Ground state structures and properties of Be atom doped boron clusters BeB<inline-formula><tex-math id="Z-20201005111348-1">\begin{document}$ _{ n}^{\bf 0/-} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20200756_Z-20201005111348-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20200756_Z-20201005111348-1.png"/></alternatives></inline-formula>(<inline-formula><tex-math id="Z-20201005111418-1">\begin{document}$ n \bf = 10$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20200756_Z-20201005111418-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20200756_Z-20201005111418-1.png"/></alternatives></inline-formula>–15)

Li Shi-Xiong; Chen De-Liang; Zhang Zheng-Ping; Long Zheng-Wen

doi:10.7498/aps.69.20200756

Abstract

A theoretical study of geometrical structures and electronic properties of Be atom doped boron clusters BeB$ _n^{0/-} $(n = 10–15) is performed using the CALYPSO approach for the global minimum search followed by density functional theory calculations. It is found that the global minima obtained for the BeB$ _{10}^{0/-} $, BeB$ _{11}^{-} $, BeB$ _{12}^{0/-} $, and BeB$ _{14}^{-} $ clusters correspond to the quasi-planar or planar structures. However, the global minima obtained for the BeB₁₁, BeB₁₃, BeB$ _{13}^{-} $, BeB₁₄ clusters correspond to the half-sandwich, cone, cage, squashed tubular structures, respectively. Interestingly, both the neutral and anionic BeB$ _{15}^{0/-} $ clusters have the axially chiral isomers which are chiral with degenerate enantiomers. Natural population analyses reveal that partial charge on Be atom transfer to boron atoms. The average binding energy values of BeB$ _n^{0/-} $ (n = 10–15) indicate that anionic clusters are overall more stable than the corresponding neutral ones, and both neutral and anionic clusters show the same trend that the stability increases gradually with the increase of B atoms number n. Chemical bonding analyses of closed-shell BeB₁₀, BeB$ _{11}^{-} $, BeB₁₂ clusters reveal that the σ bonds stabilize whole molecular skeleton, and delocalized π bonds render the structure more stable. Furthermore, the three quasi-planar closed-shell clusters possess 3 delocalized π bonds, which quite surprisingly follow the 4m + 2 Hückel rule for aromaticity. Average polarizability of single atom for each quasi-planar or planar structure is larger than other structures, it indicates that quasi-planar or planar structure has stronger electron delocalization. Specifically, BeB$ _{13}^{-} $ and BeB$ _{14}^{-} $ with large first static hyperpolarizability can lead to the remarkable NLO response. The calculated spectra indicate that BeB$ _n^{0/-} $(n = 10–15) have the meaningful characteristic peaks which can be compared with future experimental values. Our work enriches the database of geometrical structures of doped boron clusters and can provide much insight into the new doped boron clusters.

Keywords:

Authors and contacts

1.
School of Physics and Electronic Science, Guizhou Education University, Guiyang 550018, China
2.
College of Big Data and Information Engineering, Guizhou University, Guiyang 550025, China
3.
College of Physics, Guizhou University, Guiyang 550025, China

Corresponding author: Li Shi-Xiong, leesxoptics@163.com

Funds: Project Supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11804065) and the Central Guiding Local Science and Technology Development Foudation of China (Grant No. QK ZYD[2019]4012)

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References

[1]	Kroto H W, Heath J R, O’Brien S C, Curl R F, Smalley R E 1985 Nature 318 162 Google Scholar
[2]	Iijima S 1991 Nature 354 56 Google Scholar
[3]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[4]	Boustani I 1997 Phys. Rev. B 55 16426 Google Scholar
[5]	Zhai H J, Wang L S, Alexandrova A N, Boldyrev A I 2002 J. Chem. Phys. 117 7917 Google Scholar
[6]	Zhai H J, Kiran B, Li J, Wang L S 2003 Nat. Mater. 2 827 Google Scholar
[7]	Kiran B, Bulusu S, Zhai H J, Yoo S, Zeng X C, Wang L S 2005 Proc. Natl. Acad. Sci. U. S. A. 102 961 Google Scholar
[8]	Bean D E, Fowler P W 2009 J. Phys. Chem. C 113 15569 Google Scholar
[9]	Chen Q, Wei G F, Tian W J, Bai H, Liu Z P, Zhai H J, Li S D 2014 Phys. Chem. Chem. Phys. 16 18282 Google Scholar
[10]	Sergeeva A P, Popov I A, Piazza Z A, Li W L, Romanescu C, Wang L S, Boldyrev A I 2014 Acc. Chem. Res. 47 1349 Google Scholar
[11]	Jian T, Chen X, Li S D, Boldyrev A I, Li J, Wang L S 2019 Chem. Soc. Rev. 48 3550 Google Scholar
[12]	Piazza Z A, Hu H S, Li W L, Zhao Y F, Li J, Wang L S 2014 Nat. Commun. 5 3113 Google Scholar
[13]	Casillas R, Baruah T, Zope R R 2013 Chem. Phys. Lett. 557 15 Google Scholar
[14]	Pham H T, Duong L V, Pham B Q, Nguyen M T 2013 Chem. Phys. Lett. 577 32 Google Scholar
[15]	Lü J, Wang Y, Zhu L, Ma Y 2014 Nanoscale 6 11692 Google Scholar
[16]	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, Mu Y W, Wei G F, Liu Z P, Li J, Li S D, Wang L S 2014 Nat. Chem. 6 727 Google Scholar
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[19]	Dong H, Hou T, Lee S T, Li Y 2015 Sci. Rep. 5 9952 Google Scholar
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[21]	Bai H, Bai B, Zhang L, Huang W, Mu Y W, Zhai H J, Li S D 2016 Sci. Rep. 6 35518 Google Scholar
[22]	Shakerzadeh E, Biglari Z, Tahmasebi E 2016 Chem. Phys. Lett. 654 76 Google Scholar
[23]	Tang C, Zhang X 2016 Int. J. Hydrogen Energy 41 16992 Google Scholar
[24]	Li S, Zhang Z, Long Z, Chen D 2019 ACS Omega 4 5705 Google Scholar
[25]	李世雄, 张正平, 隆正文, 秦水介 2017 物理学报 66 103102 Google Scholar Li S X, Zhang Z P, Long Z W, Qin S J 2017 Acta Phys. Sin. 66 103102 Google Scholar
[26]	Popov I A, Li W L, Piazza Z A, Boldyrev A I, Wang L S 2014 J. Phys. Chem. A 118 8098 Google Scholar
[27]	Liang W Y, Das A, Dong X, Cui Z H 2018 Phys. Chem. Chem. Phys. 20 16202 Google Scholar
[28]	Wang W, Guo Y D, Yan X H 2016 RSC Advances 6 40155 Google Scholar
[29]	Saha R, Kar S, Pan S, Martinez G G, Merino G, Chattaraj P K 2017 J. Phys. Chem. A 121 2971 Google Scholar
[30]	Lü J, Wang Y, Zhu L, Ma Y 2012 J. Chem. Phys. 137 084104 Google Scholar
[31]	Adamo C, Barone V 1999 J. Chem. Phys. 110 6158 Google Scholar
[32]	Weigend F, Ahlrichs R 2005 Phys. Chem. Chem. Phys. 7 3297 Google Scholar
[33]	Frisch M J, Trucks G W, Schlegel H B et al. 2016 Gaussian 16 (Rev. A.03). Gaussian: Inc., Wallingford CT
[34]	Zubarev D Y, Boldyrev A I 2008 Phys. Chem. Chem. Phys. 10 5207 Google Scholar
[35]	Lu T, Chen F 2012 J. Comput. Chem. 33 580 Google Scholar
[36]	Humphrey W, Dalke A, Schulten K 1996 J. Mol. Graphics 14 33 Google Scholar
[37]	Cheng L 2012 J. Chem. Phys. 136 104301 Google Scholar
[38]	Mayer I 1983 Chem. Phys. Lett. 97 270 Google Scholar
[39]	Schmider H L, Becke A D 2000 J. Mol. Struct. THEOCHEM 527 51 Google Scholar

Cited By

图 1 团簇结构图, 分图中上图为正面观察、下图为侧面观察　(a) BeB₁₀; (b) BeB$ _{10}^- $; (c) BeB₁₁; (d) BeB$ _{11}^- $; (e) BeB₁₂; (f) BeB$ _{12}^- $; (g) BeB₁₃; (h) BeB$ _{13}^- $; (i) BeB₁₄; (j) BeB$ _{14}^- $; (k) BeB₁₅ I; (l) BeB$ _{15}^- $ I; (m) BeB₁₅ II; (n) BeB$ _{15}^- $ II

Figure 1. Structures of doped boron clusters BeB$_{n}^{ 0/–}$(n = 10−15): (a) BeB₁₀; (b) BeB$ _{10}^- $; (c) BeB₁₁; (d) BeB$ _{11}^- $; (e) BeB₁₂; (f) BeB$ _{12}^- $; (g) BeB₁₃; (h) BeB$ _{13}^- $; (i) BeB₁₄; (j) BeB$ _{14}^- $; (k) BeB₁₅ I; (l) BeB$ _{15}^- $ I; (m) BeB₁₅ II; (n) BeB$ _{15}^- $ II.

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图 2 分子轨道图　(a) HOMO BeB₁₀; (b) LUMO BeB₁₀; (c) HOMO BeB$_{11}^{-}$; (d) LUMO BeB$_{11}^{-}$; (e) HOMO BeB₁₂; (f) LUMO BeB₁₂; (g) HOMO BeB$_{13}^{-}$; (h) LUMO BeB$_{13}^{-}$; (i) HOMO BeB₁₄; (j) LUMO BeB₁₄; (k) HOMO BeB$_{15}^{-}$ I; (l) LUMO BeB$_{15}^{-}$ I; (m) HOMO BeB$_{15}^{-}$ II; (n) LUMO BeB$_{15}^{-}$ II

Figure 2. Molecular orbitals: (a) HOMO BeB₁₀; (b) LUMO BeB₁₀; (c) HOMO BeB$ _{11}^- $; (d) LUMO BeB$ _{11}^- $; (e) HOMO BeB₁₂; (f) LUMO BeB₁₂; (g) HOMO BeB$ _{13}^- $; (h) LUMO BeB$ _{13}^- $; (i) HOMO BeB₁₄; (j) LUMO BeB₁₄; (k) HOMO BeB$ _{15}^- $ I; (l) LUMO BeB$_{15}^{-}$ I; (m) HOMO BeB$_{15}^{-}$ II; (n) LUMO BeB$_{15}^{-}$ II.

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图 3 BeB₁₀的AdNDP分析, ON代表占据数, 黄色球代表Be原子

Figure 3. Bonding patterns of BeB₁₀ from AdNDP analyses. The occupation numbers (ONs) are indicated and the yellow ball represents Be atom.

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图 4 BeB$_{11}^{-}$的AdNDP分析, ON代表占据数, 黄色球代表Be原子

Figure 4. Bonding patterns of BeB$_{11}^{-}$ from AdNDP analyses. The occupation numbers (ONs) are indicated and the yellow ball represents Be atom.

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图 5 BeB₁₂的AdNDP分析, ON代表占据数, 黄色球代表Be原子

Figure 5. Bonding patterns of BeB₁₂ from AdNDP analyses. The occupation numbers (ONs) are indicated and the yellow ball represents Be atom.

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图 6 定域化轨道函数LOL, 等值面数值为0.5　(a) BeB₁₀; (b) BeB$_{11}^{-}$; (c) BeB₁₂

Figure 6. Localized orbital locator, the isovalue is set to 0. 5: (a) BeB₁₀; (b) BeB$_{11}^{-}$; (c) BeB₁₂.

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图 7 定域化轨道函数LOL, 等值面数值为0.56　(a) BeB₁₀; (b) BeB$_{11}^{-}$; (c) BeB₁₂

Figure 7. Localized orbital locator, the isovalue is set to 0. 56: (a) BeB₁₀; (b) BeB$_{11}^{-}$; (c) BeB₁₂.

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图 8 定域化轨道函数LOL, 等值面数值为0.6　(a) BeB₁₀; (b) BeB$_{11}^{-}$; (c) BeB₁₂

Figure 8. Localized orbital locator, the isovalue is set to 0.6. (a) BeB₁₀; (b) BeB$_{11}^{-}$ (c) BeB₁₂.

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图 9 红外光谱　(a) BeB₁₀; (b) BeB$_{10}^{-}$; (c) BeB₁₁; (d) BeB$_{11}^{-}$; (e) BeB₁₂; (f) BeB$_{12}^{-}$; (g) BeB₁₃; (h) BeB$_{13}^{-}$; (i) BeB₁₄; (j) BeB$_{14}^{-}$; (k) BeB₁₅ I; (l) BeB$_{15}^{-}$ I

Figure 9. Calculated infrared spectra: (a) BeB₁₀; (b) BeB$_{10}^{-}$; (c) BeB₁₁; (d) BeB$_{11}^{-}$; (e) BeB₁₂; (f) BeB$_{12}^{-}$; (g) BeB₁₃; (h) BeB$_{13}^{-}$; (i) BeB₁₄; (j) BeB$_{14}^{-}$; (k) BeB₁₅ I; (l) BeB$_{15}^{-}$ I.

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图 10 紫外可见光谱　(a) BeB₁₀; (b) BeB$_{11}^{-}$; (c) BeB₁₂; (d) BeB$_{13}^{-}$; (e) BeB₁₄; (f) BeB$_{15}^{-}$ I

Figure 10. Calculated UV-Vis spectra: (a) BeB₁₀; (b) BeB$_{11}^{-}$; (c) BeB₁₂; (d) BeB$_{13}^{-}$; (e) BeB₁₄; (f) BeB$_{15}^{-}$ I.

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图 11 紫外可见光谱　(a) BeB$_{10}^{-}$; (b) BeB₁₁; (c) BeB$_{12}^{-}$; (d) BeB₁₃; (e) BeB$_{14}^{-}$; (f) BeB₁₅ I

Figure 11. Calculated UV-Vis spectra: (a) BeB$_{10}^{-}$; (b) BeB₁₁; (c) BeB$_{12}^{-}$; (d) BeB₁₃; (e) BeB$_{14}^{-}$; (f) BeB₁₅ I.

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表 1 BeB$_{n}^{ 0/–}$ (n = 10—15)的几何参数

Table 1. Geometrical parameters of BeB$ _{n}^{ 0/–} $(n = 10−15).

	Symmetry	最短Be—B键长/Å	结构
BeB₁₀	C_s	1.83	准平面结构
BeB$ _{10}^- $	C_s	1.80	准平面结构
BeB₁₁	C_s	1.97	半三明治结构
BeB$ _{11}^- $	C_s	1.86	准平面结构
BeB₁₂	C_s	1.85	准平面结构
BeB$ _{12}^- $	C_2v	1.83	平面结构
BeB₁₃	C_2v	1.93	圆锥结构
BeB$ _{13}^- $	C_s	1.80	笼型结构
BeB₁₄	C₂	1.88	压扁的管状结构
BeB$ _{14}^- $	C₂	1.84	准平面结构
BeB₁₅ I	C₁	1.87	三维结构
BeB₁₅ II	C₁	1.87	三维结构
BeB$ _{15}^- $ I	C₁	1.84	三维结构
BeB$ _{15}^- $ II	C₁	1.84	三维结构

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表 2 BeB$ _{n}^{ 0/–} $(n = 10—15)的最低谐振频率和平均结合能

Table 2. The lowest frequencies and average binding energy of BeB$ _{n}^{ 0/–} $(n = 10−15).

	BeB₁₀	BeB$_{10}^{-}$	BeB₁₁	BeB$ _{11}^{-} $	BeB₁₂	BeB$ _{12}^{-} $	BeB₁₃	BeB$ _{13}^{-} $	BeB₁₄	BeB$ _{14}^{-} $	BeB₁₅ I, II	BeB$ _{15}^{-} $ I, II
最低谐振频率/cm^–1	117	109	236	65	119	65	171	228	243	103	73	91
平均结合能/eV	4.71	5.06	4.78	5.16	4.89	5.17	4.91	5.19	4.97	5.22	4.97	5.26

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表 3 BeB$ _{n}^{ 0/–} $(n = 10—15)的偶极矩, E_g, NPA电荷. 上标a, b 代表自旋向上和自旋向下电子

Table 3. The dipole moments (μ), energy gaps (E_g), and NPA charges on doped atom of BeB$ _{n}^{ 0/–} $(n = 10−15). The markers “a” and “b” denote the alpha and beta electrons, respectively.

	BeB₁₀	BeB$_{10}^{-}$	BeB₁₁	BeB$_{11}^{-}$	BeB₁₂	BeB$_{12}^{-}$	BeB₁₃	BeB$_{13}^{-}$	BeB₁₄	BeB$_{14}^{-}$	BeB₁₅ I, II	BeB$_{15}^{-}$ I, II
μ/ Debye	0.80	0.58	1.49	1.59	1.31	0.66	0.22	1.12	2.57	0.86	1.95	1.88
E_g/eV	2.94	2.81^a 2.63^b	3.10^a 2.94^b	3.48	2.93	1.67^a 3.08^b	2.93^a 3.55^b	3.33	3.80	1.85^a 1.99^b	3.23^a 2.26^b	3.35
NPA charges on doped atom	1.62	1.64	1.56	1.37	1.64	1.66	1.72	1.60	1.69	1.68	1.70	1.67

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表 4 BeB$ _n^{0/-} $(n = 10—15)的极化率

Table 4. Polarizabilities of BeB$ _n^{0/-} $(n = 10−15).

	各项同性平均极化率α	每个原子的平均极化率$\bar \alpha $	各项异性极化率Δα	第一超极化率β₀	偶极矩方向上的投影值β_prj
BeB₁₀	167.32	15.21	124.78	133.79	–59.10
BeB$ _{10}^- $	196.08	17.83	142.11	216.95	–113.85
BeB₁₁	153.17	12.76	63.19	319.45	155.00
BeB$ _{11}^- $	203.90	16.99	139.92	233.54	199.10
BeB₁₂	196.31	15.10	145.51	24.98	6.10
BeB$ _{12}^- $	223.77	17.21	164.05	254.97	–254.97
BeB₁₃	174.08	12.43	48.62	61.41	–26.71
BeB$ _{13}^- $	210.56	15.04	119.68	941.20	–901.01
BeB₁₄	191.44	12.76	73.13	450.89	–450.89
BeB$ _{14}^- $	260.09	17.34	203.63	958.78	–958.78
BeB₁₅ I	215.11	13.44	122.84	601.71	–597.78
BeB₁₅ II	215.12	13.44	122.87	604.10	–600.31
BeB$ _{15}^- $ I	235.61	14.73	130.97	516.03	–223.98
BeB$ _{15}^- $ II	235.62	14.73	130.93	517.15	–224.33

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表 5 BeB$ _n^{0/-} $(n = 10—15)的激发特性

Table 5. The excitation properties of BeB$ _n^{0/-} $(n = 10−15).

	振子强度最大的激发态的波长/nm (振子强度, 第几激发态)	第一激发态的波长/nm (振子强度)	第一个吸收峰位置/nm (对应第几激发态)
BeB₁₀	252 (0.2108, 22)	748 (0.0003)	748 (1)
BeB$ _{10}^- $	313 (0.1205, 34)	1038 (0.0001)	887 (5)
BeB₁₁	331 (0.0077, 22)	859 (0.0022)	859 (1)
BeB$ _{11}^- $	242 (0.3008, 27)	548 (0)	510 (2)
BeB₁₂	282 (0.2870, 22)	702 (0.0038)	702 (1)
BeB$ _{12}^- $	346 (0.0119, 32)	3201 (0.0003)	3201 (1)
BeB₁₃	308 (0.0377, 31)	800 (0.0015)	800 (1)
BeB$ _{13}^- $	234 (0.0875, 36)	582 (0.0003)	582 (1)
BeB₁₄	311 (0.1049, 15)	468 (0.0041)	468 (1)
BeB$ _{14}^- $	533 (0.0472, 14)	1984 (0)	982 (4—6)
BeB₁₅ I	339 (0.0295, 33)	1292 (0.0006)	1122 (1—2)
BeB$ _{15}^- $ I	276 (0.0954, 24)	531 (0.0027)	531 (1)

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[1]	Kroto H W, Heath J R, O’Brien S C, Curl R F, Smalley R E 1985 Nature 318 162 Google Scholar
[2]	Iijima S 1991 Nature 354 56 Google Scholar
[3]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[4]	Boustani I 1997 Phys. Rev. B 55 16426 Google Scholar
[5]	Zhai H J, Wang L S, Alexandrova A N, Boldyrev A I 2002 J. Chem. Phys. 117 7917 Google Scholar
[6]	Zhai H J, Kiran B, Li J, Wang L S 2003 Nat. Mater. 2 827 Google Scholar
[7]	Kiran B, Bulusu S, Zhai H J, Yoo S, Zeng X C, Wang L S 2005 Proc. Natl. Acad. Sci. U. S. A. 102 961 Google Scholar
[8]	Bean D E, Fowler P W 2009 J. Phys. Chem. C 113 15569 Google Scholar
[9]	Chen Q, Wei G F, Tian W J, Bai H, Liu Z P, Zhai H J, Li S D 2014 Phys. Chem. Chem. Phys. 16 18282 Google Scholar
[10]	Sergeeva A P, Popov I A, Piazza Z A, Li W L, Romanescu C, Wang L S, Boldyrev A I 2014 Acc. Chem. Res. 47 1349 Google Scholar
[11]	Jian T, Chen X, Li S D, Boldyrev A I, Li J, Wang L S 2019 Chem. Soc. Rev. 48 3550 Google Scholar
[12]	Piazza Z A, Hu H S, Li W L, Zhao Y F, Li J, Wang L S 2014 Nat. Commun. 5 3113 Google Scholar
[13]	Casillas R, Baruah T, Zope R R 2013 Chem. Phys. Lett. 557 15 Google Scholar
[14]	Pham H T, Duong L V, Pham B Q, Nguyen M T 2013 Chem. Phys. Lett. 577 32 Google Scholar
[15]	Lü J, Wang Y, Zhu L, Ma Y 2014 Nanoscale 6 11692 Google Scholar
[16]	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, Mu Y W, Wei G F, Liu Z P, Li J, Li S D, Wang L S 2014 Nat. Chem. 6 727 Google Scholar
[17]	Bai H, Chen Q, Zhai H J, Li S D 2015 Angew. Chem. Int. Ed. 54 941 Google Scholar
[18]	Li S X, Zhang Z P, Long Z W, Qin S J 2017 RSC Advances 7 38526 Google Scholar
[19]	Dong H, Hou T, Lee S T, Li Y 2015 Sci. Rep. 5 9952 Google Scholar
[20]	An Y, Zhang M, Wu D, Fu Z, Wang T, Xia C 2016 Phys. Chem. Chem. Phys. 18 12024 Google Scholar
[21]	Bai H, Bai B, Zhang L, Huang W, Mu Y W, Zhai H J, Li S D 2016 Sci. Rep. 6 35518 Google Scholar
[22]	Shakerzadeh E, Biglari Z, Tahmasebi E 2016 Chem. Phys. Lett. 654 76 Google Scholar
[23]	Tang C, Zhang X 2016 Int. J. Hydrogen Energy 41 16992 Google Scholar
[24]	Li S, Zhang Z, Long Z, Chen D 2019 ACS Omega 4 5705 Google Scholar
[25]	李世雄, 张正平, 隆正文, 秦水介 2017 物理学报 66 103102 Google Scholar Li S X, Zhang Z P, Long Z W, Qin S J 2017 Acta Phys. Sin. 66 103102 Google Scholar
[26]	Popov I A, Li W L, Piazza Z A, Boldyrev A I, Wang L S 2014 J. Phys. Chem. A 118 8098 Google Scholar
[27]	Liang W Y, Das A, Dong X, Cui Z H 2018 Phys. Chem. Chem. Phys. 20 16202 Google Scholar
[28]	Wang W, Guo Y D, Yan X H 2016 RSC Advances 6 40155 Google Scholar
[29]	Saha R, Kar S, Pan S, Martinez G G, Merino G, Chattaraj P K 2017 J. Phys. Chem. A 121 2971 Google Scholar
[30]	Lü J, Wang Y, Zhu L, Ma Y 2012 J. Chem. Phys. 137 084104 Google Scholar
[31]	Adamo C, Barone V 1999 J. Chem. Phys. 110 6158 Google Scholar
[32]	Weigend F, Ahlrichs R 2005 Phys. Chem. Chem. Phys. 7 3297 Google Scholar
[33]	Frisch M J, Trucks G W, Schlegel H B et al. 2016 Gaussian 16 (Rev. A.03). Gaussian: Inc., Wallingford CT
[34]	Zubarev D Y, Boldyrev A I 2008 Phys. Chem. Chem. Phys. 10 5207 Google Scholar
[35]	Lu T, Chen F 2012 J. Comput. Chem. 33 580 Google Scholar
[36]	Humphrey W, Dalke A, Schulten K 1996 J. Mol. Graphics 14 33 Google Scholar
[37]	Cheng L 2012 J. Chem. Phys. 136 104301 Google Scholar
[38]	Mayer I 1983 Chem. Phys. Lett. 97 270 Google Scholar
[39]	Schmider H L, Becke A D 2000 J. Mol. Struct. THEOCHEM 527 51 Google Scholar

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Ground state structures and properties of Be atom doped boron clusters BeB$ _{ n}^{\bf 0/-} $($ n \bf = 10$–15)

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Ground state structures and properties of Be atom doped boron clusters BeB$ _{ n}^{\bf 0/-} $($ n \bf = 10$–15)

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Corresponding author: Li Shi-Xiong, leesxoptics@163.com

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