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

Abstract

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.

1. Introduction

Clusters are composed of several to thousands of atoms or molecules whose properties depend on their size and shape. Clusters are ideal model systems for correlating microscopic structure and macroscopic properties of substances, and cluster research is of great significance to deeply understand the laws of matter transformation. Research of structure and properties of clusters can offer insight for the design and manufacture of new materials and new devices at the atomic level. Boron clusters can induce polycentric chemical bonds and adopt several interesting structures with meaningful properties [1,2,3,4,5,6]. Experimental and theoretical research has shown that B_n⁻ (n < 38) have quasi-planar or planar structures [7,8], and neutral B_n have quasi-planar, planar, wheel shaped, tubular structures or other structures [1,5,9,10,11]. In 2014, the experimental finding of cage-type all-boron cluster (borospherene) [12] B₄₀⁻ has given rise to a lot of attention on boron clusters [13,14,15,16,17,18,19,20,21]. In 2015, researchers synthesized borophene on the Ag (111) base [22], and the structural unit of borophene is a B₇ cluster. In 2021, researchers synthesized borophene crystal, which was hydrogenated with hydrogen atoms [23], and it is very stable and comparable to graphene. Interestingly, the basic unit of hydrogenated borophene happens to be a hydrogenated B₇ cluster also. The experimental findings of B₄₀⁻ and borophene offer insight for the development of new boron nanomaterials and nanodevices. Research on small boron clusters is promising as a way to provide new ideas for new nanomaterials and nanodevices.

In recent years, researchers have studied abundant doped boron clusters, and they mainly focused on doping a single metal atom in boron clusters of different sizes. Metal-atom-doped boron clusters can induce new geometrical configuration and properties [15,17,18,19,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38]. For example, anionic B₂₀⁻ and B₂₂⁻ have a quasi-planar structure [7,39]. However, single alkali-metal-atom-doped LiB₂₀⁻, NaB₂₂⁻, and KB₂₂⁻ display a double-ring configuration [25,40]. Co and Rh atom-doped boron clusters MB₁₂ (M = Co and Rh) can lead to the quasi-planar B₁₂ form, a semi-sandwich configuration [3,24]. Neutral B₂₄ has a double-ring configuration [39], while TiB₂₄ and ScB₂₄ have a cage configuration and three-ring tubular structure, respectively, after adding one Sc or Ti atom [41,42]. Anionic B₂₄⁻ has a quasi-planar structure [7], while TiB₂₄⁻ and VB₂₄⁻ have a cage configuration after adding one Ti or V atom [43]. In addition, the LiB₄₀, NaB₄₀, or KB₄₀ cage is promising for application to the field of nonlinear optics [18]; the ScB₄₀ or TiB₄₀ cage is promising for application to the field of hydrogen storage [15,17,19]; Co atom-doped CoB₁₂⁻ and Rh atom-doped RhB₁₂⁻ can improve chemical activity [27]; Co atom-doped CoB₄₀ is promising for application to molecular devices [26]; and the metal-atom-doped boron clusters ReB_n⁻(n = 3–4, 6, 8–9), MnB_n⁻(n = 6, 16), BiB_n⁻(n = 6–8), CoB₁₆⁻, La₂B_n⁻(n = 10–11), La₃B₁₈⁻, MB₈(M = Be, Mg), and M₂B₆(M = Mg, Ca, Sr) have various unique structures [29,30,31,32,33,34,35,36,37,44,45]. However, nonmetallic-atom-doped boron clusters have been poorly studied. In particular, the structural evolution of boron clusters after addition of a single nonmetallic atom is rarely studied. Similar to B₇, small boron clusters with doping are promising as the structural units of borophene and other boron nanomaterials. Selenium is one of the essential microelements in the human body and has obvious inhibitory effects on tumors. The Se atom can combine with metal atoms, such as Cd and Zn, to form semiconductor clusters or quantum dots [46,47]. These materials exhibit a variety of unique optical and electronic properties, which can be further applied in imaging and diagnosis of biological systems [48,49]. Se doping of boron clusters is promising to be a useful strategy to further increase the diversity of structural forms and to affect the properties of boron clusters. Therefore, the theoretical research of Se atom-doped small boron clusters can enrich new structures and new properties of boron clusters, and can also provide theoretical guidance for the synthesis of nanomaterials, such as borophene. Herein, to demonstrate the structural evolution of Se-doped SeB_n^0/− (n = 3–16), extensive geometric configurations were generated and predicted, using the particle swarm optimization (CALYPSO) approach [50] in combination with the density functional theory method PBE0 [51].

2. Results and Discussion

2.1. Structures and Electronic Properties

Five low-energy structures of SeB_n^0/− (n = 3–16) are shown in Figures S1–S28, and the lowest energy structures of SeB_n^0/− (n = 3–16) are displayed in Figure 1 and Figure 2. The results indicate that the low-energy structures of SeB_n^0/− (n = 3–16) trend to form planar or quasi-planar structures. Interestingly, the ground state configuration of SeB₉⁻ is three-dimensional mushroom shaped. Early theoretical and experimental research found that most of the small neutral boron clusters are quasi-planar or planar, and all small anionic boron clusters are quasi-planar or planar structures. Figure 1 and Figure 2 and the research results indicate that, after adding a Se atom, some of the lowest energy configurations of SeB_n^0/− (n = 3–16) have a skeleton of pure boron clusters, such as SeB_n (n = 3–5, 7–8, 10–14, 16) and SeB_n⁻ (n = 3–5, 7–8, 10–14, 16) [52,53]. As can be seen in Figure 1 and Figure 2, except for SeB_n⁻ (n = 5, 6, 9), each Se atom is connected to two boron atoms to form a three-ring. The lowest energy configurations of SeB_n^0/− (n = 3–5) have planar structure, and the Se atom is attached to the boron atoms of the pure boron cluster B_n^0/− (n = 3–5) [52]. The lowest energy configurations of SeB₆^0/− and SeB₁₃^0/− have quasi-planar structure, and they are different from the ground-state structures of corresponding pure boron clusters B₆^0/− and B₁₃^0/− [52]. For SeB₇^0/−, SeB₁₀^0/−, and SeB₁₂^0/−, the lowest energy configurations of neutral clusters and corresponding anionic clusters have similar structure, and the Se atoms of SeB₇, SeB₁₀, and SeB₁₂ are connected to the pure quasi-planar B₇, B₁₀, and B₁₂ clusters, respectively. However, the Se atoms of SeB₇⁻, SeB₁₀⁻, and SeB₁₂⁻ are connected to the pure quasi-planar B₇⁻, B₁₀⁻, and B₁₂⁻ clusters, which leads to the planar SeB₇⁻, SeB₁₀⁻, and SeB₁₂⁻, respectively [52]. The lowest energy structures of SeB₈^0/− have same planar structure, and the Se atom of SeB₈ is connected to the pure planar B₈ cluster. However, the Se atom of SeB₈⁻ is connected to the pure quasi-planar B₈⁻ cluster, which leads to the planar SeB₈⁻. The pure B₉^0/− have same planar wheel-shape structure [52]. However, doping of Se atom causes the anionic SeB₉⁻ to become a three-dimensional mushroom-shaped structure (with C_6V symmetry) and causes the neutral SeB₉ to become a boat-shaped structure. The lowest energy structures of SeB₁₁^0/− have similar structure, and the Se atom of SeB₁₁ is connected to the pure planar B₁₁ cluster, which leads to the slight structural change. However, the Se atom of SeB₁₁⁻ is connected to the pure planar B₁₁⁻ cluster [52]. The lowest energy configurations of SeB₁₄^0/− have same planar structure, the lowest energy configurations of SeB₁₆^0/− have same quasi-planar structure, and the Se atoms are connected to the pure planar B₁₄^0/− clusters and pure quasi-planar B₁₆^0/− clusters, respectively [52,53]. The lowest energy configurations of SeB₁₅^0/− have quasi-planar structure and exhibit two axially chiral isomers, and they are different from the ground-state configurations of pure boron cluster B₁₅^0/−. Similar to pure B₇ clusters, planar and quasi-planar Se-doped boron clusters are promising as the structural units of boron nanomaterials, which can be synthesized further into borophene.

The harmonic frequency analysis confirmed that these lowest-energy structures are actually stable (no imaginary frequency). For closed-shell clusters, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy gaps (HOMO–LUMO energy gaps) of SeB₃⁻, SeB₄, SeB₅⁻, SeB₆, SeB₇⁻, SeB₈, SeB₉⁻, SeB₁₀, SeB₁₁⁻, SeB₁₂, SeB₁₃⁻, SeB₁₄, SeB₁₅⁻, and SeB₁₆ are 2.48, 3.52, 2.14, 3.92, 2.90, 2.33, 5.08, 2.93, 2.89, 3.29, 2.28, 2.00, 2.91, and 2.27 eV, respectively. For open-shell clusters, α-HOMO–LUMO and β-HOMO–LUMO, energy gaps vary within the range of 1.92-4.39 eV. Meanwhile, the calculated HOMO–LUMO energy gaps of SeB_n^0/− (n = 3–16) clusters reveal that the SeB₉⁻ cluster possesses the largest HOMO-LUMO gap of 5.08 eV, which shows the superior chemical stability.

To further understand the stability of typical structures of SeB_n^0/− (n = 3–16), we analyzed the chemical bonding of closed-shell planar SeB₈, three-dimensional SeB₉⁻, and quasi-planar SeB₁₂ using the adaptive natural density partitioning (AdNDP) approach. Figure 3 displays the bonding patterns of planar SeB₈. For SeB₈, AdNDP analyses reveal that one lone pair (Figure 3a) is found on the Se atom and eight 2c–2e σ bonds (Figure 3b) on the peripheral ring. The remaining six bonds contain three σ bonds and three π bond, which are classified into four sets (Figure 3): one 3c–2e σ bond covers one B₃ triangle, in which two of the boron atoms are connected to the Se atoms; two 4c–2e σ bonds cover two B₄ rings; one 3c–2e π bond is distributed around the B-Se-B triangle; and two 5c–2e π bonds cover two B₅ rings. Overall, the eight 2c–2e σ bonds, one delocalized 3c–2e σ bond, and two delocalized 4c–2e σ bonds cover the planar molecule, which renders stability to the SeB₈, and the delocalized 3c–2e π bond and 5c–2e π bonds further stabilize the SeB₈ cluster. Figure 4 displays the bonding patterns of SeB₉⁻, and there are five categories. First, there is one lone pair (see Figure 4a) on the Se atom. Then, there are two 2c–2e σ bonds on the Se-B and adjacent B-B. Third, two 2c–2e π bonds cover the Se-B symmetrically. Fourth, the peripheral B₇ ring at the top of the mushroom is characterized by six localized B−B 2c–2e σ bonds. The last six delocalized 3c–2e σ bonds cover the inner B₃ triangles at the top of the mushroom. The six localized B−B 2c-2e σ bonds and six delocalized 3c–2e σ bonds are responsible for the connection between the outer B₇ ring and the inner B atom at the top of the mushroom, which enhances the stability of SeB₉⁻. Figure 5 displays the bonding patterns of quasi-planar SeB₁₂. For SeB₁₂, AdNDP analyses reveal that one lone pair (see Figure 5a) is found on the Se atom and ten 2c–2e σ bonds (see Figure 5b) on the peripheral ring. The remaining ten bonds contain seven σ bonds and three π bonds, which are classified into three sets (Figure 5): one 3c–2e π bond covers B-Se-B triangle, seven 3c–2e σ bonds cover the seven inner B₃ triangles, and two 5c–2e π bonds are distributed symmetrically around the two B₅ rings. Similar to the SeB₈, the ten 2c–2e σ bonds and seven delocalized 3c–2e σ bonds cover the quasi-planar molecule, which renders stability to the SeB₁₂ cluster, and the delocalized 3c–2e π bond and 5c–2e π bonds further stabilize the SeB₁₂ cluster. AdNDP bonding analyses revealed that the SeB₈ and SeB₁₂ possess three delocalized π bonds, which, quite surprisingly, satisfy the 4m + 2 Hückel rule for π aromaticity. Furthermore, SeB₈ and SeB₁₂ possess three delocalized σ bonds and seven delocalized σ bonds, which satisfy the 4m + 2 Hückel rule for σ aromaticity. However, the three-dimensional SeB₉⁻ cluster possesses two delocalized π bonds and six delocalized σ bonds, which satisfy the 4m Hückel rule for π and σ antiaromaticity.

To describe the electron localization or delocalization of electrons, the electron localization function (ELF) [54] of the valence electrons was analyzed, as shown in Figures S29–S31. At the isosurface value of 0.60, the isosurface maps of most of the clusters are connected on the surface of the whole molecule. Yet, the isosurface diagrams of SeB₅⁻, SeB₆⁻, SeB₉⁻, and SeB₁₁⁻ are disconnected on the surface of the whole molecule, indicating that the delocalization of the whole molecule is weaker than that of the other clusters. Figure S30 displays the ELF with the isosurface value of 0.70. The isosurface diagram of SeB₃, SeB₃⁻, SeB₄⁻, SeB₉, SeB₁₂, and SeB₁₅⁻ is still connected on the surface of the whole molecule, while the isosurface diagrams of other clusters are broken on the partial regions of the molecule, indicating that the delocalization of SeB₃, SeB₃⁻, SeB₄⁻, SeB₉, SeB₁₂, and SeB₁₅⁻ is stronger than that of the other clusters. Figure S31 displays the ELF with the isosurface value of 0.80, in which the isosurface maps of some clusters are disconnected and there are no connected regions. The isosurface maps of SeB₃, SeB₃⁻, SeB₆, SeB₇, SeB₇⁻, SeB₉⁻, SeB₁₂, and SeB₁₅⁻ show that there is still some connected area on the surface of molecule, indicating that the local delocalization of these clusters is stronger than that of other clusters. Quite specially, the isosurface diagram of SeB₉⁻ is still connected on the peripheral B₇ ring at the top of the mushroom. ELF analyses further confirm these observations based on the AdNDP analyses, such as the contributions from the valence electrons of the SeB₁₂ were partitioned in Figure S31. Isosurface maps of the SeB₁₂ (Figure S31) cover eight peripheral B-B bonds and two B-Se bonds that correspond to ten peripheral 2c–2e σ bonds, and they cover seven B₃ triangles that correspond to seven 3c–2e σ bonds. Isosurface maps on the two B₅ ring are fatter due to another two 5c–2e π bonds.

Figure S32 shows the isosurface diagram of the spin density of the open-shell clusters, and spin density can reveal the distribution of unpaired electrons. Figure S32 shows the spin density diagram with an isosurface value of 0.002, in which green represents alpha electrons and blue represents beta electrons. Figure S32 shows that the unpaired single electrons are mostly alpha electrons, and there are a small number of beta electrons on B atoms. Most of the unpaired alpha electrons are distributed on the B atoms; only a small portion of the unpaired alpha electrons are distributed on the Se atom. The spin density can reflect chemical reactions or adsorption to a certain extent. The single electrons of these clusters are mostly alpha electrons and are basically on the B atoms. The B or Se atoms with single alpha electrons can pair with free radicals or small molecules with beta single electrons to form new covalent bonds. In addition, these spin features are expected to produce interesting magnetic properties, which will further lead to potential applications in molecular devices.

2.2. Photoelectron Spectra

Photoelectron spectroscopy in combination with theoretical calculations was used to identify the structures of size-selected boron clusters [3,12,55]. To assist with future identifications of SeB_n⁻ (n = 3–16), vertical detachment energies (VDEs) were calculated and photoelectron spectra of SeB_n⁻ (n = 3–16) were simulated with the time-dependent DFT (TD-DFT) method [12,55,56].

Figure 6 presents the photoelectron spectra of SeB_n⁻ (n = 3–16). The results indicate that SeB₃⁻ has the lowest first VDE, and SeB₁₂⁻ has the largest energy gap (about 1.48 eV) between the first and second peaks. The first several peaks were used to identify boron clusters [3,12]; the peaks on the low binding energy side are of great significance. The first peaks of these photoelectron spectra (except for SeB₉⁻) come from the calculated ground-state VDEs of SeB₃⁻, SeB₄⁻, SeB₅⁻, SeB₆⁻, SeB₇⁻, SeB₈⁻, SeB₁₀⁻, SeB₁₁⁻, SeB₁₂⁻, SeB₁₃⁻, SeB₁₄⁻, SeB₁₅⁻, and SeB₁₆⁻ at 2.52, 2.62, 2.89, 2.89, 2.89, 2.76, 3.14, 3.51, 2.66, 3.43, 3.15, 3.59, and 3.36 eV, respectively. The calculated ground-state VDEs of these closed-shell clusters originate from the detachment of the electron from the molecular orbital HOMO. However, for open-shell clusters, the calculated ground-state VDE of each cluster originates from the detachment of the electron from the singly occupied molecular orbital α-SOMO. The first peak of SeB₉⁻ comes from the second VDE at 4.01 eV, which is smaller than the ground-state VDE of 4.25 eV (second peak). The second peaks of SeB₃⁻, SeB₅⁻, SeB₇⁻, SeB₁₁⁻, SeB₁₃⁻, and SeB₁₅⁻ come from the second calculated VDEs at 3.23, 4.07, 4.16, 3.81, 4.30, and 4.12 eV, respectively, which originate from detaching the electrons from HOMO-1. The second peaks of SeB₄⁻, SeB₆⁻, SeB₈⁻, SeB₁₀⁻, SeB₁₂⁻, SeB₁₄⁻, and SeB₁₆⁻ come from the second VDEs at 3.36, 4.02, 3.07, 3.48, 4.14, 3.64, and 3.63 eV, respectively, which originate from detaching the electrons from the singly occupied molecular orbital β -HOMO-1. In addition, the peaks with higher binding energy originate from detaching the electrons from lower molecular orbitals. It is noted that some of the doped anionic boron clusters have a similar skeleton as the corresponding anionic pure boron clusters. Comparing their photoelectron spectra, the addition of the Se atom results in a great change in the photoelectron spectra [52,53]. However, the photoelectron spectra of some doped boron clusters are similar to those of the corresponding anionic pure boron clusters [52,53]. For example, compared with the photoelectron spectra of pure boron clusters, the addition of Se atoms causes the first two peaks of SeB₃^- to move 0.30 eV towards the low binding energy side and causes the first two peaks of B₅^- to move 0.46 eV towards the high binding energy side [52]. For SeB₄⁻, SeB₈⁻, and SeB₁₃^-, compared with the photoelectron spectra of pure boron clusters, the addition of Se atoms causes different band characteristics [52]. Compared to the photoelectron spectra of pure boron clusters, planar SeB₇⁻ and quasi-planar B₇^- have almost the same first VDE (2.89 eV for SeB₇^-, 2.85 ± 0.02 eV for B₇⁻) [52], planar SeB₁₀^- and quasi-planar B₁₀^- have almost the same first VDE (3.14 eV for SeB₁₀⁻, 3.06 ± 0.03 eV for B₁₀⁻) [52], and quasi-planar SeB₁₄⁻ and quasi-planar B₁₄^- have almost the same first VDE (3.14 eV for SeB₁₄⁻, 3.10 ± 0.01 eV for B₁₄⁻) [52]. For SeB₁₁^-, compared to the photoelectron spectra of pure boron clusters B₁₁⁻, the addition of the Se atom causes the first peak to move 0.08 eV towards the high binding energy side and causes the second peak to move 0.25 eV towards the low binding energy side. For SeB₁₂⁻ and SeB₁₆⁻, planar SeB₁₂^- and quasi-planar B₁₂⁻ have similar band characteristics [52], and quasi-planar SeB₁₆⁻ and quasi-planar B₁₆^- have similar band characteristics [53]. Figure 6 indicates that SeB_n⁻ (n = 3–16) has different spectral features; especially the peaks at the low binding energy side can identify the SeB_n⁻ (n = 3–16). As with the discovery of other anionic boron clusters, if the photoelectron spectra of SeB_n⁻ (n = 3–16) are obtained in experiments, these simulated values can be used for the identification of SeB_n⁻ (n = 3–16).

3. Computation Details

Configuration searches of Se-doped boron clusters SeB_n^0/− (n = 3–16) were performed with CALYPSO 5.0 software in combination with Gaussian 16 software. CALYPSO is a reliable cluster configuration prediction software, and it has successfully predicted boron or doped boron clusters [11,25,40,41,45,57,58,59,60,61]. The initial structures were generated by the CALYPSO software, and then these initial structures were optimized using Gaussian 16 software at the PBE0/3-21G level for the preliminary structural search. In each generation produced by the CALYPSO software, 70% of the structures were produced by particle swarm optimization (PSO) operations, while the others were randomly generated. When cluster sizes vary from n = 3 to n = 10, nearly 100–900 isomers are initially predicted for each boron cluster of a different size. When cluster sizes vary from n = 11 to n = 16, nearly 2000 isomers are initially predicted for each boron cluster of a different size.

After the preliminary structural search, low-energy structures were then fully optimized at the PBE0/6-311+G(d) level [51,62]. After the optimizations, frequency analyses and electronic structures were studied at the PBE0/6-311+G(d) level. PBE0/6-311+G(d) is a reliable level for boron cluster [12,60,61,63,64,65]; in particular, theoretical simulated values with PBE0/6-311+G(d) are the same as the experimental values [12]. Therefore, all calculations in this article used the method PBE0/6-311+G(d) and were performed using Gaussian 16 software [66]. The analyses and isosurface map drawings were performed using Multiwfn 3.7 code [67] and the visual molecular dynamics (VMD) program [68].

4. Conclusions

DFT combined with CALYPSO software is employed to demonstrate the structural evolution of SeB_n^0/− (n = 3–16) clusters. The conclusions are summarized as follows. (1) The global minima of SeB_n^0/− (n = 3–16) clusters tend to form quasi-planar or planar structures. (2) The ground-state structure of SeB₉⁻ is a three-dimensional, mushroom-shaped, ground-state structure, and it possesses the largest HOMO–LUMO gap of 5.08 eV, which shows the superior chemical stability. (3) AdNDP bonding analyses reveal that SeB₈ is doubly aromatic, with six delocalized σ and six delocalized π electrons, whereas SeB₉⁻ is doubly antiaromatic, with twelve delocalized σ and four delocalized π electrons. Similarly, SeB₁₂ is doubly aromatic, with fourteen delocalized σ and six delocalized π electrons. (4) ELF analysis shows that SeB_n^0/− (n = 3–16) clusters have different local electron delocalization and whole-electron delocalization effects. (5) SeB_n⁻ (n = 3–16) have different photoelectron spectra, and especially the first several peaks can be used for the identification of SeB_n⁻ (n = 3–16). This research has enriched the structures of doped boron clusters.

Author Contributions

Conceptualization, S.-X.L. and Z.-W.L.; methodology, Y.-J.Y. and S.-X.L.; software, S.-X.L.; formal analysis, Z.-W.L.; investigation, S.-X.L.; data processing, Y.-J.Y.; writing—original draft preparation, Y.-J.Y.; writing—review and editing, S.-X.L. and Y.-J.Y.; supervision, D.-L.C.; funding acquisition, D.-L.C. and Y.-J.Y. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available in the article and Supplementary Materials.

Conflicts of Interest

There are no conflicts of interest to declare.

Sample Availability

Samples of the compounds are available from the authors.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures

Figure 1. Structures of SeBn. (a) SeB3 C2V; (b) SeB4 Cs; (c) SeB5 Cs; (d) SeB6 Cs; (e) SeB7 Cs; (f) SeB8 C2V; (g) SeB9 Cs; (h) SeB10; (i) SeB11 Cs; (j) SeB12 Cs; (k) SeB13 C1; (l) SeB14 Cs; (m) SeB15 I C1; (n) SeB15 II C1; (o) SeB16 C1.

Figure 2. Structures of SeBn−. (a) SeB3− C2V; (b) SeB4− Cs; (c) SeB5− Cs; (d) SeB6− C1; (e) SeB7− C2V; (f) SeB8− C2V; (g) SeB9− C6V; (h) SeB10− C1; (i) SeB11− Cs; (j) SeB12− C2V; (k) SeB13− C1; (l) SeB14− Cs; (m) SeB15− I C1; (n) SeB15− II C1; (o) SeB16− C1.

Figure 3. Bonding patterns of SeB8. ON is occupation number and the orange ball is Se atom. (a) 1 × 1c − 2e, ON = 1.9599 |e|; (b) 8 × 2c − 2e σ bonds, ON = 1.9277 − 1.9475 |e|; (c) 1 × 3c − 2e π bond, ON = 1.9653 |e|; (d) 1 × 3c − 2e σ bond, ON = 1.7792 |e|; (e) 2 × 4c − 2e σ bonds, ON = 1.8980 |e|; (f) 1 × 5c − 2e π bond, ON = 1.9445 |e|; (g) 1 × 5c − 2e π bond, ON = 1.9445 |e|.

Figure 4. Bonding patterns of SeB9−. ON is occupation number and the orange ball is Se atom. (a) 1 × 1c − 2e, ON = 1.9644 |e|; (b) 1 × 2c − 2e σ bond, ON = 1.9965 |e|; (c) 1 × 2c − 2e σ bond, ON = 1.9523 |e|; (d) 1 × 2c − 2e π bond, ON = 1.9884 |e|; (e) 1 × 2c − 2e π bond, ON = 1.9884 |e|; (f) 6 × 2c − 2e σ bonds, ON = 1.9247 |e|; (g) 6 × 3c − 2e σ bonds, ON = 1.7547 |e|.

Figure 5. Bonding patterns of SeB12. ON is occupation number and the orange ball is Se atom. (a) 1 × 1c − 2e, ON = 1.9731 |e|; (b) 10 × 2c − 2e σ bonds, ON = 1.8571 − 1.9418 |e|; (c) 1 × 3c − 2e π bond, ON = 1.9823 |e|; (d) 7 × 3c − 2e σ bonds, ON = 1.6403 − 1.9246 |e|; (e) 2 × 5c − 2e π bonds, ON = 1.8623 |e|.

Figure 6. Photoelectron spectra at the PBE0/6-311 + G * level. (a) SeB3−; (b) SeB4−; (c) SeB5−; (d) SeB6−; (e) SeB7−; (f) SeB8−; (g) SeB9−; (h) SeB10−; (i) SeB11−; (j) SeB12−; (k) SeB13−; (l) SeB14−; (m) SeB15−; (n) SeB16−.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/molecules28010357/s1, Figures S1–28: Low-lying isomers of doped boron clusters SeB_n^0/− (n = 3–16); Figures S29–31: Electron localization function (ELF) of SeB_n^0/− (n = 3–16); Figure S32: Spin density of open-shell doped boron clusters.

References

1. Boustani, I. Systematic ab initio investigation of bare boron clusters: Determination of the geometryand electronic structures of Bn (n = 2 − 14). Phys. Rev. B; 1997; 55, pp. 16426-16438. [DOI: https://dx.doi.org/10.1103/PhysRevB.55.16426]

2. Zhai, H.-J.; Wang, L.-S.; Alexandrova, A.N.; Boldyrev, A.I. Electronic structure and chemical bonding of B₅⁻ and B₅ by photoelectron spectroscopy andab initiocalculations. J. Chem. Phys.; 2002; 117, pp. 7917-7924. [DOI: https://dx.doi.org/10.1063/1.1511184]

3. Zhai, H.J.; Kiran, B.; Li, J.; Wang, L.S. Hydrocarbon analogues of boron clusters--planarity, aromaticity and antiaromaticity. Nat. Mater.; 2003; 2, pp. 827-833. [DOI: https://dx.doi.org/10.1038/nmat1012]

4. Kiran, B.; Bulusu, S.; Zhai, H.J.; Yoo, S.; Zeng, X.C.; Wang, L.S. Planar-to-tubular structural transition in boron clusters: B₂₀ as the embryo of single-walled boron nanotubes. Proc. Natl. Acad. Sci. USA; 2005; 102, pp. 961-964. [DOI: https://dx.doi.org/10.1073/pnas.0408132102]

5. Bean, D.E.; Fowler, P.W. Double Aromaticity in “Boron Toroids”. J. Phys. Chem. C; 2009; 113, pp. 15569-15575. [DOI: https://dx.doi.org/10.1021/jp905926j]

6. Chen, Q.; Wei, G.F.; Tian, W.J.; Bai, H.; Liu, Z.P.; Zhai, H.J.; Li, S.D. Quasi-planar aromatic B₃₆ and B₃₆^- clusters: All-boron analogues of coronene. Phys. Chem. Chem. Phys.; 2014; 16, pp. 18282-18287. [DOI: https://dx.doi.org/10.1039/C4CP02032D] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/25058415]

7. Sergeeva, A.P.; Popov, I.A.; Piazza, Z.A.; Li, W.L.; Romanescu, C.; Wang, L.S.; Boldyrev, A.I. Understanding boron through size-selected clusters: Structure, chemical bonding, and fluxionality. Acc. Chem. Res.; 2014; 47, pp. 1349-1358. [DOI: https://dx.doi.org/10.1021/ar400310g]

8. Jian, T.; Chen, X.; Li, S.D.; Boldyrev, A.I.; Li, J.; Wang, L.S. Probing the structures and bonding of size-selected boron and doped-boron clusters. Chem. Soc. Rev.; 2019; 48, pp. 3550-3591. [DOI: https://dx.doi.org/10.1039/C9CS00233B] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/31120469]

9. Casillas, R.; Baruah, T.; Zope, R.R. Geometry and electronic structure of neutral and charged B₂₁ clusters. Chem. Phys. Lett.; 2013; 557, pp. 15-18. [DOI: https://dx.doi.org/10.1016/j.cplett.2012.10.076]

10. Pham, H.T.; Duong, L.V.; Pham, B.Q.; Nguyen, M.T. The 2D-to-3D geometry hopping in small boron clusters: The charge effect. Chem. Phys. Lett.; 2013; 577, pp. 32-37. [DOI: https://dx.doi.org/10.1016/j.cplett.2013.05.041]

11. Lv, J.; Wang, Y.; Zhu, L.; Ma, Y. B₃₈: An all-boron fullerene analogue. Nanoscale; 2014; 6, pp. 11692-11696. [DOI: https://dx.doi.org/10.1039/C4NR01846J] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/24993287]

12. Zhai, H.J.; Zhao, Y.F.; Li, W.L.; Chen, Q.; Bai, H.; Hu, H.S.; Piazza, Z.A.; Tian, W.J.; Lu, H.G.; Wu, Y.B. et al. Observation of an all-boron fullerene. Nat. Chem.; 2014; 6, pp. 727-731. [DOI: https://dx.doi.org/10.1038/nchem.1999]

13. Bai, H.; Chen, Q.; Zhai, H.J.; Li, S.D. Endohedral and exohedral metalloborospherenes: M@B₄₀ (M=Ca, Sr) and M&B₄₀ (M=Be, Mg). Angew. Chem. Int. Ed.; 2015; 54, pp. 941-945.

14. Li, S.-X.; Zhang, Z.-P.; Long, Z.-W.; Qin, S.-J. Structures, stabilities and spectral properties of metalloborospherenes MB₄₀^0/− (M = Cu, Ag, and Au). RSC Adv.; 2017; 7, pp. 38526-38537. [DOI: https://dx.doi.org/10.1039/C7RA05932A]

15. Dong, H.; Hou, T.; Lee, S.T.; Li, Y. New Ti-decorated B₄₀ fullerene as a promising hydrogen storage material. Sci. Rep.; 2015; 5, 9952. [DOI: https://dx.doi.org/10.1038/srep09952]

16. An, Y.; Zhang, M.; Wu, D.; Fu, Z.; Wang, T.; Xia, C. Electronic transport properties of the first all-boron fullerene B₄₀ and its metallofullerene Sr@B₄₀. Phys. Chem. Chem. Phys.; 2016; 18, pp. 12024-12028. [DOI: https://dx.doi.org/10.1039/C6CP01096B]

17. Bai, H.; Bai, B.; Zhang, L.; Huang, W.; Mu, Y.W.; Zhai, H.J.; Li, S.D. Lithium-Decorated Borospherene B₄₀: A Promising Hydrogen Storage Medium. Sci. Rep.; 2016; 6, 35518. [DOI: https://dx.doi.org/10.1038/srep35518]

18. Shakerzadeh, E.; Biglari, Z.; Tahmasebi, E. M@B₄₀ (M = Li, Na, K) serving as a potential promising novel NLO nanomaterial. Chem. Phys. Lett.; 2016; 654, pp. 76-80. [DOI: https://dx.doi.org/10.1016/j.cplett.2016.05.014]

19. Tang, C.; Zhang, X. The hydrogen storage capacity of Sc atoms decorated porous boron fullerene B₄₀: A DFT study. Int. J. Hydrogen Energ.; 2016; 41, pp. 16992-16999. [DOI: https://dx.doi.org/10.1016/j.ijhydene.2016.07.118]

20. Li, S.; Zhang, Z.; Long, Z.; Chen, D. Structures, Stabilities, and Spectral Properties of Endohedral Borospherenes M@B₄₀ ^0/- (M = H₂, HF, and H₂O). ACS Omega; 2019; 4, pp. 5705-5713. [DOI: https://dx.doi.org/10.1021/acsomega.9b00209]

21. Li, S.X.; Zhang, Z.P.; Long, Z.W.; Chen, D.L. Structures, Electronic, and Spectral Properties of Doped Boron Clusters MB₁₂^0/− (M = Li, Na, and K). ACS Omega; 2020; 5, pp. 20525-20534. [DOI: https://dx.doi.org/10.1021/acsomega.0c02693]

22. Mannix, A.J.; Zhou, X.F.; Kiraly, B.; Wood, J.D.; Alducin, D.; Myers, B.D.; Liu, X.; Fisher, B.L.; Santiago, U.; Guest, J.R. et al. Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs. Science; 2015; 350, pp. 1513-1516. [DOI: https://dx.doi.org/10.1126/science.aad1080]

23. Li, Q.; Kolluru, V.S.C.; Rahn, M.S.; Schwenker, E.; Li, S.; Hennig, R.G.; Darancet, P.; Chan, M.K.Y.; Hersam, M.C. Synthesis of borophane polymorphs through hydrogenation of borophene. Science; 2021; 371, pp. 1143-1148. [DOI: https://dx.doi.org/10.1126/science.abg1874] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/33707261]

24. Popov, I.A.; Li, W.L.; Piazza, Z.A.; Boldyrev, A.I.; Wang, L.S. Complexes between planar boron clusters and transition metals: A photoelectron spectroscopy and ab initio study of CoB₁₂⁻ and RhB₁₂⁻. J. Phys. Chem. A; 2014; 118, pp. 8098-8105. [DOI: https://dx.doi.org/10.1021/jp411867q] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/24428747]

25. Liang, W.Y.; Das, A.; Dong, X.; Cui, Z.H. Lithium doped tubular structure in LiB₂₀ and LiB₂₀^-: A viable global minimum. Phys. Chem. Chem. Phys.; 2018; 20, pp. 16202-16208. [DOI: https://dx.doi.org/10.1039/C8CP01376D] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/29862386]

26. Wang, W.; Guo, Y.-D.; Yan, X.-H. The spin-dependent transport of transition metal encapsulated B₄₀ fullerene. RSC Adv.; 2016; 6, pp. 40155-40161. [DOI: https://dx.doi.org/10.1039/C6RA00179C]

27. Saha, R.; Kar, S.; Pan, S.; Martinez-Guajardo, G.; Merino, G.; Chattaraj, P.K. A Spinning Umbrella: Carbon Monoxide and Dinitrogen Bound MB₁₂^- Clusters (M = Co, Rh, Ir). J. Phys. Chem. A; 2017; 121, pp. 2971-2979. [DOI: https://dx.doi.org/10.1021/acs.jpca.6b12232]

28. Li, S.-X.; Chen, D.-L.; Zhang, Z.-P.; Long, Z.-W. Ground state structures and properties of Be atom doped boron clusters BeBn (n = 10 − 15). Acta. Physica. Sinica.; 2020; 69, 193101. [DOI: https://dx.doi.org/10.7498/aps.69.20200756]

29. Cheung, L.F.; Kocheril, G.S.; Czekner, J.; Wang, L.S. Observation of Mobius Aromatic Planar Metallaborocycles. J. Am. Chem. Soc.; 2020; 142, pp. 3356-3360. [DOI: https://dx.doi.org/10.1021/jacs.9b13417]

30. Popov, I.A.; Jian, T.; Lopez, G.V.; Boldyrev, A.I.; Wang, L.S. Cobalt-centred boron molecular drums with the highest coordination number in the CoB₁₆⁻ cluster. Nat. Commun.; 2015; 6, 8654. [DOI: https://dx.doi.org/10.1038/ncomms9654]

31. Jian, T.; Li, W.L.; Popov, I.A.; Lopez, G.V.; Chen, X.; Boldyrev, A.I.; Li, J.; Wang, L.S. Manganese-centered tubular boron cluster—MnB16 (-): A new class of transition-metal molecules. J. Chem. Phys.; 2016; 144, 154310. [DOI: https://dx.doi.org/10.1063/1.4946796] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/27389223]

32. Chen, T.T.; Li, W.L.; Bai, H.; Chen, W.J.; Dong, X.R.; Li, J.; Wang, L.S. ReB₈^- and ReB₉^-: New Members of the Transition-Metal-Centered Borometallic Molecular Wheel Family. J. Phys. Chem. A; 2019; 123, pp. 5317-5324. [DOI: https://dx.doi.org/10.1021/acs.jpca.9b03942] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/31204479]

33. Cheung, L.F.; Czekner, J.; Kocheril, G.S.; Wang, L.S. ReB₆^-: A Metallaboron Analog of Metallabenzenes. J. Am. Chem. Soc.; 2019; 141, pp. 17854-17860. [DOI: https://dx.doi.org/10.1021/jacs.9b09110]

34. Chen, T.T.; Li, W.L.; Chen, W.J.; Yu, X.H.; Dong, X.R.; Li, J.; Wang, L.S. Spherical trihedral metallo-borospherenes. Nat. Commun.; 2020; 11, 2766. [DOI: https://dx.doi.org/10.1038/s41467-020-16532-x] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/32488008]

35. Cheung, L.F.; Kocheril, G.S.; Czekner, J.; Wang, L.S. MnB₆^-: An Open-Shell Metallaboron Analog of 3d Metallabenzenes. J. Phys. Chem. A; 2020; 124, pp. 2820-2825. [DOI: https://dx.doi.org/10.1021/acs.jpca.0c00949] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/32207624]

36. Chen, W.J.; Kulichenko, M.; Choi, H.W.; Cavanagh, J.; Yuan, D.F.; Boldyrev, A.I.; Wang, L.S. Photoelectron Spectroscopy of Size-Selected Bismuth-Boron Clusters: BiB_n⁻ (n = 6 − 8). J. Phys. Chem. A; 2021; 125, pp. 6751-6760. [DOI: https://dx.doi.org/10.1021/acs.jpca.1c05846]

37. Jiang, Z.Y.; Chen, T.T.; Chen, W.J.; Li, W.L.; Li, J.; Wang, L.S. Expanded Inverse-Sandwich Complexes of Lanthanum Borides: La₂B₁₀⁻ and La₂B₁₁. J. Phys. Chem. A; 2021; 125, pp. 2622-2630. [DOI: https://dx.doi.org/10.1021/acs.jpca.1c01149]

38. Barroso, J.; Pan, S.; Merino, G. Structural transformations in boron clusters induced by metal doping. Chem. Soc. Rev.; 2022; 51, pp. 1098-1123. [DOI: https://dx.doi.org/10.1039/D1CS00747E] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35029622]

39. Chacko, S.; Kanhere, D.G.; Boustani, I. Ab initiodensity functional investigation of B₂₄ clusters: Rings, tubes, planes, and cages. Phys. Rev. B; 2003; 68, 035414. [DOI: https://dx.doi.org/10.1103/PhysRevB.68.035414]

40. Liang, W.; Das, A.; Dong, X.; Wang, M.; Cui, Z. Structural and electronic properties of MB₂₂⁻ (M = Na, K) clusters: Tubular boron versus quasi-planar boron forms. New J. Chem.; 2019; 43, pp. 6507-6512. [DOI: https://dx.doi.org/10.1039/C9NJ00661C]

41. Lv, J.; Wang, Y.; Zhang, L.; Lin, H.; Zhao, J.; Ma, Y. Stabilization of fullerene-like boron cages by transition metal encapsulation. Nanoscale; 2015; 7, pp. 10482-10489. [DOI: https://dx.doi.org/10.1039/C5NR01659B] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/26007319]

42. Yang, Y.J.; Li, S.X.; Chen, D.L.; Long, Z.W. Structural and Electronic Properties of Single-Atom Transition Metal-Doped Boron Clusters MB₂₄ (M = Sc, V, and Mn). ACS Omega; 2021; 6, pp. 30442-30450. [DOI: https://dx.doi.org/10.1021/acsomega.1c03740]

43. Li, S.X.; Yang, Y.J.; Chen, D.L.; Long, Z.W. 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). RSC Adv.; 2022; 12, pp. 16706-16716. [DOI: https://dx.doi.org/10.1039/D2RA02500K]

44. Dordevic, S.; Radenkovic, S. Electronic structure, stability, and aromaticity of M₂B₆ (M = Mg, Ca, Sr, and Ba): An interplay between spin pairing and electron delocalization. Phys. Chem. Chem. Phys.; 2022; 24, pp. 5833-5841. [DOI: https://dx.doi.org/10.1039/D1CP04791D] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35225998]

45. Dordevic, S.; Radenkovic, S. Spatial and Electronic Structures of BeB₈ and MgB₈: How far Does the Analogy Go?. Chemphyschem; 2022; 23, e202200070. [DOI: https://dx.doi.org/10.1002/cphc.202200070]

46. Alivisatos, A.P. Semiconductor Clusters, Nanocrystals, and Quantum Dots. Science; 1996; 271, pp. 933-937. [DOI: https://dx.doi.org/10.1126/science.271.5251.933]

47. Kasuya, A.; Sivamohan, R.; Barnakov, Y.A.; Dmitruk, I.M.; Nirasawa, T.; Romanyuk, V.R.; Kumar, V.; Mamykin, S.V.; Tohji, K.; Jeyadevan, B. et al. Ultra-stable nanoparticles of CdSe revealed from mass spectrometry. Nat. Mater.; 2004; 3, pp. 99-102. [DOI: https://dx.doi.org/10.1038/nmat1056]

48. Michalet, X.; Pinaud, F.F.; Bentolila, L.A.; Tsay, J.M.; Doose, S.; Li, J.J.; Sundaresan, G.; Wu, A.M.; Gambhir, S.S.; Weiss, S. Quantum dots for live cells, in vivo imaging, and diagnostics. Science; 2005; 307, pp. 538-544. [DOI: https://dx.doi.org/10.1126/science.1104274] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/15681376]

49. Medintz, I.L.; Uyeda, H.T.; Goldman, E.R.; Mattoussi, H. Quantum dot bioconjugates for imaging, labelling and sensing. Nat. Mater.; 2005; 4, pp. 435-446. [DOI: https://dx.doi.org/10.1038/nmat1390]

50. Lv, J.; Wang, Y.; Zhu, L.; Ma, Y. Particle-swarm structure prediction on clusters. J. Chem. Phys.; 2012; 137, 084104. [DOI: https://dx.doi.org/10.1063/1.4746757]

51. Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys.; 1999; 110, pp. 6158-6170. [DOI: https://dx.doi.org/10.1063/1.478522]

52. Alexandrova, A.N.; Boldyrev, A.I.; Zhai, H.-J.; Wang, L.-S. All-boron aromatic clusters as potential new inorganic ligands and building blocks in chemistry. Coord. Chem. Rev.; 2006; 250, pp. 2811-2866. [DOI: https://dx.doi.org/10.1016/j.ccr.2006.03.032]

53. Sergeeva, A.P.; Zubarev, D.Y.; Zhai, H.-J.; Boldyrev, A.I.; Wang, L.-S. A Photoelectron Spectroscopic and Theoretical Study of B₁₆⁻ and B₁₆²⁻: An All-Boron Naphthalene. J. Am. Chem. Soc.; 2008; 130, pp. 7244-7246. [DOI: https://dx.doi.org/10.1021/ja802494z] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/18479137]

54. Becke, A.D.; Edgecombe, K.E. A simple measure of electron localization in atomic and molecular systems. J. Chem. Phys.; 1990; 92, pp. 5397-5403. [DOI: https://dx.doi.org/10.1063/1.458517]

55. Chen, Q.; Li, W.L.; Zhao, Y.F.; Zhang, S.Y.; Hu, H.S.; Bai, H.; Li, H.R.; Tian, W.J.; Lu, H.G.; Zhai, H.J. et al. Experimental and theoretical evidence of an axially chiral borospherene. ACS Nano; 2015; 9, pp. 754-760. [DOI: https://dx.doi.org/10.1021/nn506262c]

56. Bauernschmitt, R.; Ahlrichs, R. Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory. Chem. Phys. Lett.; 1996; 256, pp. 454-464. [DOI: https://dx.doi.org/10.1016/0009-2614(96)00440-X]

57. Dong, X.; Jalife, S.; Vasquez-Espinal, A.; Barroso, J.; Orozco-Ic, M.; Ravell, E.; Cabellos, J.L.; Liang, W.Y.; Cui, Z.H.; Merino, G. Li₂B₂₄: The simplest combination for a three-ring boron tube. Nanoscale; 2019; 11, pp. 2143-2147. [DOI: https://dx.doi.org/10.1039/C8NR09173K]

58. Dong, X.; Liu, Y.Q.; Liu, X.B.; Pan, S.; Cui, Z.H.; Merino, G. Be₄B₁₂⁺: A Covalently Bonded Archimedean Beryllo-Borospherene. Angew. Chem. Int. Ed.; 2022; 61, e202208152. [DOI: https://dx.doi.org/10.1002/anie.202208152]

59. Wei, D.; Ren, M.; Lu, C.; Bi, J.; Maroulis, G. A quasi-plane IrB₁₈^- cluster with high stability. Phys. Chem. Chem. Phys.; 2020; 22, pp. 5942-5948. [DOI: https://dx.doi.org/10.1039/C9CP06330G]

60. Ren, M.; Jin, S.; Wei, D.; Jin, Y.; Tian, Y.; Lu, C.; Gutsev, G.L. NbB₁₂^-: A new member of half-sandwich type doped boron clusters with high stability. Phys. Chem. Chem. Phys.; 2019; 21, pp. 21746-21752. [DOI: https://dx.doi.org/10.1039/C9CP03496J]

61. Tian, Y.; Wei, D.; Jin, Y.; Barroso, J.; Lu, C.; Merino, G. Exhaustive exploration of MgBn (n = 10–20) clusters and their anions. Phys. Chem. Chem. Phys.; 2019; 21, pp. 6935-6941. [DOI: https://dx.doi.org/10.1039/C9CP00201D] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/30865191]

62. Krishnan, R.; Binkley, J.S.; Seeger, R.; Pople, J.A. Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys.; 1980; 72, pp. 650-654. [DOI: https://dx.doi.org/10.1063/1.438955]

63. Le Chen, B.; Sun, W.G.; Kuang, X.Y.; Lu, C.; Xia, X.X.; Shi, H.X.; Maroulis, G. Structural Stability and Evolution of Medium-Sized Tantalum-Doped Boron Clusters: A Half-Sandwich-Structured TaB₁₂^- Cluster. Inorg. Chem.; 2018; 57, pp. 343-350. [DOI: https://dx.doi.org/10.1021/acs.inorgchem.7b02585]

64. Li, P.; Du, X.; Wang, J.J.; Lu, C.; Chen, H. Probing the Structural Evolution and Stabilities of Medium-Sized MoBn^0/– Clusters. J. Phys. Chem. C; 2018; 122, pp. 20000-20005. [DOI: https://dx.doi.org/10.1021/acs.jpcc.8b05759]

65. Jin, S.; Chen, B.; Kuang, X.; Lu, C.; Sun, W.; Xia, X.; Gutsev, G.L. Structural and Electronic Properties of Medium-Sized Aluminum-Doped Boron Clusters AlBn and Their Anions. J. Phys. Chem. C; 2019; 123, pp. 6276-6283. [DOI: https://dx.doi.org/10.1021/acs.jpcc.9b00291]

66. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Petersson, G.A.; Nakatsuji, H. et al. Gaussian 16; Gaussian Inc.: Wallingford, CT, USA, 2016.

67. Lu, T.; Chen, F. Multiwfn: A multifunctional wavefunction analyzer. J. Comput. Chem.; 2012; 33, pp. 580-592. [DOI: https://dx.doi.org/10.1002/jcc.22885] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/22162017]

68. Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graph.; 1996; 14, pp. 33-38. [DOI: https://dx.doi.org/10.1016/0263-7855(96)00018-5] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/8744570]