Structural properties and vibrational modes ofSi34andSi46clathrates

The structural and vibrational properties of the silicon clathrates ${\mathrm{Si}}_{34}$ and ${\mathrm{Si}}_{46}$ are studied using the $O\left(N\right)\mathrm{}$ tight-binding density-matrix method of Li, Nunes, and Vanderbilt. The elastic moduli are found to be similar to those of cubic-diamond silicon. The large unit cells lead to complex Raman and infrared spectra which are obtained by calculating the full dynamical matrix directly. Certain modes are identified as molecularlike. Dispersion relations as well as the vibrational density of states are computed. The latter shows an unusual gap at approximately 16.5 THz for both clathrates. The mode-Grüneisen parameters are also calculated.