Structural, dynamic and electronic properties of amorphous Al$_2$O$_3$: ab--initio molecular dynamics calculations

First principles molecular dynamics (MD) calculations of amorphous Al$_2$O$_3$ in a system consisting of a supercell of 80 atoms is reported. A detailed analysis of the interatomic correlations allows us to conclude that the short range order is mainly composed by AlO$_4$ tetrahedra, but in contrast to classical MD results, also an important number of AlO$_5$ units are present. The vibrational density of state, calculated by means of the velocity autocorrelation function, present two main bands, a low frequency one related to the inter-tetrahedron vibration and a high frequency band related to the intra-tetrahedron vibration. By means of a geometry relaxation we obtain a fully relaxed system, and calculated its elastic properties. The reported bulk modulus is 193.4 GPa, the smallest among the several phases of alumina. The electronic properties were characterized by means of both the total and partial electronic density of states as well as by means of the electron localization function. The system present a rather small gap of 2.4 eV. The consequences of these results will be discussed.