  Based on a description of an amorphous solid as a collection of coupled
nanosize molecular clusters referred as basic blocks, we analyse the
statistical properties of its Hamiltonian. The information is then used to
derive the ensemble averaged density of the vibrational states (non-phonon)
which turns out to be a Gaussian in the bulk of the spectrum and an Airy
function in the low frequency regime. A comparison with experimental data for
five glasses confirms validity of our theoretical predictions.
