  The excess low-frequency vibrational spectrum, called boson peak, and
non-affine elastic response are the most important particularities of glasses.
Herein, the vibrational and mechanical properties of polymeric glasses are
examined by using coarse-grained molecular dynamics simulations, with
particular attention to the effects of the bending rigidity of the polymer
chains. As the rigidity increases, the system undergoes a glass transition at a
higher temperature (under a constant pressure), which decreases the density of
the glass phase. The elastic moduli, which are controlled by the decrease of
the density and the increase of the rigidity, show a non-monotonic dependence
on the rigidity of the polymer chain that arises from the non-affine component.
Moreover, a clear boson peak is observed in the vibrational density of states,
which depends on the macroscopic shear modulus $G$. In particular, the boson
peak frequency is scaled as $\omega_\mathrm{BP} \propto \sqrt{G}$. These
results provide a positive correlation between the boson peak, shear
elasticity, and the glass transition temperature.
