Comprehensive analysis of chemical bonding in boron clusters

Fluxional Behavior and Stability of the Cu2B8- Cluster: A Copper Borozene with a Freely Rotating Cu2 Dimer

We demonstrate that Cu2B8- exhibits distinct fluxional behavior, akin to that of a functional stirrer, with the Cu2 dimer freely rotating on the B8 molecular wheel. This behavior is confirmed by Born-Oppenheimer molecular dynamics simulations. The initiation of this dynamic motion is facilitated by an ultrasoft vibrational mode (less than 10 cm-1), resulting in a negligible rotational barrier of 0.03 kcal/mol, as calculated at the single-point CCSD(T) level. The high stability of Cu2B8- arises from the strong interlayer electrostatic interaction between Cu2 and B8, due to charge transfer from Cu2 to B8, along with additional covalent interactions from the delocalized π electrons of the B8 wheel to the Cu2 dimer. Notably, the Cu2 dimer in Cu2B8- features a two-center one-electron Cu-Cu single bond, while the B82- moiety displays double aromaticity, characterized by the presence of six delocalized π electrons and six delocalized σ electrons.

Exploring hydrophobicity or hydrophilicity of borophene surface via reactive molecular dynamics simulation

Borophene, a novel two-dimensional material unveiled in 1998, has garnered significant interest among researchers due to its distinct mechanical and electrical characteristics. Efforts to experimentally synthesize borophene continue to captivate researchers' interest in recent years. Given the current lack of experimental studies on the interaction between water and the borophene surface, molecular dynamics simulation offers a valuable approach for predicting the substance's reactivity with water. Additionally, such simulations can assess the hydrophilicity and hydrophobicity of borophene, providing valuable insights into its properties. In our current research, we utilized reactive molecular dynamics simulation to investigate the wetting behavior of borophene. Our findings reveal that the borophene surface exhibits hydrophobic characteristics, demonstrating anisotropic wettability. Specifically, the water contact angle was calculated to be 149.11° along the zigzag direction and 148.4° along the armchair direction. The contour map of the interaction energy between a water molecule and the borophene surface revealed a notable energy barrier in the zigzag direction. This barrier contributes to the asymmetric spreading of the water droplet on the surface. Density profiles and radial pair distribution function (RDF) diagrams of the water droplet on the borophene surface further corroborated the hydrophobic nature of borophene by indicating a significant distance between the water droplet and the surface. Moreover, analysis of the number of hydrogen bonds demonstrated that borophene efficiently utilizes nearly all its capacity to form hydrogen bonds. Additionally, we compared the wettability of borophene with that of other two-dimensional materials, such as various graphene allotropes and phosphorene, which have been subjects of recent investigation.

Searching for stable copper borozene complexes in CuB7- and CuB8. Phys Chem Chem Phys 2024;26:12928-12938. [PMID: 38456623 DOI: 10.1039/d4cp00296b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Copper has been shown to be an important substrate for the growth of borophenes. Copper-boron binary clusters are ideal platforms to study the interactions between copper and boron, which may provide insight about the underlying growth mechanisms of borophene on copper substrates. Here we report a joint photoelectron spectroscopy and theoretical study on two copper-doped boron clusters, CuB7- and CuB8-. Well resolved photoelectron spectra are obtained for the two clusters at different wavelengths and are used to understand the structures and bonding properties of the two CuBn- clusters. We find that CuB8- is a highly stable borozene complex, which possesses a half-sandwich structure with a Cu+ species interacting with the doubly aromatic η8-B82- borozene. The CuB7- cluster is found to consist of a terminal copper atom bonded to a double-chain B7 motif, but it has a low-lying isomer composed of a half-sandwich structure with a Cu+ species interacting with an open-shell η7-B72- borozene. Both ionic and covalent interactions are found to be possible in the binary Cu-B clusters, resulting in different structures.

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.

Size effects and electronic properties of zinc-doped boron clusters Zn B n (n = 1-15)

CONTEXT

To gain a deeper understanding of zinc-doped boron clusters, theoretical calculations were performed to investigate the size effects and electronic properties of zinc-doped boron clusters. The study of the electronic properties, spectral characteristics, and geometric structures of Zn B n (n = 1-15) is of great significance in the fields of semiconductor materials science, material detection, and improving catalytic efficiency. The results indicate that Zn B n (n = 1-15) clusters predominantly exhibit planar or quasi-planar structures, with the Zn atom positioned in the outer regions of the B n framework. The second stable structure of Zn B 3 is a three-dimensional configuration, indicating that the structures of zinc-doped boron clusters begin to convert from the planar or quasi-planar structures to the 3D configurations. The second low-energy structure of Zn B 15 is a novel configuration. Relative stability analyses show that the Zn B 12 has better chemical stability than other clusters with a HOMO-LUMO gap of 2.79 eV. Electric charge analysis shows that part electrons on zinc atoms are transferred to boron atoms, and electrons prefer to cluster near the B n framework. According to the electron localization function, it gets harder to localize electrons as the equivalent face value drops, and it's challenging to see covalent bond formation between zinc and boron atoms. The spectrograms of Zn B n (n = 1-15) exhibit distinct properties and notable spectral features, which can be used as a theoretical basis for the identification and confirmation of boron clusters doped with single-atom transition metals.

METHODS

The calculations were performed using the ABCluster global search technique combined with density functional theory (DFT) methods. The selected low-energy structures were subjected to geometric optimization and frequency calculations at the PBE0/6-311 + G(d) level to ensure structural stability and eliminate any imaginary frequencies. To acquire more precise relative energies, we performed single-point energies calculations for the low-lying isomers of Zn B n (n = 1-15) at the CCSD(T)/6-311 + G(d)//PBE0/6-311 + G(d) level of theory. All calculations were performed using Gaussian 09 software. To facilitate analysis, we utilized software tools such as Multiwfn, and VMD.

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.

Investigation of Pb-B Bonding in PbB2(BO)n- (n = 0-2): Transformation from Aromatic PbB2- to Pb[B2(BO)2]-/0 Complexes with BB Triple Bonds

Boron has been found to be able to form multiple bonds with lead. To probe Pb-B bonding, here we report an investigation of three Pb-doped boron clusters, PbB2-, PbB3O-, and PbB4O2-, which are produced by a laser ablation cluster source and characterized by photoelectron spectroscopy and ab initio calculations. The most stable structures of PbB2-, PbB3O-, and PbB4O2- are found to follow the formula, [PbB2(BO)n]- (n = 0-2), with zero, one, and two boronyl ligands coordinated to a triangular and aromatic PbB2 core, respectively. The PbB2- cluster contains a BB double bond and two Pb-B single bonds. The coordination of BO is observed to weaken Pb-B bonding but strengthen the BB bond in [PbB2(BO)n]- (n = 1, 2). The anionic [PbB2(BO)2]- and its corresponding neutral closed-shell [PbB2(BO)2] contain a BB triple bond. A low-lying Y-shaped isomer is also observed for PbB4O2-, consisting of a central sp2 hybridized B atom bonded to two boronyl ligands and a PbB unit.

Self-Termination of Borophene Edges

Due to boron's unique bonding nature, planar boron materials, including borophenes, boron nanoclusters, and nanoribbons, show very puzzling features, especially the superior stability of the free-standing planar boron edges. Here, we present a systematic investigation of the bonding configurations of various edges of borophene. Because of the flexibility of forming either three-center two-electron (3c-2e) or two-center two-electron bonds (2c-2e), an edge of borophene tends to be self-terminated by adopting a different bonding configuration at the edge from that in bulk. Among various borophene edge types, the double-chain-terminated flat edge is found to be significantly stable. As a consequence, we found that the double- and triple-chain borophene nanoribbons with a triangular lattice and wider ribbons with hexagonal holes in the central area are more stable than the quadruple-chain borophene nanoribbon. This study greatly deepens our understanding of the bonding configurations, electronic properties, and stabilities of planar boron nanostructures and paves the way for the rational design and synthesis of various boron materials.

Boron-based Pd3B26 alloy cluster as a nanoscale antifriction bearing system: tubular core-shell structure, double π/σ aromaticity, and dynamic structural fluxionality

Boron-based nanoclusters show unique geometric structures, nonclassical chemical bonding, and dynamic structural fluxionality. We report here on the theoretical prediction of a binary Pd3B26 cluster, which is composed of a triangular Pd3 core and a tubular double-ring B26 unit in a coaxial fashion, as identified through global structural searches and electronic structure calculations. Molecular dynamics simulations indicate that in the core-shell alloy cluster, the B26 double-ring unit can rotate freely around its Pd3 core at room temperature and beyond. The intramolecular rotation is virtually barrier free, thus giving rise to an antifriction bearing system (or ball bearing) at the nanoscale. The dimension of the dynamic system is only 0.66 nm. Chemical bonding analysis reveals that Pd3B26 cluster possesses double 14π/14σ aromaticity, following the (4n + 2) Hückel rule. Among 54 pairs of valence electrons in the cluster, the overwhelming majority are spatially isolated from each other and situated on either the B26 tube or the Pd3 core. Only one pair of electrons are primarily responsible for chemical bonding between the tube and the core, which greatly weaken the bonding within the Pd3 core and offers structural flexibility. This is a key mechanism that effectively diminishes the intramolecular rotation barrier and facilitates dynamic structural fluxionality of the system. The current work enriches the field of nanorotors and nanomachines.

Electron-Precise Dicationic Tetraboranes: Syntheses, Structures and Rearrangement to an Alkylidene Borate-Borenium Zwitterion and a 1,3-Azaborinine

Carbene-stabilized symmetrical and unsymmetrical dicationic tetraboranes, featuring an electron-precise tetraborane chain, were synthesized and fully characterized. Reactions of these tetraboranes with reductants/bases give rise to different outcomes according to the conditions employed, including: 1) reduction and rearrangement of the tetraborane chain to give a zwitterionic alkylidene borate-borenium species; 2) cleavage of the tetraborane chain to afford a 1,3-azaborinine; and 3) reduction of the supporting ligands to provide a diamino dipotassium salt. The zwitterionic alkylidene borate-borenium species can be viewed as an analogue of the base-stabilized diborenes. NMR spectroscopy and DFT calculations reveal a highly polarized B-B bond in the zwitterionic alkylidene borate-borenium, in which the formal oxidation states of the boron atoms can be considered as -1 and +2. These results suggest the considerable potential of tetraboranes as synthons for low-valent boron species.

Boron-Based Inverse Sandwich V2B7- Cluster: Double π/σ Aromaticity, Metal-Metal Bonding, and Chemical Analogy to Planar Hypercoordinate Molecular Wheels

Inverse sandwich clusters composed of a monocyclic boron ring and two capping transition metal atoms are interesting alloy cluster systems, yet their chemical bonding nature has not been sufficiently elucidated to date. We report herein on the theoretical prediction of a new example of boron-based inverse sandwich alloy clusters, V₂B₇^-, through computational global-minimum structure searches and quantum chemical calculations. This alloy cluster has a heptatomic boron ring as well as a perpendicular V₂ dimer unit that penetrates through the ring. Chemical bonding analysis suggests that the inverse sandwich cluster is governed by globally delocalized 6π and 6σ frameworks, that is, double 6π/6σ aromaticity following the (4n + 2) Hückel rule. The skeleton B-B σ bonding in the cluster is shown not to be strictly Lewis-type two-center two-electron (2c-2e) σ bonds. Rather, these are quasi-Lewis-type, roof-like 4c-2e V-B₂-V σ bonds, which amount to seven in total and cover the whole surface of inverse sandwich in a truly three-dimensional manner. Theoretical evidence is revealed for a 2c-2e Lewis σ single bond within the V₂ dimer. Direct metal-metal bonding is scarce in inverse sandwich alloy clusters. The present inverse sandwich alloy cluster also offers a new type of electronic transmutation in physical chemistry, which helps establish an intriguing chemical analogy between inverse sandwich clusters and planar hypercoordinate molecular wheels.

Theory of sigma bond resonance in flat boron materials

In chemistry, theory of aromaticity or π bond resonance plays a central role in intuitively understanding the stability and properties of organic molecules. Here we present an analogue theory for σ bond resonance in flat boron materials, which allows us to determine the distribution of two-center two-electron and three-center two-electron bonds without quantum calculations. Based on this theory, three rules are proposed to draw the Kekulé-like bonding configurations for flat boron materials and to explore their properties intuitively. As an application of the theory, a simple explanation of why neutral borophene with ~1/9 hole has the highest stability and the effect of charge doping on borophene's optimal hole concentration is provided with the assumption of σ and π orbital occupation balance. Like the aromaticity theory for carbon materials, this theory greatly deepens our understanding on boron materials and paves the way for the rational design of various boron-based materials.

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.

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

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

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

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

Understanding of the Photodetachment Spectrum of Anionic Mixed Carbon-Boron Cluster C3B5- Following Adiabatic and Nonadiabatic Quantum Chemistry Approaches

The presence of nonadiabaticity in the photodetachment bands of the anionic mixed carbon-boron cluster C₃B₅^- has been realized through ab initio electronic structure calculations and detailed analyses of quantum dynamics study on top of those electronic structures. In the course of our study, we traverse extensive first principles electronic structure calculations to compute potential energy curves and to trace the energetic locations for the conical intersections in the multidimensional surfaces. All the ab initio calculations are performed on the four low-lying electronic states of the C₃B₅ cluster, while quantum nuclear dynamics are pursued on those electronic states by applying both time-dependent and time-independent quantum chemistry frameworks. In particular, we rely on the diabatic electronic representation to construct the molecular Hamiltonian. Altogether, the simulated theoretical spectra offer exceptional agreement with the experimental attainments.

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

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

σ-Aromaticity in planar pentacoordinate aluminium and gallium clusters

Planar hypercoordinate structures are gaining immense attention due to the shift from common paradigm. Herein, our high level ab initio calculations predict that planar pentacoordinate aluminium and gallium centres in Cu5Al2+ and Cu5Ga2+ clusters are global minima in their singlet ground states. These clusters are thermodynamically and kinetically very stable. Detailed electronic structure analyses reveal the presence of σ-aromaticity which is the driving force for the stability of the planar form.

Structures and chemical bonding of boron-based B12O and B11Au clusters. A counterexample in boronyl chemistry

Boron oxide clusters have structural diversity and unique chemical bonding, and recent literature has shown that boronyl complexes dominate boron-rich oxide clusters. A counterexample in boronyl chemistry is presented in this work. Using global structural searches, electronic structure calculations, and chemical bonding analyses, we shall report on the computational design of two boron-based quasi-planar or planar clusters: B₁₂O and B₁₁Au. Contrary to expectation, the B₁₂O cluster has a circular quasi-planar shape with a peripheral B-O-B bridge, which resembles bare B₁₂ cluster. It does not contain a boronyl ligand. The isomeric boronyl complex turns out to be 10.32 kcal mol^-1 higher in energy at the single-point CCSD(T) level. In contrast, B₁₁Au cluster behaves normally with an elongated B₁₁ moiety and a terminal Au ligand. Chemical bonding analyses reveal three-fold π/σ aromaticity in circular B₁₂O cluster, including global 6π aromaticity, as well as spatially isolated inner 2σ aromaticity and outer 10σ aromaticity. The three-fold 6π/2σ/10σ aromaticity underlies the stability of B₁₂O cluster. This bonding picture is unknown for bare B₁₂ cluster and its derivatives. The elongated B₁₁Au cluster has conflicting π/σ aromaticity (with 6π versus 8σ electron-counting). The B₁₂O cluster is actually isoelectronic with bare B₁₂ cluster in terms of delocalized π/σ bonding, which inherits the structural and electronic robustness of the latter.

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.

Spatial and electronic structures of BeB8 and MgB8. How far the analogy goes?

Doping of boron clusters with Be and its heavier alkaline-earth congener, Mg usually leads to complexes of different geometry and electronic structure. In this work we showed that both neutral BeB 8 and MgB 8 exhibit a singlet ground state umbrella-like form. In addition, the stability, electronic structure, and aromaticity of the target molecules were compared. The magnetically induced current densities showed that BeB 8 and MgB 8 are double aromatic systems: π and σ electrons induce strong diatropic currents. The current densities induced in the studied complexes are of very similar intensity, but with a different spatial distribution. The found differences between the current density patterns in BeB 8 and MgB 8 arise from the very nature of the bonding interactions between the M atom and B 8 fragment, as demonstrated through the energy decomposition analysis (EDA).

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^-.

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.

The smallest 4f-metalla-aromatic molecule of cyclo-PrB2− with Pr–B multiple bonds

The concept of metalla-aromaticity proposed by Thorn–Hoffmann (Nouv. J. Chim. 1979, 3, 39) has been expanded to organometallic molecules of transition metals that have more than one independent electron-delocalized system. Lanthanides, with highly contracted 4f atomic orbitals, are rarely found in multiply aromatic systems. Here we report the discovery of a doubly aromatic triatomic lanthanide-boron molecule PrB₂⁻ based on a joint photoelectron spectroscopy and quantum chemical investigation. Global minimum structural searches reveal that PrB₂⁻ has a C_2v triangular structure with a paramagnetic triplet ³B₂ electronic ground state, which can be viewed as featuring a trivalent Pr(III,f²) and B₂⁴⁻. Chemical bonding analyses show that this cyclo-PrB₂⁻ species is the smallest 4f-metalla-aromatic system exhibiting σ and π double aromaticity and multiple Pr–B bonding characters. It also sheds light on the formation of the rare B₂⁴⁻ tetraanion by the high-lying 5d orbitals of the 4f-elements, completing the isoelectronic B₂⁴⁻, C₂²⁻, N₂, and O₂²⁺ series.

We report the smallest 4f-metalla-aromatic molecule of PrB₂⁻ exhibiting σ and π double aromaticity and multiple Pr–B bond characters.

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.

Observation of Aromatic Three-Membered Rings in Ge3C and Ge3O via Photoelectron Spectroscopy and Theoretical Calculations

The structures and chemical bonding of Ge₃C^- and Ge₃O^- as well as their neutrals are explored with anion photoelectron spectroscopy and theoretical calculations. The vertical detachment energies of Ge₃C^- and Ge₃O^- are measured to be 1.51 ± 0.04 and 2.00 ± 0.04 eV, respectively. It is found that Ge₃C^-/0 have a C_2v symmetric planar structure with the C atom interacting with three Ge atoms. Ge₃O^-/0 have the O atom interacting with two Ge atoms of the triangular Ge₃ unit. Ge₃O^- has a C_s symmetric nonplanar structure, while Ge₃O has a C_2v symmetric planar structure. Theoretical results show that the multiconfigurational effects in Ge₃C^-/0 and Ge₃O^-/0 are insignificant. Chemical bonding analyses reveal that there exist the C-Ge₃ π_⊥ orbital interaction and two π aromatic Ge₂C units in Ge₃C. There are O-Ge₃ π_⊥ orbital interaction and one doubly aromatic Ge₃ unit in Ge₃O, but the π_⊥ orbital interaction is relatively weak.

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.

Structure, stability and bonding of the leapfrog B24 0 ,±1,±2

Two new structural motifs of the B₂₄ clusters are constructed by use of the leapfrog transformation. The resulting leapfrog B₂₄ has either a bowl shape with a square vacancy or a quasi-planar 2D close-packed triangular boron sheet. The neutral and ionic forms of the latter are found to be more stable than their homologous leapfrog bowl clusters, with the exception of the dicationic B₂₄ ⁺² . While the leapfrog isomer is less stable than the tubular double ring in the neutral state, it becomes competitive in some ionic states. The nucleus independent chemical shift, electron localization function, ring current maps and the electronic structure of leapfrog B₂₄ clusters reveal them to behave as aromatics.

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.

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

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

The Na⋅⋅⋅B Bond in NaBH3 - : A Different Type of Bond

A newly introduced Na-B bond in NaBH₃ ^- has been a challenge for the chemical bonding community. Here, a series of MBH₃ ^- (M=Li, Na, K) species and NaB(CN)₃ ^- are studied within the context of quantum chemical topology approaches. The analyses suggest that M-B interaction cannot be classified as an ordinary covalent, dative, or even simple ionic interaction. The interactions are controlled by coulombic forces between the metals and the substituents on boron, for example, H or CN, more than the direct M-B interaction. On the other hand, while the characteristics of the (3, -1) critical points of the bonds are comparable to weak hydrogen bonds, not covalent bonds, the metal and boron share a substantial sum of electrons. To the best of the author's knowledge, the characteristics of these bonds are unprecedented among known molecules. Considering all paradoxical properties of these bonds, they are herein described as ionic-enforced covalent bonds.

Searching new structures of beryllium-doped in small-sized magnesium clusters: Be2 Mgn Q (Q = 0, -1; n = 1-11) clusters DFT study

Using CALYPSO method to search new structures of neutral and anionic beryllium-doped magnesium clusters followed by density functional theory (DFT) calculations, an extensive study of the structures, electronic and spectral properties of Be₂ Mg_n ^Q (Q = 0, -1; n = 2-11) clusters is performed. Based on the structural optimization, it is found that the Be₂ Mg_n ^Q (Q = 0, -1) clusters are shown by tetrahedral-based geometries at n = 2-6 and tower-like-based geometries at n = 7-11. The calculations of stability indicate that Be₂ Mg₅ ^Q=0 , Be₂ Mg₅ ^Q=-1 , and Be₂ Mg₈ ^Q=-1 clusters are "magic" clusters with high stability. The NCP shows that the charges are transferred from Mg atoms to Be atoms. The s- and p-orbitals interactions of Mg and Be atoms are main responsible for their NEC. In particular, chemical bond analysis including molecular orbitals (MOs) and chemical bonding composition for magic clusters to further study their stability. The results confirmed that the high stability of these clusters is due to the interactions between the Be atom and the Mg₅ or Mg₈ host. Finally, theoretical calculations of infrared and Raman spectra of the ground state of Be₂ Mg_n ^Q (Q = 0, -1; n = 1-11) clusters were performed, which will be absolutely useful for future experiments to identify these clusters.

The teetotum cluster Li2FeB14 and its possible use for constructing boron nanowires

Systematic density functional theory (DFT) calculations using the TPSSh functional and the def2-TZVP basis set were carried out to identify the global energy minimum structure of the Li2FeB14 cluster. Keeping the double ring tubular shape of FeB14, capping of two Li atoms leads to a teetotum form at a low spin state, in which the Fe atom is endohedrally covered by two B7 strings, and both Li atoms are attached to Fe along the C7 axis at both sides. Calculated results show that strong electrostatic interactions between 2Li+ and Fe2- arising from Li electron transfer upon doping particularly provide a key driving force for stabilizing this charge-transfer structure. The bonding pattern of the teetotum can be understood from the hollow cylinder model (HCM). TD-DFT calculations demonstrate that this cluster can also be regarded as a useful material for transparent optoelectronic devices. Furthermore, the Li2FeB14 superatom can be used as a building block for making boron-based nanowires with metallic character. Replacement of Li atoms by Mg atoms was also found to lead to nanowires.