  The vibrational properties of model amorphous materials are studied by
combining complete analysis of the vibration modes, dynamical structure factor
and energy diffusivity with exact diagonalization of the dynamical matrix and
the Kernel Polynomial Method which allows a study of very large system sizes.
Different materials are studied that differ only by the bending rigidity of the
interactions in a Stillinger-Weber modelization used to describe amorphous
silicon. The local bending rigidity can thus be used as a control parameter, to
tune the sound velocity together with local bonds directionality. It is shown
that for all the systems studied, the upper limit of the Boson peak corresponds
to the Ioffe-Regel criterion for transverse waves, as well as to a minimum of
the diffusivity. The Boson peak is followed by a diffusivity's increase
supported by longitudinal phonons. The Ioffe-Regel criterion for transverse
waves corresponds to a common characteristic mean-free path of 5-7 \AA{} (which
is slightly bigger for longitudinal phonons), while the fine structure of the
vibrational density of states is shown to be sensitive to the local bending
rigidity.
