## Introduction

Molecular geometric configuration and attributes of pure1,2,3 and doped boron clusters4,5,6,7,8,9 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 silicene12,13, germanene14, stanene15, antimonene16, bismuthene17,18 and tellurene19 have opened new pathways for modern research20,21,22. 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 materials25,26,27,28. This certainly gives reason for more systematic investigations.

Boron is the lightest metalloid chemical element, the lowest-Z element23 with a trivalent outer shell29,30. Consequently, boron does not form closed-shell electronic structures via conventional covalent bonds31,32,33, 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 motor35,36,37,38,39, 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 CoB1850,51,52. Very recently, Cui and co-workers reported tubular structures for LiB20 and LiB2053. 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 recently54,55. The alkaline-earth metal-doped boron clusters and Be-doped ones in particular have been systematically studied56,57,58. 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 BeBn0/− clusters.

## Results and Discussion

### Geometric configurations and photoelectron spectra

The determined low-energy BeBn0/− (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 BeBn0/− (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 BeB170/− 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 BeB190/− and BeB20 can be viewed as plate-like structures (in Figs S4 and S5 of Supplementary Information). The lowest-energy structures of BeBn0/− 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 BeBn0/− (n = 10, 12, 14, 16) and BeB18 feature heptacoordinate and the BeB11 and BeBn0/− (n = 13, 15) possess octacoordinate, while the BeB170/− are quasi-planar hexacoordinate structures due to the attribute of Be atom59,60. This evident structures evolution pattern contributes to form plane clusters of BeBn0/−, 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.

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 BeB100/− 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 clusters4,48 are different with BeB120/− 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 BeB160/− display quasi-plane structures. It is worth noting that adjacent alkali element Lithium doped into B20 display highly symmetrical tubular LiB200/− 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 BeBn clusters and the results are displayed in Fig. 3. Our group also simulated the PES of some other cluster system using the method62,63. 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.

### Relative stabilities

We characterize the inherent stability of the BeBn0/− (n = 10–20) clusters by computing the Eb (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 (Eb) of a cluster is clearly a measure of its thermodynamic stability. An increase in Eb means a higher stability. The value of neutral BeBn 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

$${\Delta }^{{\rm{2}}}E(Be{B}_{n})=E(Be{B}_{n-1})+E(Be{B}_{n+1})-2E(Be{B}_{n})$$
(3)
$${\varDelta }^{2}E(Be{{B}_{n}}^{-})=E(Be{B}_{n-1}^{-})+E(Be{B}_{n+1}^{-})-2E(Be{B}_{n}^{-})$$
(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 (Egap) which provides a valuable index of the stability of clusters. Large values indicate strong chemical stability. We summarize the Egap values of the lowest-energy BeBn0/− 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.

### Chemical banding

To deeply perceive the bonding nature of BeB16 (C2v 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 πp and πp orbitals are a direct interaction 2p orbitals of B atoms. The HOMO-n (n = 1, 4, 8) feature σp and σp orbitals. The HOMO-n (n = 3, 6, 7) features σp, σp, σsp and σsp 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.

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 BeBn0/− in Fig. S3 indicate that electron transfer from Be atom to boron fragment. The NPA data of BeBn0/ (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 BeBn0/− (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 BeBn 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 BeBn0/− (n = 10–20) clusters. The global explorations of Be-doped boron cluster system was implemented by utilizing particle swarm optimization (PSO) algorithm64,65,66. The effectiveness of this structural prediction method, has been successfully tested on the identification of ground-state structures of various systems67,68,69. 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.