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Rare earth doped boron clusters have attracted much attention due to their special optical, electrical and magnetic properties. The geometric structures, stability, electronic properties and aromaticity of negative rare earth doped boron clusters $ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8) are investigated with the artificial bee colony algorithm combined with density functional theory calculations at the PBE0/RE/SDD//B/6-311+G* level of theory. Calculations show that the ground state structures of $ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8) are all of C2 symmetry, and the doped lanthanide atom is located in a “boat-shaped” structure at the top center. By comparing with the experimental photoelectron spectra, it is confirmed that the ground state structure of $ {\text{LaB}}_{8}^ - $ is a “zither-like” three-dimensional structure, and the ground state structure of $ {\text{ScB}}_{8}^ - $ is an “umbrella” structure with C7v symmetry formed by the scandium atom at the “umbrella handle”. The electron localization between RE—B is not as good as that between B—B. The simulated photoelectron spectra have similar spectral characteristics to the experimental results. The lowest energy structures of $ {\text{LaB}}_{6}^ - $ and $ {\text{ScB}}_{6}^ - $ are σ-π double aromatic clusters, and the structures exhibit aromaticity. The density of states of low-energy isomers shows that the open shell $ {\text{ScB}}_{8}^ - $ density of states spectrum exhibits spin polarization phenomenon, which is expected to assemble magnetic material components. These studies contribute to understanding the evolution of structure and properties of nanomaterials, and provide important theoretical support for designing nanomaterials with practical value.
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Keywords:
- density functional theory /
- rare earth doped clusters /
- structural optimization /
- aromaticity
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图 1 在PBE0/RE/SDD//B/6-311+G*理论水平下, $ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8) 团簇低能异构体的结构、点群对称性、相对能
Figure 1. Structures, symmetry point group and relative energy (eV) of the lower-lying isomers for $ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8) clusters at the PBE0/RE/SDD//B/6-311+G* level of theory.
图 2 $ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8)团簇低能异构体的定域化轨道指示函数等值面图
Figure 2. $ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8) isosurface of localized orbital locator function of low energy isomers.
图 3 $ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8)团簇低能异构体的模拟光电子能谱图, $ {\text{LaB}}_{8}^ - $的实验光电子能谱来自于文献[32], 共同绘制在$ {\text{LaB}}_{8}^ - $-Ⅰ处用红色曲线表示
Figure 3. Simulated PES spectra for low-lying isomers of $ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8) clusters, the experimental PES spectra of the anionic ground state structure of $ {\text{LaB}}_{8}^ - $ was obtained from Ref. [32].
图 4 $ {\text{LaB}}_{6}^ - $的芳香性分析图
Figure 4. Adaptive natural density partitioning (AdNDP) bonding analyses of $ {\text{LaB}}_{6}^ - $.
图 5 $ {\text{ScB}}_{6}^ - $-Ⅰ的芳香性分析轨道图
Figure 5. Adaptive natural density partitioning (AdNDP) bonding analyses of $ {\text{ScB}}_{6}^ - $-Ⅰ.
图 6 $ {\text{ScB}}_{6}^ - $-Ⅲ的芳香性分析图
Figure 6. Adaptive natural density partitioning (AdNDP) bonding analyses of $ {\text{ScB}}_{6}^ - $-Ⅲ.
图 7 0.60 eV的半峰展宽下$ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8) 能量最低结构的总态密度图与局部态密度图
Figure 7. Total density of states (TDOS) and partial density of states (PDOS) plot of the lowest energy structures of $ {\text{REB}}_n^ - $ (RE = La, Sc; n = 6, 8) with a full width at half-maximum (FWHM) of 0.60 eV.
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[1] 张超江, 许洪光, 徐西玲, 郑卫军 2021 物理学报 70 023601
Google Scholar
Zhang C J, Xu H G, Xu X L, Zheng W J 2021 Acta Phys. Sin. 70 023601
Google Scholar
[2] Boustani I 1997 Phys. Rev. B 5 16426
[3] Kiran B, Bulusu S, Zhai H J, Yoo S, Zeng X C, Wang L S 2005 Proc. Natl. Acad. Sci. 102 961
Google Scholar
[4] 李世雄, 张正平, 隆正文, 秦水介 2017 物理学报 6 103102
Google Scholar
Li S X, Zhang Z P, Long Z W, Qin S J 2017 Acta Phys. Sin. 6 103102
Google Scholar
[5] 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
[6] Jian T, Chen X, Li S D, Boldyrev A I, Li J, Wang L S 2019 Chem. Soc. Rev. 48 3550
Google Scholar
[7] Wang L S 2016 Int. Rev. Phys. Chem. 35 69
Google Scholar
[8] Bai H, Chen T T, Chen Q, Zhao X Y, Zhang Y Y, Chen W J, Li W L, Cheng L F, Bai B, Cavanagh J, Huang W, Li S D, Li J, Wang L S 2019 Nanoscale 11 23286
Google Scholar
[9] 刘立仁, 雷雪玲, 陈杭, 祝恒江 2009 物理学报 58 5355
Google Scholar
Liu L R, Lei X L, Chen H, Zhu H J 2009 Acta Phys. Sin. 58 5355
Google Scholar
[10] Pham H T, Duong L V, Pham B Q, Nguyen M T 2013 Chem. Phys. Lett. 577 32
Google Scholar
[11] Zhai H J, Alexandrova A N, Birch K A, Boldyrev A I, Wang L S 2003 Angew. Chem. Int. Ed. 42 6004
Google Scholar
[12] 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 Nature Chem. 6 727
Google Scholar
[13] Islas R, Heine T, Ito K, Schleyer P V, Merino G 2007 J. Am. Chem. Soc. 129 14767
Google Scholar
[14] Romanescu C, Galeev T R, Li W L, Boldyrev A I, Wang L S 2013 Acc. Chem. Res. 46 350
Google Scholar
[15] Saha R, Kar S, Pan S, Martínez-Guajardo G, Merino G, Chattaraj P K 2017 J. Phys. Chem. A 121 2971
Google Scholar
[16] 李世雄, 陈德良, 张正平, 隆正文 2020 物理学报 69 193101
Google Scholar
Li S X, Chen D L, Zhang Z P, Long Z W 2020 Acta Phys. Sin. 69 193101
Google Scholar
[17] Li H F, Wang H Q, Zhang J M, Qin L X, Zheng H, Zhang Y H 2024 Molecules 29 1692
Google Scholar
[18] 蒋贤明, 王怀谦, 曹宇, 孙之惠, 曹玉芳, 吴伟宾 2018 高等学校化学学报 39 1976
Google Scholar
Jiang X M, Wang H Q, Cao Y, Sun Z H, Cao Y F, Wu W B 2018 Chemical Journal of Chinese Universities 39 1976
Google Scholar
[19] Zheng H, Wang H Q, Li H F, Zhang J M, Zhang Y H, Qin L X, Mei X J, Jiang K L, Zeng J K, Zhang B, Wu W H 2024 Chem. Phys. 583 112321
Google Scholar
[20] Wen S H, Zhou J J, Zheng K Z, Bednarkiewicz A, Liu X G, Jin D Y 2018 Nat. Commun. 9 2415
Google Scholar
[21] Jiang L Y, Wang H Q, Li H F, Xie B, Zhang J M, Ji J Y 2023 Chem. Phys. 567 111819
Google Scholar
[22] Wang H Q, Li H F 2014 RSC Adv. 4 29782
Google Scholar
[23] Yi Z G, Luo Z C, Qin X, Chen Q S, Liu X G 2020 Acc. Chem. Res. 53 2692
Google Scholar
[24] Qin L X, Li H F, Xiao B W, Zhang J M, Zeng J K, Mei X J, Zhang Y H, Zheng H, Wang H Q 2023 Chem. Phys. 575 112064
Google Scholar
[25] Li W L, Chen T T, Xing D H, Chen X, Li J, Wang L S 2018 Proc. Natl. Acad. Sci. 115 E6972
[26] Robinson P J, Zhang X X, McQueen T, Bowen K H, Alexandrova A N 2017 J. Phys. Chem. A 121 1849
Google Scholar
[27] Chen T T, Li W L, Li J, Wang L S 2019 Chem. Sci. 10 2534
Google Scholar
[28] Zuo J N, Zhang L L, Chen B L, He K H, Dai W, Ding K W, Lu C 2024 J. Phys. Condens. Matter 36 015302
Google Scholar
[29] Xiang Z Y, Luo Z J, Bi J, Jin S Y, Zhang Z Q, Lu C 2022 J. Phys. Condens. Matter 34 445302
Google Scholar
[30] Jin S Y, Sun W G, Chen B L, Kuang X Y, Lu H Y, Lu C 2021 J. Phys. Chem. A 125 4126
Google Scholar
[31] Lu C, Gong W, Li Q, Chen C 2020 J. Phys. Chem. Lett. 11 9165
Google Scholar
[32] Li W L, Chen T T, Chen W J, Li J, Wang L S, 2021 Nat. Commun. 12 6467
Google Scholar
[33] Zhang J, Dolg M 2015 Phys. Chem. Chem. Phys. 17 24173
Google Scholar
[34] Frisch M J, Trucks G W, Schlegel H B, et al. 2016 Gaussian 09 (Revision Ed. 01) (Wallingford, CT: Gaussian, Inc.
[35] Lu T, Chen F W 2012 J. Comput. Chem. 33 580
Google Scholar
[36] Humphrey W, Dalke A, Schulten K 1996 J. Mol. Graph. 14 33
Google Scholar
[37] Dolg M, Stoll H, Savin A, Preuss H 1989 Theor. Chim. Acta. 75 173
Google Scholar
[38] Peterson A, Kirk F, Detlev G, Erich S H, Michael D 2003 J. Chem. Phys. 119 11113
Google Scholar
[39] Binkley, Stephen J, Pople, John A, Hehre, Warren J 1980 J. Am. Chem. Soc. 102 939
Google Scholar
[40] Adamo C, Barone V 1999 J. Chem. Phys. 110 6158
Google Scholar
[41] Wadt W R, Hay P J 1985 J. Chem. Phys. 82 284
Google Scholar
[42] Krishnan R, Binkley J S, Seeger R, Pople J A 1980 J. Chem. Phys. 72 650
Google Scholar
[43] Tozer D J, Handy N C 1998 J. Chem. Phys. 109 10180
Google Scholar
[44] Alexandrova A N, Boldyrev A I, Zhai H J, Wang L S, Steiner E, Fowler P W 2003 J. Phys. Chem. A 107 1362
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