环和纳米管径向呼吸振动模式的一个简单理论模型

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.

A Simple Theoretical Model for Ring and Nanotube Radial Breathing Mode

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.