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

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

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][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 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 BeB 11 − are quasi-planar structures. The lowest-energy structure BeB 11 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 BeB 17 0/− like a trapezoid and its center portion appear on the convex. The lowest-energy structure of BeB 18 53 . We report BeB 20 and BeB 20 − 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 radius 61 .
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 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: 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 Δ 2 E. The relevant formulae are www.nature.com/scientificreports www.nature.com/scientificreports/ 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: BeB 11 and BeB 16 − , which means that they feature higher stability www.nature.com/scientificreports www.nature.com/scientificreports/ than the others. Consequently, based on the above analyses, we can reach a definitive conclusion that the BeB 16 − can seen as a "magic" cluster.  www.nature.com/scientificreports www.nature.com/scientificreports/ 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|  www.nature.com/scientificreports www.nature.com/scientificreports/  www.nature.com/scientificreports www.nature.com/scientificreports/ 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 BeB 16 − cluster possesses π-aromaticity, which result to the robust relative stability for BeB 16 − cluster. The Wiberg bond index of BeB 16 − , 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 BeB 16 − cluster. It is worth noting that due to planar structure and chemical bonding characteristics of BeB 16 − cluster, also inspired by fascinating prospect of two-dimensional monolayer metallo-borophene 4 , we successfully build a schematic of possibility of metallo-borophene (not optimized) based on BeB 16 − unit cluster presented in Fig. S6 of Supplementary Information, which indicated the BeB 16 − 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 BeB 16 − cluster characterized by enhanced stability is clearly a "magic" cluster. Chemical bonding analysis indicated that BeB 16 − 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 BeB 16 − cluster. The planar BeB 16 − 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][65][66] . The effectiveness of this structural prediction method, has been successfully tested on the identification of ground-state structures of various systems [67][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 PBE0 70 functional and 6-311 + G(d) 71 , as performed via Gaussian 09 package 72 . The PES of Be-doped boron clusters was simulated utilizing TD-DFT method 73 . We then analyzed chemical bonding of BeB 16 − cluster relying on the NBO and AdNDP methods 74 at the PBE0/6-311 + G(d) level to display valuable insights into the nature of the bonding by using Multiwfn 75 . The bond orders, bond lengths and NPA are also computed by using the same basis set and method.