Vibrational properties of amorphous silicon from tight-binding O(N) calculations

We present an O(N) algorithm to study the vibrational properties of amorphous silicon within the framework of tight-binding approach. The dynamical matrix elements have been evaluated numerically in the harmonic approximation exploiting the short-range nature of the density matrix to calculate the vibrational density of states which is then compared with the same obtained from a standard O(N-4) algorithm. For the purpose of illustration, an 1000-atom model is studied to calculate the localization properties of the vibrational eigenstates using the participation numbers calculation.