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.