物理化学学报 >> 2008, Vol. 24 >> Issue (09): 1579-1583.doi: 10.1016/S1872-1508(08)60065-0

研究论文 上一篇    下一篇

环和纳米管径向呼吸振动模式的一个简单理论模型

周桃, 徐灿, 张小芳, 程川, 陈亮, 许莹   

  1. 兰州大学磁性和磁性材料教育部重点实验室, 兰州 730000
  • 收稿日期:2008-02-19 修回日期:2008-04-30 发布日期:2008-09-10
  • 通讯作者: 徐灿 E-mail:cxulzu@yahoo.com

A Simple Theoretical Model for Ring and Nanotube Radial Breathing Mode

ZHOU Tao, XU Can, ZHANG Xiao-Fang, CHENG Chuan, CHEN Liang, XU Ying   

  1. Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, P. R. China
  • Received:2008-02-19 Revised:2008-04-30 Published:2008-09-10
  • Contact: XU Can E-mail:cxulzu@yahoo.com

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摘要： 用密度泛函方法在B3LYP/6-31G(d)基组下计算了(MgO)n和(BeO)n环(n=3-10)的径向呼吸振动. 大环的径向呼吸振动频率正比于环直径的倒数, 但键长的变化导致频率偏离了这种线性关系. 随着环直径的减小, 直径倒数的三次方和键长的变化将导致频率更大地偏离线性行为. 从化学键的角度出发利用一维谐振子及弹簧的串并联思想, 解释了这种线性关系和偏离现象. 这种模型还可以用于研究纳米管的径向呼吸振动频率.

关键词: 径向呼吸振动模式, 直径, 环, 纳米管, 键长

Abstract: The radial breathing modes (RBMs) of (MgO)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.

Key words: Radial breathing mode, Diameter, Ring, Nanotubes, Bond length