Vibrational Anomalies Are Not Generally Due to Fractal Geometry: Comments on Proteins

Deviations in a $d$-dimensional Euclidean connected lattice of the spectral number (cumulative) of vibrational states from the frequently generalized formula $N\left(\omega \right)\propto {\omega }^d$, i.e., density $\rho \left(\omega \right)\propto {\omega }^{d-1\mathrm{}}$, are common at very low frequency in many materials (e.g., crystalline), and are not related to disorder or fractal connectivity. These anomalies have been shown to be due to strong anisotropy, or to noncentral molecular-type forces, or both. The apparent spectral densities seen in globular and sheet proteins are compatible with conventional theoretical models dominated by molecular bond-bending or torsional forces.