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

Abstract

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 BeB_n^0/− (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 C_2v 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.

Introduction

Molecular geometric configuration and attributes of pure^1–3 and doped boron clusters^4–9 have drawn much attention in recent years. The use of boron clusters as subunits in novel bioactive architectures with potential use as drugs is of primary importance¹⁰. From a Materials Science perspective the emergence of graphene¹¹ and synthetic two-dimensional structures as silicene^12,13, germanene¹⁴, stanene¹⁵, antimonene¹⁶, bismuthene^17,18 and tellurene¹⁹ have opened new pathways for modern research^20–22. Relying on experimental and theoretical work, Hersam’s group²³ have confirmed and established the synthesis of 2D boron polymorphs (borophene) characterized by anisotropy and metallicity, and paved the way to investigations leading to the discovery of novel materials. Recently, it was reported that magnesium diboride (MgB₂), which consists of graphene-like honeycomb networks of sandwiched boron, shows superconductivity²⁴. It should be noted that beryllium has the same valence electrons number with magnesium. Be-doped boron clusters appear to have significant potential candidate as layered 2D materials^25–28. This certainly gives reason for more systematic investigations.

Boron is the lightest metalloid chemical element, the lowest-Z element²³ with a trivalent outer shell^29,30. Consequently, boron does not form closed-shell electronic structures via conventional covalent bonds^31–33, but favors delocalized chemical bonds with electron pairs shared among three (or more) atoms instead. Recently, systematic investigations of pure boron clusters in term of the anisotropy and polymorphism have brought forth new significant findings leading to the design of new borides. A selection of characteristic architectures of pure boron clusters includes: tank tread³⁴, wankel motor^35–39, wheel-like⁴⁰, boron nanotubes⁴¹, B₁₂ icosahedra⁴², buckyballs⁴³, fullerene⁴⁴, B₃₆ with hexagonal holes (HHs)⁴⁵, naphthalene⁴⁶, borospherene⁴⁷ and more. Co and Rh doped B₁₂⁻ clusters featured half-sandwich structure has been reported by Wang and co-workers⁴⁸. There followed the Co-centered boron molecular drums structure for the CoB₁₆⁻ cluster⁴⁹. Additional work by the same group includes the Mn-centered tubular boron cluster for MnB₁₆⁻, a drum and quasi-planar structure for RhB₁₈⁻ and the planar CoB₁₈^−50–52. Very recently, Cui and co-workers reported tubular structures for LiB₂₀ and LiB₂₀⁻⁵³. These impressive findings reveal that single metal atom doping leads to new opportunities for the use of boron clusters as geometrical ligands.

Several theoretical investigations of boron clusters with doping transition-element serve as the object of discovering new materials recently^54,55. The alkaline-earth metal-doped boron clusters and Be-doped ones in particular have been systematically studied^56–58. Nevertheless, more systematic work is needed to systematize and deepen our understanding of Be-doped boron clusters. To fill the existing lacunae and bring forth new insights on medium-sized Be-doped boron clusters, we have thoroughly investigated BeB_n^0/− clusters.

Results and Discussion

Geometric configurations and photoelectron spectra

The determined low-energy BeB_n^0/− (n = 10–20) are showed in Figs 1 and 2. We labeled each isomer using nt/t⁻ (t = a, b, c), therein nt stands for the neutral clusters and nt⁻ stands for the anionic clusters. The lowest-energy structures BeB_n^0/− (n = 10, 12, 13, 14, 15, 16) and BeB₁₁⁻ are quasi-planar structures. The lowest-energy structure BeB₁₁ shows a half-sandwich structure consisting of one half-sandwich structure composed by eleven boron atoms and one Be atom in the center. The lowest-energy structures BeB₁₇^0/− like a trapezoid and its center portion appear on the convex. The lowest-energy structure of BeB₁₈ and BeB₂₀⁻ are 3D cage-like structure. The lowest-energy structure BeB₁₈⁻ with a parallelogram located in the center displays a planar structure. The ground-state structures BeB₁₉^0/− and BeB₂₀ can be viewed as plate-like structures (in Figs S4 and S5 of Supplementary Information). The lowest-energy structures of BeB_n^0/− clusters are generally evolutional from the quasi-planar to 3D cage-like or plate-like structures. For plane and quasi-planar structures, the coordinate number of Be atom is interesting. The BeB_n^0/− (n = 10, 12, 14, 16) and BeB₁₈⁻ feature heptacoordinate and the BeB₁₁⁻ and BeB_n^0/− (n = 13, 15) possess octacoordinate, while the BeB₁₇^0/− are quasi-planar hexacoordinate structures due to the attribute of Be atom^59,60. This evident structures evolution pattern contributes to form plane clusters of BeB_n^0/−, which are potential two-dimensional material. The metastable of nb/b⁻ (n = 10–13) clusters display half-sandwich architectural feature, while when the cluster sizes increase n ≥ 14, the clusters are varies cage-like, quasi-planar and plate-like structures. The nc/c⁻ (n = 10–18) clusters display half-sandwich, plane, cage-like structures, different from the larger size isomers (n ≥ 19) are double-ring and plate-like structures.

Figure 1.

Low-lying geometrical structures of BeB_n (n = 10–20) clusters. “a” stands for the lowest-energy structures. “b” and “c” stand for the metastable state structures.

Figure 2.

Low- lying geometrical structures of BeB_n⁻ (n = 10–20) clusters. “a” stands for the lowest-energy structures. “b” and “c” stand for the metastable state structures.

To get a deep understand to differences between different metal-doped clusters, we provide a comparison for doped boron clusters. The transition-metal doped boron clusters, NbB₁₀⁻ and TaB₁₀⁻, are wheels structures with high coordination number⁴, while BeB₁₀^0/− clusters are quasi-planar structures with one B-Be unit inside. For doped B₁₂ clusters, the prior works report that half-sandwich structures VB₁₀⁻, CoB₁₂⁻ and RhB₁₂⁻ clusters^4,48 are different with BeB₁₂^0/− clusters, which are standard quasi-planar structures featuring a triangle in the center. Compare with drum-like CoB₁₆⁻ cluster⁴⁹ and tubular-like MnB₁₆⁻ cluster⁵⁰, the ground state BeB₁₆^0/− display quasi-plane structures. It is worth noting that adjacent alkali element Lithium doped into B₂₀ display highly symmetrical tubular LiB₂₀^0/− clusters⁵³. We report BeB₂₀ and BeB₂₀⁻ are plate-like and 3D cage-like structures, respectively. The reason for the structural differences of same-sized clusters may be doped-metals have different valence electron and atomic radius⁶¹.

Photoelectron spectra (PES) analysis, obtained via a TD–DFT approach, is of absolute importance for the assessment of the nature of the determined lowest-energy structures. We simulated the PES of BeB_n⁻ clusters and the results are displayed in Fig. 3. Our group also simulated the PES of some other cluster system using the method^62,63. The PES pattern of the BeB₁₀⁻ possesses five peaks located at 3.26, 3.75, 4.18, 4.75 and 5.77 eV. The PES of BeB₁₁⁻ possesses four clear peaks at 3.45, 4.21, 4.59, and 5.01 eV, with B and C peaks forming a broad bond. For BeB₁₂⁻, we observe three major peaks at 2.90, 4.21 and 4.50 eV, wherein the double-peak feature (A and B) is prominent and broad. The BeB₁₃⁻ PES contains five major peaks at 3.16, 3.49, 4.32, 4.75 and 5.22 eV. The relevant broad bond is found at triple-peak feature consisted of peaks B, C and D. Five peaks are observed for BeB₁₄⁻ at 3.33, 3.86, 4.16, 4.63 and 5.45 eV. The peaks A, B and C constitute a relatively wide bond. For BeB₁₅⁻ there are five major peaks at 3.46, 4.28, 4.64, 5.06 and 5.82 eV, whereas the BeB₁₆⁻ spectrum has only two sparse peaks at 4.08 and 5.25 eV. The well-structure spectrum of BeB₁₇⁻ shows five peaks at 3.90, 4.32, 4.79, 5.13 and 5.49 eV, suggesting a greater span triple-peak feature (B, C and D). A crowded spectrum pattern BeB₁₈⁻ has five peaks observed at 3.59, 3.98, 4.21, 5.13 and 5.57 eV, with two broad bonds. There are five peaks in the spectrum of BeB₁₉⁻ at 3.63, 4.73, 5.13, 5.51 and 5.82 eV, therein an unfitted bond is located at the range between 4.5 to 6.0 eV. The spectrum of BeB₂₀⁻ possesses five peaks at 2.59, 3.36, 4.43, 4.85 and 5.79 eV.

Figure 3.

The simulated PES of BeB_n⁻ (n = 10–20) clusters.

Relative stabilities

We characterize the inherent stability of the BeB_n^0/− (n = 10–20) clusters by computing the E_b (eV), according to the following formula:

$$E_b(Be{B}_n)=[nE(B)+E(Be)-E(Be{B}_n)]/(n+1)$$ 1

$$E_b(Be{B}_n^{-})=[(n-1)E(B)+E(B^{-})+E(Be)-E(Be{B}_n^{-})]/(n+1)$$ 2

The average binding energy (E_b) of a cluster is clearly a measure of its thermodynamic stability. An increase in E_b means a higher stability. The value of neutral BeB_n clusters less than the value of their anionic counterparts in Fig. S1(a), indicating that the anionic clusters feature higher thermodynamically. The trend of the curves for both neutral and anionic are gradually upward indicated that the high thermodynamic stability with the cluster size increases. The second vital physical quantity we take into account here is the Δ²E. The relevant formulae are

$${\mathrm{\Delta }}^{\mathrm{2}}E(Be{B}_n)=E(Be{B}_{n-1})+E(Be{B}_{n+1})-2E(Be{B}_n)$$ 3

$${\Delta }^{2}E(Be{B_n}^{-})=E(Be{B}_{n-1}^{-})+E(Be{B}_{n+1}^{-})-2E(Be{B}_n^{-})$$ 4

As inferred from Fig. S1(b), both of the neutral and anionic curves show odd-even alteration. The evident peak values generated at n = even number, suggest that clusters with the even boron atoms feature higher stability than which with odd boron atoms. Finally, we discuss the HOMO-LUMO energy gap (E_gap) which provides a valuable index of the stability of clusters. Large values indicate strong chemical stability. We summarize the E_gap values of the lowest-energy BeB_n^0/− clusters in Table 1, and the line chart is displayed in Fig. S1(c). From the latter we can clearly see some apparent local maxima: BeB₁₁ and BeB₁₆⁻, which means that they feature higher stability than the others. Consequently, based on the above analyses, we can reach a definitive conclusion that the BeB₁₆⁻ can seen as a “magic” cluster.

Table 1.

The calculated electronic states, symmetries, average binding energies (E_b, in eV) and energy gaps (E_gap, in eV) of BeB_n^0/− clusters in the size range of n = 10–20.

BeBn					BeBn−
n	Sta.	Sym.	Eb	Egap	Sta.	Sym.	Eb	Egap
10	1A′	Cs	4.69	2.93	2A″	Cs	5.06	2.81
11	2A′	Cs	4.73	3.30	1A1	C2v	5.08	2.36
12	1A′	Cs	4.87	2.94	2A2	C2v	5.17	1.66
13	2A″	Cs	4.84	1.74	3B2	C2v	5.14	2.17
14	3A″	Cs	4.90	2.47	2A″	Cs	5.23	2.14
15	2A″	Cs	4.93	1.85	1A′	Cs	5.20	1.89
16	1A′	Cs	4.99	1.77	2B2	C2v	5.29	2.93
17	2A′	Cs	5.03	2.17	1A′	Cs	5.30	2.03
18	1A	C1	5.08	2.60	2A	C1	5.32	1.89
19	2A	C1	5.18	1.97	1A	C1	5.25	2.39
20	1A	C1	5.10	2.67	2A′	Cs	5.31	2.09

Chemical banding

To deeply perceive the bonding nature of BeB₁₆⁻ (C_2v symmetry), we display eleven MO figures for BeB₁₆⁻, including one LUMO, one HOMO and nine HOMO-n (n = 1–9) in Fig. 4 by analyzing the chemical bonding. The LUMO, HOMO, HOMO-2, HOMO-5 and HOMO-9 dominated primarily by π_p and π_p^∗ orbitals are a direct interaction 2p orbitals of B atoms. The HOMO-n (n = 1, 4, 8) feature σ_p and σ_p^∗ orbitals. The HOMO-n (n = 3, 6, 7) features σ_p, σ_p^∗, σ_sp and σ_sp^∗ orbitals. AdNDP analysis distributes 51 valence electrons into different regions as reflected by the occupation numbers (ONs) in Fig. 5. We divide it into three sets. The first set consists of twelve 2c-2e (1.79–1.93 |e|) localized σ-bonds. The second set consists of nine delocalized σ-bonds, which are five 3c-2e (1.79–1.86 |e|), two 4c-2e (1.72 |e|), and two 4c-2e (1.79 |e|). The five delocalized π-bonds in last set involving two 4c-2e (1.81 |e|), two 4c-2e (1.83 |e|) and one 17c-2e (2.00 |e|). It is worth nothing that the ON of the 17c-2e π-bonds maintain ON of 2.00 |e|. All values of the ONs listed above ranging from 1.72–2.00 |e| are approaching the ideal value 2.00 |e|, which means that the results we calculate is fairly credible. Furthermore, the ten π electrons conform to the 4n + 2 rule (n = 2), indicating the BeB₁₆⁻ cluster possesses π-aromaticity, which result to the robust relative stability for BeB₁₆⁻ cluster.

Figure 4.

Molecular orbitals for BeB₁₆⁻ cluster corresponding to different energy level.

Figure 5.

AdNDP analysis of BeB₁₆⁻ cluster.

The Wiberg bond index of BeB₁₆⁻, showed in Fig. S2(a), indicate that the bond orders values of B-B (0.13–0.35) greater than the Be-B (0.06–0.11). For Fig. S2(b), the B-B bond lengths (1.54–1.80 Å) are shorter than Be-B bond lengths (1.85–2.03 Å). The results of bond orders and bond lengths show that the peripheral B-B bonds are stronger than the inner Be-B bonds. We have also performed the NPA (natural charge of atom) calculations of BeB_n^0/− in Fig. S3 indicate that electron transfer from Be atom to boron fragment. The NPA data of BeB_n^0/− (n = 10–20) clusters are summarized in Table S1. From what has been discussed, we come to the conclusion that the B-B σ-bonds and the aromaticity decide the high stability of BeB₁₆⁻ cluster. It is worth noting that due to planar structure and chemical bonding characteristics of BeB₁₆⁻ cluster, also inspired by fascinating prospect of two-dimensional monolayer metallo-borophene⁴, we successfully build a schematic of possibility of metallo-borophene (not optimized) based on BeB₁₆⁻ unit cluster presented in Fig. S6 of Supplementary Information, which indicated the BeB₁₆⁻ cluster is a potential motif for metallo-borophene.

Conclusions

In summary, the ground-state BeB_n^0/− (n = 10–20) structure obey the evolution rule: quasi-planar to 3D cage-like or plate-like structures, which the doped Be atom contributed to the plane or quasi-plane structures. We hope that the simulated PES can provide valuable guidance for future research on BeB_n clusters and borophene. Based on the relative stability analysis, the BeB₁₆⁻ cluster characterized by enhanced stability is clearly a “magic” cluster. Chemical bonding analysis indicated that BeB₁₆⁻ cluster adapt π-aromaticity and the strong interaction of B-B σ-bonds which is deemed as the dominant reasons for the inherent stability of BeB₁₆⁻ cluster. The planar BeB₁₆⁻ cluster may serve as a motif for the design of a new boron-based functional material to complement the metallo-borophene effort for synthetic 2D materials development. Our present findings on Be-doped boron clusters should provide valuable information for further explorations of novel cluster architectures.

Computational Methods

We used the CALYPSO code to search the BeB_n^0/− (n = 10–20) clusters. The global explorations of Be-doped boron cluster system was implemented by utilizing particle swarm optimization (PSO) algorithm^64–66. The effectiveness of this structural prediction method, has been successfully tested on the identification of ground-state structures of various systems^67–69. To ensure high efficiency in structure predicting, we proceeded to 50 generations for each size, where each generation contains 30 structures. PSO algorithm produces sixty percent of the structures and the rest is generated randomly. The top fifty low-lying isomers were reoptimized with PBE0⁷⁰ functional and 6–311 + G(d)⁷¹, as performed via Gaussian 09 package⁷². The PES of Be-doped boron clusters was simulated utilizing TD-DFT method⁷³. We then analyzed chemical bonding of BeB₁₆⁻ cluster relying on the NBO and AdNDP methods⁷⁴ at the PBE0/6-311 + G(d) level to display valuable insights into the nature of the bonding by using Multiwfn⁷⁵. The bond orders, bond lengths and NPA are also computed by using the same basis set and method.

Author Contributions

X.Y.K. and C.L. conceived the idea. D.L.K., W.G.S. and C.L. performed the calculations. D.L.K., W.G.S., H.X.S., B.L.C., X.X.X. and G.M. wrote the manuscript. All authors reviewed the manuscript.

Competing Interests

The authors declare no competing interests.

Supplementary information

Supplementary information accompanies this paper at 10.1038/s41598-019-50905-7.