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
Fund Project: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)
Received Date:19 May 2020
Accepted Date:29 June 2020
Available Online:28 August 2020
Published Online:05 October 2020
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/-} $(n = 10–15) have the meaningful characteristic peaks which can be compared with future experimental values. Our work enriches the database of geometrical structures of doped boron clusters and can provide much insight into the new doped boron clusters. Keywords:Be atom doped boron clusters/ ground state structures/ electronic structure/ spectra
掺Be硼团簇BeB$ _{n}^{ 0/–} $ (n = 10—15)的部分基态参数列于表3, 包含了偶极矩、自然布居分析(NPA)得到的掺杂Be原子上的电荷、最高占据轨道(HOMO)和最低空轨道(LUMO)之间的HOMO—LUMO能隙Eg (Eg = EL–EH). 图2仅显示了闭壳层结构的最高占据轨道和最低空轨道轨道图, BeB10 的HOMO轨道为明显的π轨道, BeB$ _{11}^{-} $, BeB12 的LUMO为明显的π轨道. Eg的大小能反映电子从占据轨道向空轨道发生跃迁的性质, Eg越小, 第一激发态具有越大的波长. 对于闭壳层团簇, BeB12有最小的Eg, 说明其第一激发态的波长最大. Be原子有2个价电子, 由表3掺杂原子的自然布居分析(NPA)结果可得, Be原子上显示正电荷, 说明电子转移到硼原子, 但2个价电子并没有完全转移到硼原子. 由表3可以看到, 手性对称的BeB$ _{15}^{0/-} $其结构I和II具有相同的HOMO—LUMO能隙和偶极矩. 图 2 分子轨道图 (a) HOMO BeB10; (b) LUMO BeB10; (c) HOMO BeB$_{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 Figure2. 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.
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
Eg/eV
2.94
2.81a 2.63b
3.10a 2.94b
3.48
2.93
1.67a 3.08b
2.93a 3.55b
3.33
3.80
1.85a 1.99b
3.23a 2.26b
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
表3BeB$ _{n}^{ 0/–} $(n = 10—15)的偶极矩, Eg, NPA电荷. 上标a, b 代表自旋向上和自旋向下电子 Table3.The dipole moments (μ), energy gaps (Eg), and NPA charges on doped atom of BeB$ _{n}^{ 0/–} $(n = 10?15). The markers “a” and “b” denote the alpha and beta electrons, respectively.
图 4 BeB$_{11}^{-}$的AdNDP分析, ON代表占据数, 黄色球代表Be原子 Figure4. Bonding patterns of BeB$_{11}^{-}$ from AdNDP analyses. The occupation numbers (ONs) are indicated and the yellow ball represents Be atom.
图 5 BeB12的AdNDP分析, ON代表占据数, 黄色球代表Be原子 Figure5. Bonding patterns of BeB12 from AdNDP analyses. The occupation numbers (ONs) are indicated and the yellow ball represents Be atom.
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
图 2 分子轨道图 (a) HOMO BeB10; (b) LUMO BeB10; (c) HOMO BeB
图 3 BeB10的AdNDP分析, ON代表占据数, 黄色球代表Be原子
图 4 BeB
图 5 BeB12的AdNDP分析, ON代表占据数, 黄色球代表Be原子
图 6 定域化轨道函数LOL, 等值面数值为0.5 (a) BeB10; (b) BeB
图 7 定域化轨道函数LOL, 等值面数值为0.56 (a) BeB10; (b) BeB
图 8 定域化轨道函数LOL, 等值面数值为0.6 (a) BeB10; (b) BeB
图 9 红外光谱 (a) BeB10; (b) BeB
图 10 紫外可见光谱 (a) BeB10; (b) BeB
图 11 紫外可见光谱 (a) BeB
