On The Low-Frequency Vibrational Modes of C${}_{60}$

Abstract

The vibrational spectrum of C${}_{60}$ is compared to the spectrum of a classical isotropic elastic spherical shell. We show correlations between the low frequency modes of C${}_{60}$ and those of the spherical shell. We find the spherical model gives the approximate frequency ordering for the low frequency modes. We estimate a Poisson ratio of $\sigma \approx 0.30$ and a transverse speed of sound of $v_s\approx 1800$ m/s for the equivalent elastic shell. We also find that $\omega ({\mathrm{M}}_1)/\omega ({\mathrm{M}}_0)=\sqrt{\frac{3}{2}}$ for the shell modes ${\mathrm{M}}_0$ and ${\mathrm{M}}_1$, independent of elastic constants. We find that this ratio compares favorably with an experimental value of 1.17.

arXiv comment11 pages, 3 figures in Postscript, uses REVTEX, to be published in Chem. Phys. Lett