Home

Citation: ZHOU Tao, XU Can, ZHANG Xiao-Fang, CHENG Chuan, CHEN Liang, XU Ying. A Simple Theoretical Model for Ring and Nanotube Radial Breathing Mode[J]. Acta Physico-Chimica Sinica, ;2008, 24(09): 1579-1583. doi: 10.1016/S1872-1508(08)60065-0 shu

A Simple Theoretical Model for Ring and Nanotube Radial Breathing Mode

1.
Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, P. R. China

Received Date: 19 February 2008
Available Online: 17 June 2008

The radial breathing modes (RBMs) of (M )n and (BeO)n rings (n=3-10) were calculated using the density functional theory at B3LYP/6-31G(d) level. It was found that for large rings, the radial breathing mode (RBM) frequency was inversely proportional to the centre diameter, but the variation of bond length may lead to deviations from a linear behavior. The deviations caused by inverse cubic term of diameter and variation of bond length, became dramatic with the decrease of ring diameter. From the point of chemical bond view, using one-dimensional harmonic oscillator and the method of cascade and parallel connection of “springs”, the linear relation and deviations were explained. The model can be applied to nanotubes.
- Radial breathing mode,
- Diameter,
- Ring,
- Nanotubes,
- Bond length
1. [1]
  Xiufang Wang , Donglin Zhao , Kehua Zhang , Xiaojie Song . “Preparation of Carbon Nanotube/SnS₂ Photoanode Materials”: A Comprehensive University Chemistry Experiment. University Chemistry, 2024, 39(4): 157-162. doi: 10.3866/PKU.DXHX202308025
2. [2]
  Hailang JIA , Hongcheng LI , Pengcheng JI , Yang TENG , Mingyun GUAN . Preparation and performance of N-doped carbon nanotubes composite Co₃O₄ as oxygen reduction reaction electrocatalysts. Chinese Journal of Inorganic Chemistry, 2024, 40(4): 693-700. doi: 10.11862/CJIC.20230402
3. [3]
  Shuhong Xiang , Lv Yang , Yingsheng Xu , Guoxin Cao , Hongjian Zhou . Selective electrosorption of Cs(Ⅰ) from high-salinity radioactive wastewater using CNT-interspersed potassium zinc ferrocyanide electrodes. Acta Physico-Chimica Sinica, 2025, 41(9): 100097-0. doi: 10.1016/j.actphy.2025.100097
4. [4]
  Chen Pu , Daijie Deng , Henan Li , Li Xu . Fe_0.64Ni_0.36@Fe₃NiN Core-Shell Nanostructure Encapsulated in N-Doped Carbon Nanotubes for Rechargeable Zinc-Air Batteries with Ultralong Cycle Stability. Acta Physico-Chimica Sinica, 2024, 40(2): 2304021-0. doi: 10.3866/PKU.WHXB202304021
5. [5]
  Zhanhui Yang , Jiaxi Xu . (m+n+…) or [m+n+…]cycloaddition?. University Chemistry, 2025, 40(3): 387-389. doi: 10.12461/PKU.DXHX202406032
6. [6]
  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
7. [7]
  Haihua Yang , Minjie Zhou , Binhong He , Wenyuan Xu , Bing Chen , Enxiang Liang . Synthesis and Electrocatalytic Performance of Iron Phosphide@Carbon Nanotubes as Cathode Material for Zinc-Air Battery: a Comprehensive Undergraduate Chemical Experiment. University Chemistry, 2024, 39(10): 426-432. doi: 10.12461/PKU.DXHX202405100
8. [8]
  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
9. [9]
  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
10. [10]
  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
11. [11]
  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
12. [12]
  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
13. [13]
  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
14. [14]
  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): 2408015-0. doi: 10.3866/PKU.WHXB202408015
15. [15]
  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
16. [16]
  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
17. [17]
  Ruolin CHENG , Yue WANG , Xiyao NIU , Huagen LIANG , Ling LIU , Shijian LU . Efficient photothermal catalytic CO₂ cycloaddition over W₁₈O₄₉/rGO composites. Chinese Journal of Inorganic Chemistry, 2025, 41(7): 1276-1284. doi: 10.11862/CJIC.20240424
18. [18]
  Hanxue LIU , Shijie LI , Meng REN , Xuling XUE , Hongke LIU . Design and antitumor properties of dehydroabietic acid functionalized cyclometalated iridium(Ⅲ) complex. Chinese Journal of Inorganic Chemistry, 2025, 41(8): 1483-1494. doi: 10.11862/CJIC.20250031
19. [19]
  Ruoxi Sun , Yiqian Xu , Shaoru Rong , Chunmiao Han , Hui Xu . The Enchanting Collision of Light and Time Magic: Exploring the Footprints of Long Afterglow Lifetime. University Chemistry, 2024, 39(5): 90-97. doi: 10.3866/PKU.DXHX202310001
20. [20]
  Mengfei He , Chao Chen , Yue Tang , Si Meng , Zunfa Wang , Liyu Wang , Jiabao Xing , Xinyu Zhang , Jiahui Huang , Jiangbo Lu , Hongmei Jing , Xiangyu Liu , Hua Xu . Epitaxial Growth of Nonlayered 2D MnTe Nanosheets with Thickness-Tunable Conduction for p-Type Field Effect Transistor and Superior Contact Electrode. Acta Physico-Chimica Sinica, 2025, 41(2): 2310029-0. doi: 10.3866/PKU.WHXB202310029

Get Citation

PDF

XML

Metrics

PDF Downloads(1779)
Abstract views(4483)
HTML views(262)

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

Address：Zhongguancun North First Street 2,100190 Beijing, PR China Tel: +86-010-82449177-888

DownLoad: Full-Size Img PowerPoint

Return