar Zinc-Doped Gold Cluster: Au9Zn. J Phys Chem A 2021;125:4606-4613. [PMID: 34014680 DOI: 10.1021/acs.jpca.1c02954]

The strong relativistic effects result in many interesting chemical and physical properties for gold and gold compounds. One of the most surprising findings has been that small gold clusters prefer planar structures. Dopants can be used to tune the electronic and structural properties of gold nanoclusters. Here we report an experimental and theoretical investigation of a Zn-doped gold cluster, Au₉Zn^-. Photoelectron spectroscopy reveals that Au₉Zn^- is a highly stable electronic system with an electron binding energy of 4.27 eV. Quantum chemical studies show that the global minimum of Au₉Zn^- has a D_3h structure with a closed-shell electron configuration (¹A₁'), which can be viewed as replacing the central Au atom by Zn in the open-shell parent Au₁₀^- cluster. The high electronic stability of Au₉Zn^- is corroborated by its extremely large HOMO-LUMO gap of 3.3 eV. Chemical bonding analyses revealed that the D_3h Au₉Zn^- are bonded by two sets of delocalized σ bonds, giving rise to double σ aromaticity and its remarkable stability. Two planar low-lying isomers are also observed, corresponding to a similar triangular structure with the Zn atom on the edge and another one with one of the corner Au atoms moved to the edge of the triangle.

Transition-metal-like bonding behaviors of a boron atom in a boron-cluster boronyl complex [(η7-B7)-B-BO]. Chem Sci 2021;12:8157-8164. [PMID: 34194706 PMCID: PMC8208299 DOI: 10.1039/d1sc00534k]

Boron displays many unusual structural and bonding properties due to its electron deficiency. Here we show that a boron atom in a boron monoxide cluster (B₉O⁻) exhibits transition-metal-like properties. Temperature-dependent photoelectron spectroscopy provided evidence of the existence of two isomers for B₉O⁻: the main isomer has an adiabatic detachment energy (ADE) of 4.19 eV and a higher energy isomer with an ADE of 3.59 eV. The global minimum of B₉O⁻ is found surprisingly to be an umbrella-like structure (C_6v, ¹A₁) and its simulated spectrum agrees well with that of the main isomer observed. A low-lying isomer (C_s, ¹A′) consisting of a BO unit bonded to a disk-like B₈ cluster agrees well with the 3.59 eV ADE species. The unexpected umbrella-like global minimum of B₉O⁻ can be viewed as a central boron atom coordinated by a η⁷-B₇ ligand on one side and a BO ligand on the other side, [(η⁷-B₇)-B-BO]⁻. The central B atom is found to share its valence electrons with the B₇ unit to fulfill double aromaticity, similar to that in half-sandwich [(η⁷-B₇)-Zn-CO]⁻ or [(η⁷-B₇)-Fe(CO)₃]⁻ transition-metal complexes. The ability of boron to form a half-sandwich complex with an aromatic ligand, a prototypical property of transition metals, brings out new metallomimetic properties of boron.

The global minimum of the B₉O⁻ cluster is found to have an umbrella-like structure, where the central B atom exhibits transition-metal-like bonding properties, coordinated by a η⁷-B₇ ligand on one side and a BO ligand on the other.

Expanded Inverse-Sandwich Complexes of Lanthanum Borides: La2B10- and La2B11. J Phys Chem A 2021;125:2622-2630. [PMID: 33739102 DOI: 10.1021/acs.jpca.1c01149]

Inverse-sandwich structures have been observed recently for dilanthanide boride clusters, in which two Ln atoms sandwich a monocyclic B_x ring for x = 7-9. An interesting question is if larger B_x rings are possible to form such inverse-sandwich clusters. Here we address this question by investigating La₂B₁₀^- and La₂B₁₁^- using photoelectron spectroscopy and ab initio quantum chemical calculations. Photoelectron spectra of La₂B₁₀^- and La₂B₁₁^- show complicated, but well-resolved, spectral features that are used to compare with theoretical calculations. We have found that global minimum structures of the two clusters are based on the octa-boron ring. The global minimum of La₂B₁₀^- consists of two chiral enantiomers with C₁ symmetry, which can be viewed as adding a B₂ unit off-plane to the B₈ ring, whereas that of La₂B₁₁^- can be viewed as adding a B₃ unit in-plane to the B₈ ring in a second coordination shell. Chemical bonding analyses reveal localized B-B bonds on the edge of the clusters and delocalized bonds in the expanded boron frameworks. The interactions between the La atoms and the boron frameworks include the unique (d-p)δ bonding, which was found to be the key for inverse-sandwich complexes with monocyclic boron rings. The current study confirms that the largest monocyclic boron ring to form the inverse-sandwich structures is B₉ and provide insights into the structural evolutions of larger lanthanide boride clusters.

Spontaneous bond dissociation cascades induced by Ben clusters (n = 2,4)

High-level single and multireference ab initio calculations show that the Be₄ cluster behaves as a very efficient Lewis acid when interacting with conventional Lewis bases such as ammonia, water or hydrogen fluoride, to the point that the corresponding acid-base interaction triggers a sequential dissociation of all the bonds of the Lewis base. Notably, this behavior is already found for the simplest beryllium cluster, the Be₂ dimer. However, whereas for Be₂ the first dissociation process involves a low activation barrier which is above the reactants, for Be₄ all the bond dissociation processes involve barriers below the entrance channel leading to a cascade of successive exothermic processes, which end up spontaneously in a global minimum in which the bonding patterns of both the base and the Lewis acid are completely destroyed. Indeed, the global minimum, in all cases, is stabilized by three-center Be-H-Be bonds and covalent interactions between the Be atoms and the basic center of the base, which replace the initial metallic bond stabilizing the Be₄ cluster. As a consequence, in the global minimum the basic atoms (N, O and F) behave as hyper-coordinated centers. Also importantly, the Be₄ cluster and its complexes present RHF-UHF instabilities (not reported before for Be₄), which require the use of multireference methods to correctly describe them.

Application of Optimization Algorithms in Clusters

The structural characterization of clusters or nanoparticles is essential to rationalize their size and composition-dependent properties. As experiments alone could not provide complete picture of cluster structures, so independent theoretical investigations are needed to find out a detail description of the geometric arrangement and corresponding properties of the clusters. The potential energy surfaces (PES) are explored to find several minima with an ultimate goal of locating the global minima (GM) for the clusters. Optimization algorithms, such as genetic algorithm (GA), basin hopping method and its variants, self-consistent basin-to-deformed-basin mapping, heuristic algorithm combined with the surface and interior operators (HA-SIO), fast annealing evolutionary algorithm (FAEA), random tunneling algorithm (RTA), and dynamic lattice searching (DLS) have been developed to solve the geometrical isomers in pure elemental clusters. Various model or empirical potentials (EPs) as Lennard-Jones (LJ), Born-Mayer, Gupta, Sutton-Chen, and Murrell-Mottram potentials are used to describe the bonding in different type of clusters. Due to existence of a large number of homotops in nanoalloys, genetic algorithm, basin-hopping algorithm, modified adaptive immune optimization algorithm (AIOA), evolutionary algorithm (EA), kick method and Knowledge Led Master Code (KLMC) are also used. In this review the optimization algorithms, computational techniques and accuracy of results obtained by using these mechanisms for different types of clusters will be discussed.

B48-: a bilayer boron cluster

Size-selected negatively-charged boron clusters (B_n^-) have been found to be planar or quasi-planar in a wide size range. Even though cage structures emerged as the global minimum at B₃₉^-, the global minimum of B₄₀^- was in fact planar. Only in the neutral form did the B₄₀ borospherene become the global minimum. How the structures of larger boron clusters evolve is of immense interest. Here we report the observation of a bilayer B₄₈^- cluster using photoelectron spectroscopy and first-principles calculations. The photoelectron spectra of B₄₈^- exhibit two well-resolved features at low binding energies, which are used as electronic signatures to compare with theoretical calculations. Global minimum searches and theoretical calculations indicate that both the B₄₈^- anion and the B₄₈ neutral possess a bilayer-type structure with D_2h symmetry. The simulated spectrum of the D_2h B₄₈^- agrees well with the experimental spectral features, confirming the bilayer global minimum structure. The bilayer B₄₈^-/0 clusters are found to be highly stable with strong interlayer covalent bonding, revealing a new structural type for size-selected boron clusters. The current study shows the structural diversity of boron nanoclusters and provides experimental evidence for the viability of bilayer borophenes.

An unbiased confirmation of the participating isomers of C2B5- in the formation of its photo-detachment spectra: a theoretical study

The primary goal of the present article is to provide an unbiased structural confirmation of C2B5-, relying on its available experimental photo-detachment spectra. The study is performed from scratch by optimizing the lowest energy isomers of C2B5- and later, suitable molecular vibronic Hamiltonians are constructed by analyzing the normal modes of these optimized isomers. The Hamiltonians' parameters are evaluated from the fits of the calculated ab initio single point energies using a state of the art multireference configuration (MRCI) level of theory employing a correlation consistent polarized triple zeta (cc-pVTZ) basis set. The state-averaged variant of the MRCI level of theory is also applied to deal with the highly interactive electronic states of both of the isomers. A detailed analysis of the potential energy curves along the totally symmetric vibrational modes is performed to understand the energy modulation between the different electronic states and also to find the energetic locations of the conical intersections. The introduction of the non-symmetric vibrational modes in the Hamiltonians help to understand the impact of non-adiabaticity during energy modulation in the coupled surfaces. Later, both adiabatic and non-adiabatic nuclear dynamics are performed on the electronic states of both of the isomers using the constructed reduced and full-dimensional Hamiltonians. The results of the adiabatic dynamics are used to assign the positions of the simulated photo-detachment bands, while the non-adiabatic dynamics improve the shape of those bands. Finally, we compare our theoretical findings with the available experimental photo-detachment spectra of C2B5- to provide an unbiased structural confirmation of the participating isomers of C2B5- in its photo-detachment spectra.

Diffusion Monte Carlo method on small boron clusters using single- and multi- determinant-Jastrow trial wavefunctions

Multireference character in some small boron clusters could be significant, and a previous all-electron fixed-node diffusion quantum Monte Carlo (FN-DMC) calculation with the single-determinant-Jastrow (SDJ) trial wavefunction shows that the atomization energy (AE) of B₄ ⁺ is overestimated by about 1.4 eV compared with the coupled cluster method with single, doubles, and perturbative triples [CCSD(T)] results. All-electron FN-DMC calculations and those with the pseudopotential (PP) using SDJ and multi-determinant-Jastrow (MDJ) trial wavefunctions with B3LYP orbitals as well as CC calculations at different levels are carried out on B_n ^Q (n = 1-5, Q = -1, 0, 1) clusters. The obtained FN-DMC energies indicate that the node error of the employed SDJ trial wavefunction in all-electron calculations is different from that with the PP for some clusters. The error of AEs and dissociation energies (DEs) from all-electron FN-DMC calculations is larger than that with the PP when the SDJ trial wavefunction is employed, while errors of CC methods do not depend on whether the PP is used. AEs and DEs of the boron clusters are improved significantly when MDJ trial wavefunctions are used in both all-electron calculations and those with the PP, and their error is similar to that of CCSD(T) compared with CCSDT(Q) results. On the other hand, reasonable adiabatic electron detachment energies (ADEs) and ionization potentials (AIPs) are achieved with FN-DMC using SDJ trial wavefunctions and MDJ is less effective on ADEs and AIPs. Furthermore, the relative energy between two structures of B₉ ^- is predicted reliably with FN-DMC using the SDJ trial wavefunction and the effect of MDJ is negligible, while density functional theory results using different exchange-correlation functionals differ significantly.

Structures and Properties of CoB19 +/0/- Clusters

A global search for the lowest energy structure of Co atom-doped boron clusters (CoB19 +, CoB19, and CoB19 - clusters) was conducted. The lowest energy structures of them are remarkably different from those of B20 and CoB18 - clusters. CoB19 + clusters have a bowl-shaped geometry, where the Co atom is at the bottom of the bowl and is coordinated with eight B atoms. The CoB19 cluster presents seven- and eight-membered B rings. The CoB19 - cluster can be viewed as a structure that evolves from a Co-doped boron plane. The coordination number of CoB19 and CoB19 - clusters are 16 and 14, respectively. Several low-lying isomers have quasi-planar structures for the CoB19 - cluster. Some properties including charge transformation and distribution, HOMO-LUMO gaps, molecular orbital distribution, and stability of neutral CoB19 are discussed. CoB19 + and CoB19 - exhibit magnetism with a net moment of 1.0 and 0.94 μB because of odd number of electrons.

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.

Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be6B11- Flux-Ional Cluster

The starting point to understanding cluster properties is the putative global minimum and all the nearby local energy minima; however, locating them is computationally expensive and difficult. The relative populations and spectroscopic properties that are a function of temperature can be approximately computed by employing statistical thermodynamics. Here, we investigate entropy-driven isomers distribution on Be₆B₁₁⁻ clusters and the effect of temperature on their infrared spectroscopy and relative populations. We identify the vibration modes possessed by the cluster that significantly contribute to the zero-point energy. A couple of steps are considered for computing the temperature-dependent relative population: First, using a genetic algorithm coupled to density functional theory, we performed an extensive and systematic exploration of the potential/free energy surface of Be₆B₁₁⁻ clusters to locate the putative global minimum and elucidate the low-energy structures. Second, the relative populations’ temperature effects are determined by considering the thermodynamic properties and Boltzmann factors. The temperature-dependent relative populations show that the entropies and temperature are essential for determining the global minimum. We compute the temperature-dependent total infrared spectra employing the Boltzmann factor weighted sums of each isomer’s infrared spectrum and find that at finite temperature, the total infrared spectrum is composed of an admixture of infrared spectra that corresponds to the spectra of the lowest-energy structure and its isomers located at higher energies. The methodology and results describe the thermal effects in the relative population and the infrared spectra.

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.