Citation: XING Sheng-Kai, LI Yun, ZHAO Xue-Zhuang, CAI Zun-Sheng, SHANG Zhen-Feng, WANG Gui-Chang. Molecular Symmetry of Möbius Cyclacenes[J]. Acta Physico-Chimica Sinica, ;2011, 27(05): 1000-1004. doi: 10.3866/PKU.WHXB20110518 shu

Molecular Symmetry of Möbius Cyclacenes

1.
College of Chemistry, Nankai University, Tianjin 300071, P. R. China

Received Date: 15 December 2010
Available Online: 2 April 2011

Generally speaking, the highest symmetry of a Möbius cyclacene molecule is C₂ group based on the point group theory. We here investigated two isomers of cyclacene that were composed of 18 benzene units, i.e., a hoop-like Hückel [18]-cyclacene (HC-[18]) and a Möbius strip-like Möbius[18]- cyclacene (MC-[18]). We found that in addition to being described by C₂ point group transformation, the molecular symmetry of Möbius cyclacene may also be characterized by the so-called torus screw rotation (TSR) symmetrical transformation, which is a symmetry operation of the torus group introduced here. The torus ortho nal curvilinear coordinates were also introduced to express the TSR transformation. Furthermore, both the symmetry adapted atom set and the atomic orbital set that refers to the TSR transformation are discussed. Because the TSR symmetry has cyclic group characteristics, we can establish the irreducible representations and related characteristics for this cyclic group. In addition, for these cyclacenes the irreducible representation of their molecular orbitals (MOs) may be pure while their corresponding symmetry adaptive linear combination of atomic orbital (SALC-AO) components can be numerous.
- Möbius cyclacene,
- Molecular symmetry,
- Cyclacene,
- Torus screw rotation transformation,
- Torus ortho nal curvilinear coordinates,
- Torus group
1. [1]
  
  (1) Rzepa, H. S. Chem. Rev. 2005, 105, 3697.
2. [2]
  (2) Craig, D. P., Paddock, N. L. Nature 1958, 181, 1052.
3. [3]
  (3) Craig, D. P. J. Chem. Soc. 1959, 997.
4. [4]
  (4) Heilbronner, E. Tetrahedron Lett. 1964, 5, 1923.
5. [5]
  (5) Zimmerman, H. E. Accounts Chem. Res. 1971, 4, 272.
6. [6]
  (6) Walba, D. M.; Richards, R. M.; Haltiwanger, R. C. J. Am. Chem. Soc. 1982, 104, 3219.
7. [7]
  (7) Walba, D. M.; Homan, T. C.; Richards, R. M.; Haltiwanger, R. C. New J. Chem. 1993, 17, 661.
8. [8]
  (8) Qiu, W. Y.; Zhang, F. L. Chemistry 1988, 11, 59.
9. [9]
  [邱文元, 张伏龙. 化学通报, 1988, 11, 59.]
10. [10]
  (9) Ajami, D.; Oeckler, O.; Simon, A.; Herges, R. Nature 2003, 426, 819.
11. [11]
  (10) Ajami, D.; Hess, K.; K?hler, F.; N?ther, C.; Oeckler, O.; Simon, A.; Yamamoto, C.; Okamoto, Y.; Herges, R. Chem. Eur. J. 2006, 12, 5434.
12. [12]
  (11) Herges, R. Chem. Rev. 2006, 106, 4820.
13. [13]
  (12) Geuenich, D.; Hess, K.; Koehler, F.; Herges, R. Chem. Rev. 2005, 105, 3758.
14. [14]
  (13) Andre, J. M.; Champagne, B.; Perpete, E. A.; Guillaume, M. Int. J. Quantum Chem. 2001, 84, 608.
15. [15]
  (14) Martin-Santamaria, S.; Rzepa, H. S. J. Chem. Soc. Perkin Trans. 2000, 2, 2372.
16. [16]
  (15) Stantos, M. C.; Alvarez, F. Chem. Phys. Lett. 2009, 471, 276.
17. [17]
  (16) Jiang, D. E.; Dai, S. J. Phys. Chem. C 2008, 112, 5348.
18. [18]
  (17) Lemi, T. J. Mol. Struct. -Theochem 1998, 454, 83.
19. [19]
  (18) Xu, H. L.; Li, Z. R.; Wang, F. F.; Wu, D.; Harigaya, K.; Gu, F. L. Chem. Phys. Lett. 2008, 454, 323.
20. [20]
  (19) Armstrong, M. A. Basic Topology; Peking University Press: Beijing, 1983; pp 160-162; translated by Sun, Y. F.
21. [21]
  [Armstrong, M. A. 基础拓扑学. 孙以丰, 译. 北京: 北京大学出版社, 1983: 160-162.]
22. [22]
  (20) Wang, R. H.; Guo, K. X. Symmetry Group of Crystallography; Science Press: Beijing, 1990; pp 348-349.
23. [23]
  [王仁卉, 郭可信. 晶体学中的对称群. 北京: 科学出版社, 1990: 348-349.]
24. [24]
  (21) Yang, Z. R. Fractal Physics; Shanghai Scientific and Technological Education Publishing House: Shanghai, 1996; pp 1-25.
25. [25]
  [杨展如. 分形物理学. 上海: 上海科技教育出版社, 1996: 1-25.]
26. [26]
  (22) Cotton, F. A. Chemical Application of Group Theory, 3rd ed.; Wiley: New York, 1990; pp 68-99.
27. [27]
  (23) Xing, S. K.; Li, Y.; Zhao, X. Z.; Shang, Z. F.; Xu, X. F.; Cai, Z. S.; Wang, G. C.; Li, R. F. Acta Phys.-Chim. Sin. 2010, 26, 1947.
28. [28]
  [邢生凯, 李云, 赵学庄, 尚贞锋, 许秀芳, 蔡遵生, 王贵昌, 李瑞芳. 物理化学学报, 2010, 26, 1947.]
29. [29]
  (24) Zhao, X. Z.; Wang, G. C.; Xu, X. F.; Pan, Y. M.; Shang, Z. F.; Li, R. F.; Li, Z. C. J. Math. Chem. 2008, 43(2), 485.
30. [30]
  (25) Zhao, X. Z.; Shang, Z. F.; Li, Z. C.; Xu, X. F.; Wang, G. C.; Li, R. F.; Li, Y. J. Math. Chem. 2010, 48(2), 187.
31. [31]
  (26) Xu, G. X.; Li, L. M.; Wang, D. M. Quantum Chemistry (Basic Theorem and ab initio Method); Science Press: Beijing, 2008; pp 445-449.
32. [32]
  [徐光宪, 黎乐民, 王德明. 量子化学(基本原理和从头计算法), 第二版. 北京: 科学出版社, 2008: 445-450.]
1. [1]
  Conghao Shi , Ranran Wang , Juli Jiang , Leyong Wang . The Illustration on Stereoisomers of Macrocycles Containing Multiple Chiral Centers via Tröger Base-based Macrocycles. University Chemistry, 2024, 39(7): 394-397. doi: 10.3866/PKU.DXHX202311034
2. [2]
  Zhanhui Yang , Jiaxi Xu . (m+n+…) or [m+n+…]cycloaddition?. University Chemistry, 2025, 40(3): 387-389. doi: 10.12461/PKU.DXHX202406032
3. [3]
  Junjie Zhang , Yue Wang , Qiuhan Wu , Ruquan Shen , Han Liu , Xinhua Duan . Preparation and Selective Separation of Lightweight Magnetic Molecularly Imprinted Polymers for Trace Tetracycline Detection in Milk. University Chemistry, 2024, 39(5): 251-257. doi: 10.3866/PKU.DXHX202311084
4. [4]
  Zhiwen HUANG , Qi LIU , Jianping LANG . W/Cu/S cluster-based supramolecular macrocycles and their third-order nonlinear optical responses. Chinese Journal of Inorganic Chemistry, 2025, 41(1): 79-87. doi: 10.11862/CJIC.20240184
5. [5]
  Qianwen Han , Tenglong Zhu , Qiuqiu Lü , Mahong Yu , Qin Zhong . 氢电极支撑可逆固体氧化物电池性能及电化学不对称性优化. Acta Physico-Chimica Sinica, 2025, 41(1): 2309037-. doi: 10.3866/PKU.WHXB202309037
6. [6]
  Tao Wen , Tao Zhang , Changguo Sun , Jinyu Liu . Preparation of Dess-Martin Reagent and Its Application in Oxidizing Cyclohexanol. University Chemistry, 2024, 39(5): 20-26. doi: 10.3866/PKU.DXHX202309055
7. [7]
  Keweiyang Zhang , Zihan Fan , Liyuan Xiao , Haitao Long , Jing Jing . Unveiling Crystal Field Theory: Preparation, Characterization, and Performance Assessment of Nickel Macrocyclic Complexes. University Chemistry, 2024, 39(5): 163-171. doi: 10.3866/PKU.DXHX202310084
8. [8]
  Chi Li , Jichao Wan , Qiyu Long , Hui Lv , Ying Xiong . N-Heterocyclic Carbene (NHC)-Catalyzed Amidation of Aldehydes with Nitroso Compounds. University Chemistry, 2024, 39(5): 388-395. doi: 10.3866/PKU.DXHX202312016
9. [9]
  Hongling Yuan , Jialin Xie , Jiawei Wang , Jixiang Zhao , Jiayan Liu , Qing Feng , Wei Qi , Min Liu . Cyclic Olefin Copolymer (COC): The Agile Vanguard in the Realm of Materials. University Chemistry, 2024, 39(7): 294-298. doi: 10.12461/PKU.DXHX202311041
10. [10]
  Guojie Xu , Fang Yu , Yunxia Wang , Meng Sun . Introduction to Metal-Catalyzed β-Carbon Elimination Reaction of Cyclopropenones. University Chemistry, 2024, 39(8): 169-173. doi: 10.3866/PKU.DXHX202401060
11. [11]
  Hong Zheng , Xin Peng , Chunwang Yi . The Tale of Caprolactam Cyclic Oligomers: The Ever-changing Life of “Princess Cyclo”. University Chemistry, 2024, 39(9): 40-47. doi: 10.12461/PKU.DXHX202403058
12. [12]
  Zhuoyan Lv , Yangming Ding , Leilei Kang , Lin Li , Xiao Yan Liu , Aiqin Wang , Tao Zhang . Light-Enhanced Direct Epoxidation of Propylene by Molecular Oxygen over CuO_x/TiO₂ Catalyst. Acta Physico-Chimica Sinica, 2025, 41(4): 100038-. doi: 10.3866/PKU.WHXB202408015
13. [13]
  Fugui XI , Du LI , Zhourui YAN , Hui WANG , Junyu XIANG , Zhiyun DONG . Functionalized zirconium metal-organic frameworks for the removal of tetracycline from water. Chinese Journal of Inorganic Chemistry, 2025, 41(4): 683-694. doi: 10.11862/CJIC.20240291
14. [14]
  Ruolin CHENG , Haoran WANG , Jing REN , Yingying MA , Huagen LIANG . Efficient photocatalytic CO₂ cycloaddition over W₁₈O₄₉/NH₂-UiO-66 composite catalyst. Chinese Journal of Inorganic Chemistry, 2024, 40(3): 523-532. doi: 10.11862/CJIC.20230349
15. [15]
  Jianjun LI , Mingjie REN , Lili ZHANG , Lingling ZENG , Huiling WANG , Xiangwu MENG . UV-assisted degradation of tetracycline hydrochloride by MnFe₂O₄@activated carbon activated persulfate. Chinese Journal of Inorganic Chemistry, 2024, 40(10): 1869-1880. doi: 10.11862/CJIC.20240187
16. [16]
  Shengyan Yang , Xiangzhen Meng , Xin Wang , Yang Zhang . Construction and Exploration of an Online-Offline Blended “Eight-Link” Teaching Method for Physical Chemistry Experiments Based on OBE Concept. University Chemistry, 2024, 39(11): 28-37. doi: 10.3866/PKU.DXHX202402019
17. [17]
  Hong RAO , Yang HU , Yicong MA , Chunxin LÜ , Wei ZHONG , Lihua DU . Synthesis and in vitro anticancer activity of phenanthroline-functionalized nitrogen heterocyclic carbene homo- and heterobimetallic silver/gold complexes. Chinese Journal of Inorganic Chemistry, 2024, 40(12): 2429-2437. doi: 10.11862/CJIC.20240275
18. [18]
  Jiahui YU , Jixian DONG , Yutong ZHAO , Fuping ZHAO , Bo GE , Xipeng PU , Dafeng ZHANG . The morphology control and full-spectrum photodegradation tetracycline performance of microwave-hydrothermal synthesized BiVO₄:Yb³⁺,Er³⁺ photocatalyst. Journal of Fuel Chemistry and Technology, 2025, 53(3): 348-359. doi: 10.1016/S1872-5813(24)60514-1
19. [19]
  Jinwang Wu , Qijing Xie , Chengliang Zhang , Haifeng Shi . 自旋极化增强ZnFe_1.2Co_0.8O₄/BiVO₄ S型异质结光催化性能降解四环素. Acta Physico-Chimica Sinica, 2025, 41(5): 100050-. doi: 10.1016/j.actphy.2025.100050
20. [20]
  Ke QIAO , Yanlin LI , Shengli HUANG , Guoyu YANG . Advancements in asymmetric catalysis employing chiral iridium (ruthenium) complexes. Chinese Journal of Inorganic Chemistry, 2024, 40(11): 2091-2104. doi: 10.11862/CJIC.20240265

Get Citation

PDF

XML

Metrics

PDF Downloads(1232)
Abstract views(2698)
HTML views(119)

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142