Atomic and electronic structures of neutral and charged boron and boron-rich clusters

Evolution of B13n (n = + 3 to - 3) wheel with electron injection/abstraction: an insight from electronic structure analysis

CONTEXT

The planar B13+1 cluster, a prototypical molecular 'Wankel motor', has captivated the scientific community with its exceptional stability as well as rotor action. The present study is an exploration of how incremental electron injection/abstraction influences the electronic structure of B13 clusters with B13+1 as a reference one. It has been found that seven different charge states (from + 3 to - 3) of B13 cluster are possible, among which B13-1 triplet is the lowest energy cluster. For B13n clusters, n =  + 3 to - 2, the clusters are planar and possess C2v symmetry and their relative atomic arrangement is similar to B13+1 ground state (GS) structure in which a triangular boron core is encircled by ten peripheral boron atoms. B13-3 cluster has a different geometric arrangement of atoms like that of the B13+1 transition state (TS) structure; remains planar, possesses C2v symmetry. The different atomic arrangement of B13-3 can be assigned to the electronic structural relaxation to reduce the electronic stress arising from high negative charge. B13+1 cluster is characterized by a unique electron density distribution in the cluster plane which is analogous to a 'tri-spoke wheel' configuration. In it, three spokes of electron dense lines connect the triangular core to the nearly circular periphery. The present study unveils how the injection or abstraction of electrons modifies the electronic topology in the cluster plane and how the spoke-wheel geometry evolves. It has been found that, in the + 3 and + 2 charge states, the wheel consists of four and five spokes respectively. On the other hand, for all other clusters, the overall electronic topology resembles that of the tri-spoke wheel-like B13+1 cluster. AIM analysis helped to trace out and characterize the evolution of the spoke-wheel topology with electron density at ring critical points and the bond paths.

METHODS

Density Functional Theory (DFT), utilizing the 6-311 + G(d) basis set and the PBE1PBE hybrid density functional, has been employed to determine the minimum energy structures of B13 clusters with different charged states. The calculations have been performed using a superfine integration grid and very tight optimization settings, as implemented in GAUSSIAN 09 Revision D.01. To address potential instabilities in SCF calculations, wavefunction stability has been thoroughly analysed. AIM analysis and various real-space functions, including electron density, Localized Orbital Locator (LOL), Phase-Space defined Fisher Information Density (PS-FID), and Electron Localization Function (ELF), have been investigated. Multiwfn 3.8 was utilized for plotting these functions.

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.

Computational screening of transition-metal doped boron nanotubes as efficient electrocatalysts for water splitting

The search for efficient and low-cost electrocatalysts for the oxygen evolution reaction (OER) and the hydrogen evolution reaction (HER) is of utmost importance for the production of hydrogen and oxygen via water splitting. In this work, the catalytic performance of the OER and HER on transition metal doped boron nanotubes (BNTs) was investigated using density functional theory. It was found that the doped transition metal atoms determine the catalytic activity of the BNTs. Rhodium-doped BNTs exhibited excellent OER activity, while cobalt-doped BNTs displayed great catalytic activity toward the HER. Volcano relationships were found between the catalytic activity and the adsorption strength of reaction intermediates. Rhodium- and cobalt-doped BNTs exhibited great OER and HER catalytic activity due to the favorable adsorption strength of reaction intermediates. This work sheds light on the design of novel electrocatalysts for water splitting and provides helpful guidelines for the future development of advanced electrocatalysts.

Rhodium-doped BNTs demonstrated excellent OER activity, while cobalt-doped BNTs exhibited the best catalytic activity toward the HER among 12 different transition metal-doped BNTs.

Embedded-atom method interatomic potential for boron nanostructures

Parameters of embedded-atom method interatomic potential for boron are presented in this paper. The potential parameters were determined by means of ab initio data for boron cluster B₂₀, triangular boron sheet, and body-centered cubic structure. The potential has been tested against basic properties of various boron structures. They are face-centered cubic, diamond-like, body-centered tetragonal, icosahedron B₁₂ and icosahedral chain structures. One can conclude that the proposed potential provides a reasonable representation of the interatomic interaction in boron nanostructures, and it is intended for use in large-scale molecular dynamics simulations of boron nanomaterials.

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

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

Density functional theory study on structure and stability of BeBn+ clusters

RATIONALE

Boride compounds hold promise for broad applications in the field of optoelectronics due to their high-temperature resistant, corrosion resistant and antioxidant properties. In order to reveal the formation mechanism of alkali and alkaline earth metal doped boron clusters, theoretical studies of these systems are required.

METHODS

All the possible geometrical structures of BeB_n⁺ clusters (n = 1-8) were optimized at the B3LYP/6-311+G(d) level; the harmonic vibration frequencies were obtained to examine the true stability and give the zero-point vibration energy at that theoretical level. The single point energies of all the structures were computed at the CCSD(T)/aug-cc-pVDZ level. For the most stable structures, the average binding energy (E_b ), the fragmentation energy (E_F ) and second-order difference of total energy (Δ₂ E) were used to evaluate the relative stability of clusters.

RESULTS

Most of the BeB_n⁺ clusters are planar in structure; the B atoms tend to aggregate to form a boron ring, and the coordinating Be atoms are on the periphery of the clusters. The fragmentation energy and second-order difference of total energy show that there is an obvious odd-even alteration as n increases, and local-maxima when n is odd.

CONCLUSIONS

A systematic theoretical investigation on the geometries, stabilities and electronic properties of BeB_n⁺ clusters has been carried out where n = 1-8. The results provide a useful reference for understanding the formation mechanism and stability of these clusters, as well as guidance for finding larger size clusters.

Double C-H bond activation of acetylene by atomic boron in forming aromatic cyclic-HBC2BH in solid neon

The organo-boron species formed from the reactions of boron atoms with acetylene in solid neon are investigated using matrix isolation infrared spectroscopy with isotopic substitutions as well as quantum chemical calculations. Besides the previously reported single C-H bond activation species, a cyclic-HBC2BH diboron species is formed via double C-H bond activation of acetylene. It is characterized to have a closed-shell singlet ground state with planar D2h symmetry. Bonding analysis indicates that it is a doubly aromatic species involving two delocalized σ electrons and two delocalized π electrons. This finding reveals the very first example of double C-H bond activation of acetylene in forming new organo-boron compounds.

Comparative study of small boron, silicon and germanium clusters: B(m)Si(n) and B(m)Ge(n) (m + n = 2-4)

Chemically speaking, atomic clusters are very rich, allowing their application in a broad range of technological areas such as developing functional materials, heterogeneous catalysis, and building optical devices. In this work, high level computational chemistry methods were used in a systematic manner to improve the characterization of small clusters formed by boron, silicon, germanium, mixed boron/silicon, and mixed boron/germanium. Calculations were carried out with both ab initio [MP2 and CCSD(T)] and density functional (B3LYP) methods with extended basis sets. The CCSD(T) results were then extrapolated to the complete basis set (CBS) limit. Finally, geometrical parameters, vibrational frequencies, and relative energies were then obtained and compared to data presented in the literature. Graphical Abstract Small boron, silicon and germanium clusters: BmSin and BmGen (m + n = 2-4).

Understanding boron through size-selected clusters: structure, chemical bonding, and fluxionality

Boron is an interesting element with unusual polymorphism. While three-dimensional (3D) structural motifs are prevalent in bulk boron, atomic boron clusters are found to have planar or quasi-planar structures, stabilized by localized two-center-two-electron (2c-2e) σ bonds on the periphery and delocalized multicenter-two-electron (nc-2e) bonds in both σ and π frameworks. Electron delocalization is a result of boron's electron deficiency and leads to fluxional behavior, which has been observed in B13(+) and B19(-). A unique capability of the in-plane rotation of the inner atoms against the periphery of the cluster in a chosen direction by employing circularly polarized infrared radiation has been suggested. Such fluxional behaviors in boron clusters are interesting and have been proposed as molecular Wankel motors. The concepts of aromaticity and antiaromaticity have been extended beyond organic chemistry to planar boron clusters. The validity of these concepts in understanding the electronic structures of boron clusters is evident in the striking similarities of the π-systems of planar boron clusters to those of polycyclic aromatic hydrocarbons, such as benzene, naphthalene, coronene, anthracene, or phenanthrene. Chemical bonding models developed for boron clusters not only allowed the rationalization of the stability of boron clusters but also lead to the design of novel metal-centered boron wheels with a record-setting planar coordination number of 10. The unprecedented highly coordinated borometallic molecular wheels provide insights into the interactions between transition metals and boron and expand the frontier of boron chemistry. Another interesting feature discovered through cluster studies is boron transmutation. Even though it is well-known that B(-), formed by adding one electron to boron, is isoelectronic to carbon, cluster studies have considerably expanded the possibilities of new structures and new materials using the B(-)/C analogy. It is believed that the electronic transmutation concept will be effective and valuable in aiding the design of new boride materials with predictable properties. The study of boron clusters with intermediate properties between those of individual atoms and bulk solids has given rise to a unique opportunity to broaden the frontier of boron chemistry. Understanding boron clusters has spurred experimentalists and theoreticians to find new boron-based nanomaterials, such as boron fullerenes, nanotubes, two-dimensional boron, and new compounds containing boron clusters as building blocks. Here, a brief and timely overview is presented addressing the recent progress made on boron clusters and the approaches used in the authors' laboratories to determine the structure, stability, and chemical bonding of size-selected boron clusters by joint photoelectron spectroscopy and theoretical studies. Specifically, key findings on all-boron hydrocarbon analogues, metal-centered boron wheels, and electronic transmutation in boron clusters are summarized.

Probing the structures and chemical bonding of boron-boronyl clusters using photoelectron spectroscopy and computational chemistry: B4(BO)(n)- (n = 1-3)

The electronic and structural properties of a series of boron oxide clusters, B(5)O(-), B(6)O(2)(-), and B(7)O(3)(-), are studied using photoelectron spectroscopy and density functional calculations. Vibrationally resolved photoelectron spectra are obtained, yielding electron affinities of 3.45, 3.54, and 4.94 eV for the corresponding neutrals, B(5)O, B(6)O(2), and B(7)O(3), respectively. Structural optimizations show that these oxide clusters can be formulated as B(4)(BO)(n)(-) (n = 1-3), which involve boronyls coordinated to a planar rhombic B(4) cluster. Chemical bonding analyses indicate that the B(4)(BO)(n)(-) clusters are all aromatic species with two π electrons.

LARGE-SCALE FIRST PRINCIPLES CONFIGURATION INTERACTION CALCULATIONS OF OPTICAL ABSORPTION IN BORON CLUSTERS

We have performed systematic large-scale all-electron correlated calculations on boron clusters B n(n = 2 - 5), to study their linear optical absorption spectra. Several possible isomers of each cluster were considered, and their geometries were optimized at the coupled-cluster singles doubles (CCSD) level of theory. Using the optimized ground-state geometries, the excited states of different clusters were computed using the multi-reference singles-doubles configuration–interaction (MRSDCI) approach, which includes electron correlation effects at a sophisticated level. These CI wave functions were used to compute the transition dipole matrix elements connecting the ground and various excited states of different clusters, eventually leading to their linear absorption spectra. The convergence of our results with respect to the basis sets, and the size of the CI expansion were carefully examined. The contribution of configurations to many body wave-function of various excited states suggests that the excitations involved are collective, plasmonic type.

Density functional theory study of BnC clusters

B(n)C clusters (n = 3-10) were studied at the density functional theory (DFT) (B3LYP)/6-311G** level of theory. The calculations predicted that the most stable configurations of the B(n) C clusters are the (n + 1)-membered cyclic structures. For boron-carbon clusters, the configurations containing greater numbers of three-membered boron rings are more favorable, except for the B(7)C and B(9)C clusters. Through molecular orbital analysis of these B(n)C clusters, we have concluded that π-electron delocalization plays a crucial role in the stability of n + 1-membered cyclic structures. In this paper, the relative stability of each cluster is discussed based on their single atomic-binding energies. The capability of clusters to obtain or lose an electron was also discussed, based on their vertical electron detachment energies (VDEs), adiabatic electron detachment energies (ADEs), vertical electron affinities (VEAs) and adiabatic electron affinities (AEAs).

Search for structures, potential energy surfaces, and stabilities of planar BnP(n = 1 ∼ 7)

We have systematically explored and investigated the geometrical structures, stability, growth pattern, bonding character, and potential energy surface (PES) of the possible isomers of each cluster for planar B(n)P (n = 1 ∼ 7) at the CCSD(T)/6-311+;G(d)//B3LYP/6-311+G(d) level. A large number of planar structures for the possible isomers of B(n)P (n = 1 ∼ 7) and transition states are located. Isomers 1a ∼ 7a of B(n)P are the lowest-energy structures and 2a, 4a, as well as 6a are more stable than their neighbors. For the lowest-energy structures (1a ∼ 7a) of B(n)P, P atom lies at the apex and tends to form two B-P bonds with boron atoms. They exhibit planar zigzag growth feature or approximately spherical-like growth pattern. Results from molecular orbital analysis demonstrate that the formation of the delocalized π MOs and the σ-radial and σ-tangential MOs plays a critical role in stabilizing the structures of lowest-energy isomers (2a ∼ 7a) of B(n)P. Importantly, isomers 3a, 3c, 3d, 4a, 4b, 5b, and 5c of B(n)P are stable both thermodynamically and kinetically at the CCSD(T)/6-311+G(d)// B3LYP/6-311+G(d) level and detectable in laboratory, which is valuable for further experimental studies of B(n)P.

Hydrogen storage behavior of one-dimensional TiBx chains

We designed a series of one-dimensional TiB(x) (x = 2-6) chains used for hydrogen storage. Among them, TiB(5) possesses the lowest heat of formation and the highest binding energy, and is the most energetically favorable configuration. The binding energy per atom in TiB(5) is even larger than that in a Ti dimer, which suggests the preference of Ti atoms to combine with B(5) clusters rather than clustering. Each Ti atom in the TiB(5) chain can host four hydrogen molecules (corresponding to a hydrogen storage capacity of 7.3 wt%) with an average binding energy of 43.7 kJ mol(-1)/H(2). The significant charge transfer and strong Kubas sigma-H(2) interaction between H(2) and Ti atoms contribute to the ideal dihydrogen binding energies.

Structure and stability of B5C and C5B clusters

Geometry optimizations and vibrational frequencies of B5C and C5B clusters were calculated with the Becke-3LYP method using the 6-311+G(d) basis set and some stable configurations of B5C and C5B clusters have been found. The most stable structure of B5C is a planar six-membered ring. However, for C5B clusters, the most stable structure is linear with a boron atom in position 3. Various configurations of B5C clusters containing three-membered boron rings have predominance in energy, whereas various configurations of C5B clusters containing three-membered carbon rings are disadvantageous in energy. In B5C clusters, isomer2 can be converted into isomer1 by surmounting an energy barrier of 43.83 kJ.mol(-1). In C5B clusters, the conversions of isomer5 into isomer2 and isomer7 into isomer2 have energy barriers of 19.66 and 20.57 kJ.mol(-1), respectively.

Structure and stability of small boron and boron oxide clusters

To rationally design and explore a potential energy source based on the highly exothermic oxidation of boron, density functional theory (DFT) was used to characterize small boron clusters with 0-3 oxygen atoms and a total of up to ten atoms. The structures, vibrational frequencies, and stabilities were calculated for each of these clusters. A quantum molecular dynamics procedure was used to locate the global minimum for each species, which proved to be crucial given the unintuitive structure of many of the most stable isomers. Additionally, due to the plane-wave, periodic DFT code used in this study a straightforward comparison of these clusters to the bulk boron and B2O3 structures was possible despite the great structural and energetic differences between the two forms. Through evaluation of previous computational and experimental work, the relevant low-energy structures of all but one of the pure boron clusters can be assigned with great certainty. Nearly all of the boron oxide clusters are described here for the first time, but there are strong indications that the DFT procedure chosen is particularly well suited for the task. Insight into the trends in boron and boron oxide cluster stabilities, as well as the ultimate limits of growth for each, are also provided. The work reported herein provides crucial information towards understanding the oxidation of boron at a molecular level.

Structure and Stability of Al-Doped Boron Clusters by the Density-Functional Theory

The geometries, stabilities, and electronic properties of Bn and AlBn clusters, up to n=12, have been systematically investigated by using the density-functional approach. The results of Bn clusters are in good agreement with previous conclusions. When the Al atom is doped in Bn clusters, the lowest-energy structures of the AlBn clusters favor two-dimensional and can be obtained by adding one Al atom on the peripheral site of the stable Bn when n<or=5. Starting from n=6, the lowest-energy structures of AlBn clusters favor three-dimensional and can be described as an Al atom being capped on the Bn clusters. The average atomic binding energies, fragmentation energies, and second-order energy differences are calculated and discussed. Maximum peaks were observed for clusters of sizes n=5, 8, 11, especially for the AlB8 cluster, implying that these clusters possess relatively higher stability. The adiabatic IP and EA of AlBn and Bn clusters are discussed and compared with some available experimental results. A distinct phenomena for AlBn clusters is that all even n, but n=10, have higher adiabatic ionization potentials than odd n.

The Conversion among Various B4C Clusters: A Density Functional Theoretical Study

Geometry optimizations and vibration frequencies of B4C clusters were performed with Becke-3LYP method using 6-31G(d) basis set. We have found 14 stable isomers, and the most stable structure among them is the five-member ring containing two three-member boron rings. We also analyzed these stable isomers in detail, and the results show that the structures containing three-member boron rings are predominant in energy for B4C clusters. In terms of MO and NBO analysis, the three-centered bond and the pi-electron delocalization play an important role in stabilizing the planar five-member rings of these B4C clusters. Our calculations suggest that isomer4 can be converted into isomer7 with only an energy barrier of 0.31 kJ mol(-1) at the B3LYP/6-311G+(3df) level. Although the planar structures of the five-member rings (isomers12-14) can be converted with each other, the conversions of isomer14 to isomer13 and isomer13 to isomer12 have high-energy barriers of 70.99 and 68.51 kJ mol(-1) at the B3LYP/6-31G(d) level, respectively.

Structural and electronic properties of boron-doped lithium clusters: Ab initio and DFT studies

The lowest-energy structures and electronic properties of the BLi(n) (n = 1-7) clusters are reported using the B3LYP, MP2, and CCSD(T) methods with the aug-cc-pVDZ basis set. Though the results at the B3LYP level agree well with those at the CCSD(T) level, the MP2 method is rather unsatisfactory. The first three-dimensional ground state in the BLi(n) clusters occurs for BLi(4), and the impurity B atom is seen to be trapped in a Li cage from the BLi(6) cluster onwards. The evolution of the binding energies, vertical ionization potentials, and polarizability with size of cluster shows the BLi(5) cluster to be most stable among the BLi(n) clusters. Besides, the BLi(5) cluster is also found to have the largest reaction enthalpy (49.8 kcal/mol) upon losing a Li atom, which is different from the previous prediction. The unique stability of the 8-valence electron BLi(5) can be understood from the cluster electronic shell model (CSM). However, in contradiction to the prediction of the CSM, the 2s level is filled prior to the 1d level in the BLi(n) clusters.