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基于密度泛函理论结合粒子群优化算法程序CALYPSO研究了掺Be硼团簇BeB
$ _{n}^{ 0/–} $ ( n= 10—15)的基态几何结构; 然后采用密度泛函理论分析了最低能量结构的电子结构、极化率、红外光谱、紫外可见光谱特性. 研究结果表明: BeB$ _{10}^{ 0/–} $ , BeB$ _{11}^- $ , BeB$ _{12}^{0/−} $ , BeB$ _{14}^- $ 具有平面或准平面结构; BeB 11, BeB 13, BeB$ _{13}^- $ , BeB 14分别具有半三明治结构、圆锥结构、笼型结构、压扁的管状结构; BeB$ _{15}^{0/−} $ 呈现手性对称结构. 自然布居分析(NPA)表明掺杂Be原子将电子转移给硼原子. 团簇的平均结合能分析可得, 阴离子比相应中性团簇的稳定性强; 另外, 随着 n的增加, 中性和阴离子团簇的稳定性增强. 准平面结构BeB 10, BeB$ _{11}^- $ , BeB 12团簇的适应性自然密度划分(AdNDP)分析表明, σ 键促进了整个分子的稳定性, 多中心π键进一步稳定了整个分子; 另外, 这三个团簇满足6个π电子Hückel规则(4 m+ 2), 具有芳香性. 极化率分析可得, 平面或准平面结构的每个原子的平均极化率大于其它结构, 说明平面或准平面结构的电子离域效应较大; BeB$ _{13}^- $ , BeB$ _{14}^- $ 具有较大的第一超极化率, 说明具有较强的非线性光学响应. 红外光谱分析表明这些团簇具有不同的特征峰, 可用于鉴别这些结构; 闭壳层结构团簇的紫外可见光谱在可见光波段都有吸收峰, 开壳层结构团簇的紫外可见光谱在红外光波段都有吸收峰.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 BeB 11, BeB 13, BeB$ _{13}^{-} $ , BeB 14clusters 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 BeB 10, BeB$ _{11}^{-} $ , BeB 12clusters 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 4 m+ 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.[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] -
Symmetry 最短Be—B键长/Å 结构 BeB10 Cs 1.83 准平面结构 BeB$ _{10}^- $ Cs 1.80 准平面结构 BeB11 Cs 1.97 半三明治结构 BeB$ _{11}^- $ Cs 1.86 准平面结构 BeB12 Cs 1.85 准平面结构 BeB$ _{12}^- $ C2v 1.83 平面结构 BeB13 C2v 1.93 圆锥结构 BeB$ _{13}^- $ Cs 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 BeB15I C1 1.87 三维结构 BeB15II 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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BeB10 BeB$_{10}^{-}$ BeB11 BeB$ _{11}^{-} $ BeB12 BeB$ _{12}^{-} $ BeB13 BeB$ _{13}^{-} $ BeB14 BeB$ _{14}^{-} $ BeB15I, 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 下载:
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BeB10 BeB$_{10}^{-}$ BeB11 BeB$_{11}^{-}$ BeB12 BeB$_{12}^{-}$ BeB13 BeB$_{13}^{-}$ BeB14 BeB$_{14}^{-}$ BeB15I, 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
2.63b3.10a
2.94b3.48 2.93 1.67a
3.08b2.93a
3.55b3.33 3.80 1.85a
1.99b3.23a
2.26b3.35 NPA charges
on doped atom1.62 1.64 1.56 1.37 1.64 1.66 1.72 1.60 1.69 1.68 1.70 1.67 下载:
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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βprj 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 BeB15I 215.11 13.44 122.84 601.71 –597.78 BeB15II 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 下载:
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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) BeB15I 339 (0.0295, 33) 1292 (0.0006) 1122 (1—2) BeB$ _{15}^- $ I 276 (0.0954, 24) 531 (0.0027) 531 (1) 下载:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]
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