Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.


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.

Figure 1

Low-lying geometrical structures of BeBn (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 BeBn (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 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.

Figure 3

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

Relative stabilities

We characterize the inherent stability of the BeBn0/− (n = 10–20) clusters by computing the Eb (eV), according to the following formula:


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

$${\Delta }^{{\rm{2}}}E(Be{B}_{n})=E(Be{B}_{n-1})+E(Be{B}_{n+1})-2E(Be{B}_{n})$$
$${\varDelta }^{2}E(Be{{B}_{n}}^{-})=E(Be{B}_{n-1}^{-})+E(Be{B}_{n+1}^{-})-2E(Be{B}_{n}^{-})$$

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.

Table 1 The calculated electronic states, symmetries, average binding energies (Eb, in eV) and energy gaps (Egap, in eV) of BeBn0/− clusters in the size range of n = 10–20.

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.

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 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.


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.


  1. 1.

    Pham, H. T., Muya, J. T., Buendia, F., Ceulemans, A. & Nguyen, M. T. Formation of the quasi-planar B50 boron cluster: topological path from B10 and disk aromaticity. Phys. Chem. Chem. Phys. 21, 7039 (2019).

    CAS  Article  Google Scholar 

  2. 2.

    Chen, Q. et al. Planar B38 and B37 clusters with a double-hexagonal vacancy: molecular motifs for borophenes. Nanoscale. 9, 4550–4557 (2017).

    CAS  Article  Google Scholar 

  3. 3.

    Arasaki, Y. & Takatsuka, K. Chemical bonding and nonadiabatic electron wavepacket dynamics in densely quasi-degenerate excited electronic state manifold of boron clusters. J. Chem. Phys. 150, 114101 (2019).

    ADS  Article  Google Scholar 

  4. 4.

    Li, W. L. et al. planar boron clusters to borophenes and metalloborophenes. Nat. Rev. Chem. 1, 0071 (2017).

    CAS  Article  Google Scholar 

  5. 5.

    Li, P. F., Du, X. D., Wang, J. J., Lu, C. & Chen, H. H. Probing the Structural Evolution and Stabilities of Medium-Sized MoBn 0/− Clusters. J. Phys. Chem. C 122, 20000–20005 (2018).

    CAS  Article  Google Scholar 

  6. 6.

    Li, W. L. et al. Recent Progress on the investigations of boron clusters and boron-based materials (I): borophene. Sci. Sin. Chim. 48, 98–107 (2018).

    Article  Google Scholar 

  7. 7.

    Jian, T. et al. Probing the structures and bonding of size-selected boron and doped-boron clusters. Chem. Soc. Rev. 48, 3550 (2019).

    CAS  Article  Google Scholar 

  8. 8.

    Li, W. L. et al. Observation of highly stable and symmetric lanthanide octa-boron inverse sandwich complexes. Proc. Natl. Acad. Sci. USA 115, 30 (2018).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Chen, T. T., Li, W. L., Chen, W. J., Li, J. & Wang, L. S. La3B14 : an inverse triple-decker lanthanide boron cluster. Chem. Commun. 55, 7864 (2019).

    CAS  Article  Google Scholar 

  10. 10.

    Hawthorne, M. F. & Maderna, A. Applications of Radiolabeled Boron Clusters to the Diagnosis and Treatment of Cancer. Chem. Rev. 99, 3421–3434 (1999).

    CAS  Article  Google Scholar 

  11. 11.

    Geim, A. K. & Novoselov, K. S. Photoelectron Spectroscopy and Ab Initio Study of B3 and B4 Anions and Their Neutrals. Nat. Mater. 6, 183–191 (2007).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Vogt, P. et al. Silicene: Compelling Experimental Evidence for Graphenelike Two-Dimensional Silicon. Phys. Rev. Lett. 108, 155501 (2012).

    ADS  Article  Google Scholar 

  13. 13.

    Cahangirov, S. et al. Electronic Structure of Silicene on Ag(111): Strong Hybridization Effects. Phys. Rev. B 88, 035432 (2013).

    ADS  Article  Google Scholar 

  14. 14.

    Davila, M. E., Xian, L., Cahangirov, S., Rubio, A. & Lay, G. L. Germanene: A Novel Two-Dimensional Germanium Allotrope Akin to Graphene and Silicene. New J. Phys. 16, 095002 (2014).

    ADS  Article  Google Scholar 

  15. 15.

    Zhu, F. F. et al. Epitaxial Growth of Two-Dimensional Stanene. Nat. Mater. 14, 1020–1025 (2015).

    ADS  CAS  Article  Google Scholar 

  16. 16.

    Ji, J. P. et al. Two-Dimensional Antimonene Single Crystals Grown by Van Der Waals Epitaxy. Nat. Commun. 7, 13352 (2016).

    ADS  CAS  Article  Google Scholar 

  17. 17.

    Nagao, T. et al. Nanofilm Allotrope and Phase Transformation of Ultrathin Bi Film on Si(111)–7 × 7. Phys. Rev. Lett. 93, 105501 (2004).

    ADS  CAS  Article  Google Scholar 

  18. 18.

    Reis, F. et al. Bismuthene on a SiC Substrate: A Candidate for a High-Temperature Quantum Spin Hall Material. Science 357, 287–290 (2017).

    MathSciNet  ADS  CAS  Article  Google Scholar 

  19. 19.

    Zhu, Z. L. et al. Multivalency-Driven Formation of Te-Based Monolayer Materials: A Combined First Principles and Experimental Study. Phys. Rev. Lett. 119, 106101 (2017).

    ADS  Article  Google Scholar 

  20. 20.

    Yu, X. H., Zhang, X. M. & Yan, X. W. Stability of the Fe12O12 cluster. Nano. Res. 11, 3574–3581 (2008).

    Article  Google Scholar 

  21. 21.

    Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and Optoelectronics of Two-Dimensional Transition Metal Dichalcogenides. Nat. Nanotechnol. 7, 699–712 (2012).

    ADS  CAS  Article  Google Scholar 

  22. 22.

    Ling, X., Wang, H., Huang, S. X., Xia, F. N. & Dresselhaus, M. S. The Renaissance of Black Phosphorus. Proc. Natl. Acad. Sci. USA 112, 4523–4530 (2015).

    ADS  CAS  Article  Google Scholar 

  23. 23.

    Mannix, A. J., Zhang, Z. H., Guisinger, N. P., Yakobson, B. I. & Hersam, M. C. Borophene as a Prototype for Synthetic 2D Materials Development. Nat. Nanotechnol. 13, 444–450 (2018).

    ADS  CAS  Article  Google Scholar 

  24. 24.

    Nagamatsu, J., Nakagawa, N., Muranaka, T., Zenitani, Y. & Akimitsu, J. Superconductivity at 39 K in Magnesium Diboride. Nature 410, 63–64 (2001).

    ADS  CAS  Article  Google Scholar 

  25. 25.

    Li, Q. S. & Jin, Q. Theoretical Study on the Aromaticity of the Pyramidal MB6 (M = Be, Mg, Ca, and Sr) Clusters. J. Phys. Chem. A 107, 7869–7873 (2013).

    Article  Google Scholar 

  26. 26.

    Adamska, L., Sadasivam, S., Foley, J. J., Darancet, P. & Sharifzadeh, S. First-Principles Investigation of Borophene as a Monolayer Transparent Conductor. J. Phys. Chem. C 122, 4037–4045 (2018).

    CAS  Article  Google Scholar 

  27. 27.

    Er, S., Wijs, G. A. & Brocks, G. DFT Study of Planar Boron Sheets: A New Template for Hydrogen Storage. J. Phys. Chem. C 113, 18962–18967 (2009).

    CAS  Article  Google Scholar 

  28. 28.

    Jiang, H. R., Lu, Z. H., Wu, M. C., Ciucci, F. & Zhao, T. S. Borophene: A Promising Anode Material Offering High Specific Capacity and High Rate Capability for Lithium-Ion Batteries. Nano Energy 23, 97–104 (2016).

    CAS  Article  Google Scholar 

  29. 29.

    Albert, B. & Hillebrecht, H. Boron: Elementary Challenge for Experimenters and Theoreticians. Angew. Chem. Int. Ed. 48, 8640–8668 (2009).

    CAS  Article  Google Scholar 

  30. 30.

    Pelaz, L. et al. B Diffusion and Clustering in Ion Implanted Si: The Role of B Cluster Precursors. Appl. Phys. Lett. 70, 2285–2287 (1997).

    ADS  CAS  Article  Google Scholar 

  31. 31.

    Qgitsu, T., Schwegler, E. & Galli, G. β-Rhombohedral Boron: At the Crossroads of the Chemistry of Boron and the Physics of Frustration. Chem. Rev. 113, 3425–3449 (2013).

    Article  Google Scholar 

  32. 32.

    Sergeeva, A. P. et al. Understanding Boron through Size-Selected Clusters: Structure, Chemical Bonding, and Fluxionality. Acc. Chem. Res. 47, 1349–1358 (2014).

    CAS  Article  Google Scholar 

  33. 33.

    Oganov, A. R. et al. Ionic High Pressure form of Elemental Boron. Phys. Rev. Lett. 457, 863–867 (2009).

    CAS  Google Scholar 

  34. 34.

    Wang, Y. J. et al. Chemical Bonding and Dynamic Fluxionality of a B15 + Cluster: a Nanoscale Double-Axle Tank Tread. Phys. Chem. Chem. Phys. 18, 15774–15782 (2016).

    CAS  Article  Google Scholar 

  35. 35.

    Guajardo, G. M. et al. Unravelling Phenomenon of Internal Rotation in B13 + through Chemical Bonding Analysis. Chem. Commun. 47, 6242–6244 (2011).

    Article  Google Scholar 

  36. 36.

    Jimѐnez-Halla, J. O. C., Islas, R., Heine, T. & Merino, G. B19 : An Aromatic Wankel Motor. Angew. Chem. Int. Ed. 49, 5668–5671 (2010).

    Article  Google Scholar 

  37. 37.

    Morene, D. et al. B18 2−: A Quasi-Planar Bowl Member of the Wankel Motor Family. Chem. Commun. 50, 8140–8143 (2014).

    Article  Google Scholar 

  38. 38.

    Cervantes-Navarro, F. et al. Stop Rotating! One Substitution Halts the B19 Motor. Chem. Commun. 50, 10680–10682 (2014).

    CAS  Article  Google Scholar 

  39. 39.

    Merino, G. & Heine, T. And Yet It Rotates: The Starter for a Molecular Wankel Motor. Angew. Chem. Int. Ed. 51, 10226–10227 (2012).

    CAS  Article  Google Scholar 

  40. 40.

    Heina, T. & Merino, G. What Is the Maximum Coordination Number in a Planar Structure? Angew. Chem. Int. Ed. 51, 4275–4276 (2012).

    Article  Google Scholar 

  41. 41.

    Dong, X. et al. Li2B12 and Li3B12: Pediction of the Smallest Tubular and Cage-like Boron Structures. Angew. Chem. Int. Ed. 57, 4627–4631 (2018).

    CAS  Article  Google Scholar 

  42. 42.

    Lau, K. C. & Pandey, R. Highly Conductive Boron Nanotubes: Transport Properties, Work Functions, and Structural Stabilities. J. Phys. Chem. C 111, 2906–2912 (2007).

    CAS  Article  Google Scholar 

  43. 43.

    Muya, J. T. et al. Jahn-Teller Instability in Cationic Boron and Carbon Buckyballs B80 + and C60 +: A Comparative Study. Phys. Chem. Chem. Phys. 15, 2892–2835 (2013).

    Article  Google Scholar 

  44. 44.

    Muya, J. T., Gopakumar, G., Nguyen, M. T. & Ceulemans, A. The Leapfrog Principle for Boron Fullerenes: A Theoretical Study of Structure and Stability of B112. Phys. Chem. Chem. Phys. 13, 7524–7533 (2011).

    CAS  Article  Google Scholar 

  45. 45.

    Piazzi, Z. A. et al. Planar Hexagonal B36 as a Potential Basis for Extended Single-Atom Layer Boron Sheets. Nat. Commun. 5, 3113 (2014).

    ADS  Article  Google Scholar 

  46. 46.

    Sergeeva, A. P., Zubarev, D. Y., Zhai, H. J., Boldyrev, A. I. & Wang, L. S. A Photoelectron Spectroscopic and Theoretical Study of B16 and B16 2−: An All-Boron Naphthalene. J. Am. Chem. Soc. 130, 7244–7246 (2008).

    CAS  Article  Google Scholar 

  47. 47.

    Gerardo, M. G. et al. Dynamical Behavior of Borospherene: A Nanobubble. Sci. Rep. 5, 11287 (2015).

    ADS  Article  Google Scholar 

  48. 48.

    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 118, 8098–8105 (2014).

    CAS  Article  Google Scholar 

  49. 49.

    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. 6, 8654 (2015).

    ADS  CAS  Article  Google Scholar 

  50. 50.

    Jian, T. et al. Manganese-Centered Tubular Boron Cluster-MnB16 : A New Class of Transition-Metal Molecules. J. Chem. Phys. 114, 154310 (2016).

    ADS  Article  Google Scholar 

  51. 51.

    Jian, T. et al. Competition between Drum and Quasi-Planar Structures in RhB18 : Motifs for Metallo-Boronanotubes and Metallo-Borophenes. Chem. Sci. 7, 7020–7027 (2016).

    CAS  Article  Google Scholar 

  52. 52.

    Li, W. L. et al. The Planar CoB18 Cluster as a Motif for Metallo-Borophenes. Angew. Chem. Int. Ed. 55, 7358–7363 (2016).

    CAS  Article  Google Scholar 

  53. 53.

    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. 20, 16202–16208 (2018).

    CAS  Article  Google Scholar 

  54. 54.

    Li, W. L. et al. Observation of a Metal-Centered B2-Ta@B18 Tubular Molecular Rotor and a Perfect Ta@B20 Boron Drum with the Record Coordination Number of Twenty. Chem. Commun. 53, 1587–1590 (2017).

    CAS  Article  Google Scholar 

  55. 55.

    Li, P. F. et al. A Detailed Investigation into the Geometric and Electronic Structures of CoBQ n (n = 2−10, Q = 0, −1) Clusters. New J. Chem. 41, 11208–11214 (2017).

    CAS  Article  Google Scholar 

  56. 56.

    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. 54, 941–945 (2015).

    CAS  Article  Google Scholar 

  57. 57.

    Liu, C., Si, H., Han, P. & Tang, M. S. Density Functional Theory Study on Structure and Stability of BeBn + Clusters. Rapid Commun. Mass Spectrom. 31, 1437–1444 (2017).

    ADS  CAS  Article  Google Scholar 

  58. 58.

    Guo, J. C. et al. Coaxial Triple-Layered versus Helical Be6B11 Clusters: Dual Structural Fluxionality and Multifold Aromaticity. Angew. Chem. Int. Ed. 56, 10174–10177 (2017).

    CAS  Article  Google Scholar 

  59. 59.

    Pu, Z. F., Ge, M. F. & Li, Q. S. MB2 (M = Be, Mg, Ca, Sr, and Ba): Planar Octacoordinate Alkaline Earth Metal Atoms Enclosed by Boron Rings. Sci. China Chem. 53, 1737–1745 (2010).

    CAS  Article  Google Scholar 

  60. 60.

    Li, S. D., Miao. C. Q., Guo, J. C. & Ren, G. M. Planar Tetra-, Penta-, Hexa-, Hepta-, and Octacoordinate Silicoons: A Universal Structural Pattern. J. Am. Chem. Soc, 126, 16227–16231 (2004).

    CAS  Article  Google Scholar 

  61. 61.

    Sun, W. G., Xia, X. X., Lu, C., Kuang, X. Y. & Hermann, A. Probing the structural and electronic properties of zirconium doped boron clusters: Zr distorted B12 ligand framework. Phys. Chem. Chem. Phys. 20, 23740 (2018).

    CAS  Article  Google Scholar 

  62. 62.

    Sun, W. G. et al. Evolution of the Structural and Electronic Properties of Medium-Sized Sodium Clusters: A Honeycomb-like Na20 Cluster. Inorg. Chem. 56, 1241–1248 (2017).

    CAS  Article  Google Scholar 

  63. 63.

    Chen, B. L. et al. Insights into the effects produced by doping of medium-sized boron clusters with ruthenium. Phys. Chem. Chem. Phys. 20, 30376–30383 (2018).

    CAS  Article  Google Scholar 

  64. 64.

    Wang, H. et al. CALYPSO Structure Prediction Method and Its Wide Application. Comput. Mater. Sci. 112, 406−415 (2016).

    CAS  Article  Google Scholar 

  65. 65.

    Lv, J., Wang, Y. C., Zhu, L. & Ma, Y. M. Particle-Swarm Structure Prediction on Clusters. J. Chem. Phys. 137, 084104 (2012).

    ADS  Article  Google Scholar 

  66. 66.

    Wang, Y. C., Lv, J., Zhu, L. & Ma, Y. M. Crystal Structure Prediction via Particle-Swarm Optimization. Phys. Rev. B 82, 094116 (2010).

    ADS  Article  Google Scholar 

  67. 67.

    Lu, S. H., Wang, Y. C., Liu, H. Y., Miao, M. S. & Ma, Y. M. Self-Assembled Ultrathin Nanotubes on Diamond (100) Surface. Nat. Commun. 5, 3666 (2014).

    ADS  CAS  Article  Google Scholar 

  68. 68.

    Wang, H., Tse, J. S., Tanaka, K., Litaka, T. & Ma, Y. M. Superconductive Sodalite-like Clathrate Calcium Hydride at High Pressures. Proc. Natl. Acad. Sci. USA 24, 6463−6466 (2012).

    ADS  Article  Google Scholar 

  69. 69.

    Li, Y. W., Hao, J., Liu, H. Y., Li, Y. L. & Ma, Y. M. The Metallization and Superconductivity of Dense Hydrogen Sulfide. J. Chem. Phys. 140, 174712 (2014).

    ADS  Article  Google Scholar 

  70. 70.

    Adamo, C. & Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 110, 6158−6170 (1999).

    ADS  CAS  Article  Google Scholar 

  71. 71.

    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. 72, 650−654 (1980).

    ADS  CAS  Article  Google Scholar 

  72. 72.

    Frisch, M. J. et al. Gaussian 09 (Revision C.0), Gaussian, Inc., Wallingford, CT, (2009).

  73. 73.

    Casida, M. E., Jamorski, C., Casida, K. C. & Salahub, D. R. Molecular Excitation Energies to High-Lying Bound States from Time-Dependent Density-Functional Response Theory: Characterization and Correction of the Time-Dependent Local Density Approximation Ionization Threshold. J. Chem. Phys. 108, 4439–4449 (1998).

    ADS  CAS  Article  Google Scholar 

  74. 74.

    Zubarev, D. Y. & Boldyrev, A. I. Developing Paradigms of Chemical Bonding: Adaptive Natural Density Partitioning. Phys. Chem. Chem. Phys. 10, 5207–5217 (2008).

    CAS  Article  Google Scholar 

  75. 75.

    Lu, T. & Chen, F. W. Multiwfn: A multifunctional wavefunction analyzer. Comput. Phys. Commun. 33, 580−592 (2012).

    Google Scholar 

Download references


This work was supported by the National Natural Science Foundation of China (Nos. 11574220 and 11874043) and the Program for Science & Technology Innovation Talents in Universities of Henan Province (No. 15HASTIT020).

Author information




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.

Corresponding authors

Correspondence to Xiaoyu Kuang or George Maroulis.

Ethics declarations

Competing Interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kang, D., Sun, W., Shi, H. et al. Probing the structure and electronic properties of beryllium doped boron clusters: A planar BeB16 cluster motif for metallo-borophene. Sci Rep 9, 14367 (2019).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing