Voronoi-Delaunay analysis of normal modes in a simple model glass

We combine a conventional harmonic analysis of vibrations in a soft-sphere glass with a Voronoi-Delaunay geometrical analysis of the structure. ``Structure potentials'' (tetrahedricity, sphericity, or perfectness) are introduced to describe the shape of the local atomic configurations (Delaunay simplices) as a function of the atomic coordinates. Apart from the highest and lowest frequencies the amplitude weighted ``structure potential'' varies only little with frequency. The movement of atoms in soft vibrational modes causes transitions between different ``perfect'' realizations of local structure. As for the potential energy a dynamic matrix can be defined for the ``structure potential.'' Its expectation value with respect to the vibrational modes increases nearly linearly with frequency and shows a clear indication of the boson peak. The structure eigenvectors of this dynamical matrix are strongly correlated to the vibrational ones. Four subgroups of modes can be distinguished.