Theoretical study of the vibrational modes and their pressure dependence in the pure clathrate-II silicon framework

We study the vibrational properties of pure type-II silicon clathrate $({\mathrm{Si}}_{136})$ using first-principles electronic structure methods. The results of our calculations are consistent with recent Raman experiments. We explore the effects of pressure on its open framework and determine the equation of state and pressure dependence of the vibrational modes and the electronic band gap.