Lithium doped tubular structure in LiB20 and LiB20-: a viable global minimum

Structural Evolution of Small-Sized Phosphorus-Doped Boron Clusters: A Half-Sandwich-Structured PB15 Cluster

The present study is a theoretical investigation into the structural evolution, electronic properties, and photoelectron spectra of phosphorus-doped boron clusters PBn0/- (n = 3-17). The results of this study revealed that the lowest energy structures of PBn- (n = 3-17) clusters, except for PB17-, exhibit planar or quasi-planar structures. The lowest energy structures of PBn (n = 3-17), with the exceptions of PB7, PB9, and PB15, are planar or quasi-planar. The ground state of PB7 has an umbrella-shaped structure, with C6V symmetry. Interestingly, the neutral cluster PB15 has a half-sandwich-like structure, in which the P atom is attached to three B atoms at one end of the sandwich, exhibiting excellent relative and chemical stability due to its higher second-order energy difference and larger HOMO-LUMO energy gap of 4.31 eV. Subsequently, adaptive natural density partitioning (AdNDP) and electron localization function (ELF) analyses demonstrate the bonding characteristics of PB7 and PB15, providing support for the validity of their stability. The calculated photoelectron spectra show distinct characteristic peaks of PBn- (n = 3-17) clusters, thus providing theoretical evidence for the future identification of doped boron clusters. In summary, our work has significant implications for understanding the structural evolution of doped boron clusters PBn0/- (n = 3-17), motivating further experiments regarding doped boron clusters.

Transition Metal Behavior of Heavier Alkaline Earth Elements in Doped Monocyclic and Tubular Boron Clusters

Quantum chemical calculations are carried out to design highly symmetric-doped boron clusters by employing the transition metal behavior of heavier alkaline earth (Ae = Ca, Sr, and Ba) metals. Following an electron counting rule, a set of monocyclic and tubular boron clusters capped by two heavier Ae metals were tested, which leads to the highly symmetric Ae2B8, Ae2B18, and Ae2B30 clusters as true minima on the potential energy surface having a monocyclic ring, two-ring tubular, and three-ring tubular boron motifs, respectively. Then, a thorough global minimum (GM) structural search reveals that a monocyclic B8 ring capped with two Ae atoms is indeed a GM for Ca2B8 and Ba2B8, while for Sr2B8 it is a low-lying isomer. Similarly, the present search also unambiguously shows the most stable isomers of Ae2B18 and Ae2B30 to be highly symmetric two- and three-ring tubular boron motifs, respectively, capped with two Ae atoms on each side of the tube. In these Ae-doped boron clusters, in addition to the electrostatic interactions, a substantial covalent interaction, specifically the bonding occurring between (n - 1)d orbitals of Ae and delocalized orbitals of boron motifs, provides the essential driving force behind their highly symmetrical structures and overall stability.

PB12+ and P2B12+/0/-: The Novel B12 Cage Doped by Nonmetallic P Atoms

A new kind of nonmetallic atom-doped boron cluster is described herein theoretically. When a phosphorus atom is added to the B12 motif and loses an electron, a novel B12 cage is obtained, composed of two B3 rings at both ends and one B6 ring in the middle, forming a triangular bifrustum. Interestingly, this B12 cage is formed by three B7 units joined together from three directions at an angle of 120°. When two P atoms are added to the B12 motif, this novel B12 cage is also obtained, and two P atoms are attached to the B3 rings at both ends of the triangular bifrustum, forming a triangular bipyramid (Johnson solid). Amazingly, the global minimums of neutral, monocationic, and monoanionic P2B12+/0/- have the same cage structure with a D3h symmetry; this is the smallest boron cage with the same structure. The P atom has five valence electrons, according to adaptive natural density partitioning bonding analyses of cage PB12+ and P2B12, in addition to one lone pair, the other three electrons of the P atom combine with an electron of each B atom on the B3 ring to form three 2c-2e σ bonds and form three electron sharing bonds with B atoms through covalent interactions, stabilizing the B12 cage. The calculated photoelectron spectra can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of PnB12- (n = 1-2).

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.

Structural Evolution and Electronic Properties of Two Sulfur Atom-Doped Boron Clusters

We present a theoretical study of structural evolution, electronic properties, and photoelectron spectra of two sulfur atom-doped boron clusters S2Bn0/- (n = 2-13), which reveal that the global minima of the S2Bn0/- (n = 2-13) clusters show an evolution from a linear-chain structure to a planar or quasi-planar structure. Some S-doped boron clusters have the skeleton of corresponding pure boron clusters; however, the addition of two sulfur atoms modified and improved some of the pure boron cluster structures. Boron is electron-deficient and boron clusters do not form linear chains. Here, two sulfur atom doping can adjust the pure boron clusters to a linear-chain structure (S2B20/-, S2B30/-, and S2B4-), a quasi-linear-chain structure (S2B6-), single- and double-chain structures (S2B6 and S2B9-), and double-chain structures (S2B5, and S2B9). In particular, the smallest linear-chain boron clusters S2B20/- are shown with an S atom attached to each end of B2. The S2B2 cluster possesses the largest highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap of 5.57 eV and the S2B2- cluster possesses the largest average binding energy Eb of 5.63 eV, which shows the superior chemical stability and relative stability, respectively. Interestingly, two S-atom doping can adjust the quasi-planar pure boron clusters (B7-, B10-, and B120/-) to a perfect planar structure. AdNDP bonding analyses reveal that linear S2B3 and planar SeB11- have π aromaticity and σ antiaromaticity; however, S2B2, planar S2B6, and planar S2B7- clusters have π antiaromaticity and σ aromaticity. Furthermore, AdNDP bonding analyses reveal that planar S2B4, S2B10, and S2B12 clusters are doubly (π and σ) aromatic, whereas S2B5-, S2B8, S2B9-, and S2B13- clusters are doubly (π and σ) antiaromatic. The electron localization function (ELF) analysis shows that S2Bn0/- (n = 2-13) clusters have different electron delocalization characteristics, and the spin density analysis shows that the open-shell clusters have different characteristics of electron spin distribution. The calculated photoelectron spectra indicate that S2Bn- (n = 2-13) have different characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these doped boron clusters. Our work enriches the new database of geometrical structures of doped boron clusters, provides new examples of aromaticity for doped boron clusters, and is promising to offer new ideas for nanomaterials and nanodevices.

Geometric and electronic diversity of metal doped boron clusters

Being intermediate between small compounds and bulk materials, nanoparticles possess unique properties different from those of atoms, molecules, and bulk matter. In the past two decades, a combination of cluster structure prediction algorithms and experimental spectroscopy techniques was successfully used for exploration of the ground-state structures of pure and metal-doped boron clusters. The fruitfulness of this dual approach is well illustrated by the discovery of intriguing microstructures and unique physicochemical properties such as aromaticity and bond fluxionality for both boron and metal-doped boron clusters. Our review starts with an overview of geometrical configurations of pure boron clusters B_n, which are presented by planar, nanotube, bilayer, fullerene-like and core-shell structures, in a wide range ofnvalues. We consider next recent advances in studies of boron clusters doped with metal atoms paying close and thoughtful attention to modifications of geometric and electronic structures of pure boron clusters by heteroatoms. Finally, we discuss the possibility of constructing boron-based nanomaterials with specific functions from metal-boron clusters. Despite a variety of fruitful results obtained in numerous studies of boron clusters, the exploration of boron-based chemistry has not yet reached its peak. The intensive research continues in this area, and it should be expected that it brings exciting discoveries of intriguing new structures.

Structural Evolution and Electronic Properties of Selenium-Doped Boron Clusters SeBn0/- (n = 3-16)

A theoretical research of structural evolution, electronic properties, and photoelectron spectra of selenium-doped boron clusters SeB_n^0/- (n = 3-16) is performed using particle swarm optimization (CALYPSO) software in combination with density functional theory calculations. The lowest energy structures of SeB_n^0/- (n = 3-16) clusters tend to form quasi-planar or planar structures. Some selenium-doped boron clusters keep a skeleton of the corresponding pure boron clusters; however, the addition of a Se atom modified and improved some of the pure boron cluster structures. In particular, the Se atoms of SeB₇^-, SeB₈^-, SeB₁₀^-, and SeB₁₂^- are connected to the pure quasi-planar B₇^-, B₈^-, B₁₀^-, and B₁₂^- clusters, which leads to planar SeB₇^-, SeB₈^-, SeB₁₀^-, and SeB₁₂^-, respectively. Interestingly, the lowest energy structure of SeB₉^- is a three-dimensional mushroom-shaped structure, and the SeB₉^- cluster displays the largest HOMO-LUMO gap of 5.08 eV, which shows the superior chemical stability. Adaptive natural density partitioning (AdNDP) bonding analysis reveals that SeB₈ is doubly aromatic, with 6 delocalized π electrons and 6 delocalized σ electrons, whereas SeB₉^- is doubly antiaromatic, with 4 delocalized π electrons and 12 delocalized σ electrons. Similarly, quasi-planar SeB₁₂ is doubly aromatic, with 6 delocalized π electrons and 14 delocalized σ electrons. The electron localization function (ELF) analysis shows that SeB_n^0/- (n = 3-16) clusters have different local electron delocalization and whole electron delocalization effects. The simulated photoelectron spectra of SeB_n^- (n = 3-16) have different characteristic bands that can identify and confirm SeB_n^- (n = 3-16) combined with future experimental photoelectron spectra. Our research enriches the geometrical structures of small doped boron clusters and can offer insight for boron-based nanomaterials.

Designing a Four-Ring Tubular Boron Motif through Metal Doping

Tubular boron clusters represent a class of extremely unusual geometries that can be regarded as a key indicator for the 2D-to-3D boron structural evolution as well as the embryos for boron nanotubes. While a good number of pure boron or metal-doped boron tubular clusters have been reported so far, most of them are two-ring tubular structures, and their higher-ring analogues are very scarce. We report herein the first example of a four-ring tubular boron motif in the cagelike global minimum of Be₂B₂₄⁺. Global-minimum searches of MB₂₄^q and M₂B₂₄^q (M = alkali/alkaline-earth metals; q = 1+, 0, 1-) reveal that the most stable structure of Be₂B₂₄⁺ is a C_2v-symmetric cage having a four-ring tubular boron moiety, whereas it is a high-lying isomer for those having a two/three-ring tubular boron motif for all other systems. The B₂₄ framework in Be₂B₂₄⁺ can be viewed as consisting of two two-ring B₁₂ tubular structures linked together at one side of the B₆ rings along the high-symmetry axis and two offside B₆ rings capped by two Be atoms. The Be₂-B₂₄ bonding is best described as Be₂²⁺ in an excited triplet state, forming two highly polarized covalent bonds with B₂₄^- in a quartet spin state. The unique ability of beryllium to make strong covalent and electrostatic interactions makes the Be₂B₂₄⁺ cluster stable in such an unusual geometry.

Structures, and electronic and spectral properties of single-atom transition metal-doped boron clusters MB24 - (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni)

A theoretical study of geometrical structures, electronic properties, and spectral properties of single-atom transition metal-doped boron clusters MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) is performed using the CALYPSO approach for the global minimum search, followed by density functional theory calculations. The global minima obtained for the MB₂₄ ^- (M = Sc, Ti, V, and Cr) clusters correspond to cage structures, and the MB₂₄ ^- (M = Mn, Fe, and Co) clusters have similar distorted four-ring tubes with six boron atoms each. Interestingly, the global minima obtained for the NiB₂₄ ^- cluster tend to a quasi-planar structure. Charge population analyses and valence electron density analyses reveal that almost one electron on the transition-metal atoms transfers to the boron atoms. The electron localization function (ELF) of MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) indicates that the local delocalization of MB₂₄ ^- (M = Sc, Ti, V, Cr, and Ni) is weaker than that of MB₂₄ ^- (M = Mn, Fe, and Co), and there is no obvious covalent bond between doped metal and B atoms. The spin density and spin population analyses reveal that open-shell MB₂₄ ^- (M = Ti, Cr, Fe, and Ni) has different spin characteristics which are expected to lead to interesting magnetic properties and potential applications in molecular devices. The polarizability of MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) shows that MB₂₄ ^- (M = Mn, Fe, and Co) has larger first hyperpolarizability, indicating that MB₂₄ ^- (M = Mn, Fe, and Co) has a strong nonlinear optical response. Hence, MB₂₄ ^- (M = Mn, Fe, and Co) might be considered as a promising nonlinear optical boron-based nanomaterial. The calculated spectra indicate that MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) has different and meaningful characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these single-atom transition metal-doped boron clusters. Our work enriches the database of geometrical structures of doped boron clusters and can provide an insight into new doped boron clusters.

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.

Exploring the structure and electronic properties of germanium doped boron clusters using density functional theory based global optimization method

Density functional theory calculations to investigate the effect of single and double germanium atom doping on the geometric structure and electronic properties of boron clusters with 10 to 20 atoms.

Highly stable actinide(III) complexes supported by doubly aromatic ligands

Owing to the electron-deficient nature of boron atom, the structures and properties of boron clusters can be enriched by doping various metal atoms, including lanthanide metal atoms. Nevertheless, the viability...

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.

Structural and Electronic Properties of Single-Atom Transition Metal-Doped Boron Clusters MB24 (M = Sc, V, and Mn)

A theoretical study of geometrical structures, electronic properties, and spectral properties of single-atom transition metal-doped boron clusters MB24 (M = Sc, V, and Mn) is performed using the CALYPSO approach for the global minimum search, followed by density functional theory calculations. The global minima obtained for the VB24 and MnB24 clusters correspond to cage structures. Interestingly, the global minima obtained for the ScB24 cluster tend to a three-ring tubular structure. Population analyses and valence electron density analyses reveal that partial electrons on transition-metal atoms transfer to boron atoms. The localized orbital locator of MB24 (M = Sc, V, and Mn) indicates that the electron delocalization of ScB24 is stronger than that of VB24 and MnB24, and there is no obvious covalent bond between doped metals and B atoms. The spin density and spin population analyses reveal that MB24 (M = Sc, V, and Mn) have different spin characteristics which are expected to lead to interesting magnetic properties and potential applications in molecular devices. The calculated spectra indicate that MB24 (M = Sc, V, and Mn) has meaningful characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these single-atom transition metal-doped boron clusters. Our work enriches the database of geometrical structures of doped boron clusters and can provide an insight into new doped boron clusters.

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.

Structures, Electronic, and Spectral Properties of Doped Boron Clusters MB12 0/- (M = Li, Na, and K)

Structures and electronic properties of alkali metal atom-doped boron clusters MB12 0/- (M = Li, Na, K) are determined using the CALYPSO method for the global minimum search followed by density functional theory. It is found that the global minima obtained for the neutral clusters correspond to the half-sandwich structure and those of the monoanionic clusters correspond to the boat-shaped structure. The neutral MB12 (M = Li, Na, K) can be considered as a member of the half-sandwich doped B12 clusters, and the geometrical pattern of anion MB12 - (M = Li, Na, K) is a new structure that is different from other doped B12 clusters. Natural population and chemical bonding analyses reveal that the alkali metal atom-doped boron clusters MB12 - are characterized as charge transfer complexes, M+B12 2-, resulting in symmetrically distributed chemical bonds and electrostatic interactions between cationic M+ and boron atoms. The calculated spectra indicate that MB12 0/- (M = Li, Na, K) has meaningful spectral features that can be compared with future experimental data. Our work enriches the varieties of geometrical structures of doped boron clusters and can provide much insight into boron nanomaterials.

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.

LiB13: A New Member of Tetrahedral-Typed B13 Ligand Half-Surround Cluster

It will get entirely unusual derivatives with gratifying chemical bonding schemes for boron clusters by doping with lithium, the lightest alkalis. The geometric structures and electronic properties of the LiBn0/- (n = 10-20) clusters have been studied through Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) structural search approach along with the density functional theory (DFT) calculations. The low-lying candidates of LiBn0/- (n = 10-20) are reoptimized at the B3LYP functional in conjunction with 6-311 + G(d) basis set. Three forms of geometric configurations are identified for the ground-state structures of LiBn0/- clusters: half-sandwich-type, quasi-planar and drum-type structures. The photoelectron spectra (PES) of the LiBn- clusters have been calculated through time-dependent density functional theory (TD-DFT). A promising LiB13 with tetrahedral-typed B13 ligand half-surround cluster and robust stability is uncovered. The molecular orbital and adaptive natural density partitioning (AdNDP) analysis show that B-B bonds in the B13 moiety combined with the interaction between the B13 shell and Li atom stabilize the C2v LiB13 cluster. Our results advance the fundamental understanding about the alkali metal doped boron clusters.

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

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

Structural and electronic properties of MB22− (M = Na, K) clusters: tubular boron versus quasi-planar boron forms

Electron deficiency of boron atom has led to the abundant chemical properties of boron clusters, such as intriguing structures, unique multi-center bonding and electronic properties, as well as the structural evolution from planar to three-dimensional forms.

Stable global tubular boron clusters in Na2B18 and Na2B18−

The optimal electrostatic interactions arising from the doping effect play a crucial role in stabilizing the tubular structure against the planar and quasi-planar preferences of the negatively charged boron clusters.