Due to the intrinsic shortness of time-step, atomistic molecular simulations can access only a tiny region of the dynamical response of condensed matter systems, i.e. the high-frequency region. For example, in the dynamical deformation of materials, only deformation rates/frequencies above 1010 Hz can be accessed. Coarse-graining methods do not provide a suitable solution to this problem, due to the presence of fudge parameters which limit their predictive power. We recently developed a new methodology based on the concept of nonaffine displacements, which are ubiquitous in disordered (and sometimes also in ordered) condensed matter systems. This framework, in principle, allows one to predict the dynamical response of materials across the entire time-scale spectrum. The method has been shown to be predictive on the example of a glassy material of Kremer-Grest polymer chains, and preliminary results at the atomistic level for real systems (polyethylene, DCPD, NBOH, etc) will be shown. Possible avenues for combined experimental (Raman/IR/neutron scattering) and theoretical/simulation studies will be discussed. Then I will briefly show some recent results [2,3] on the theoretical modelling of vibrational modes and the vibrational density of states of solids, both ordered and disordered, which explains the recent experimental observations (by various experimental groups) of glassy vibrational anomalies in perfectly ordered crystals.
 V.V. Palyulin, C. Ness, R. Milkus, R. Elder, T.W. Sirk, A.Zaccone, Soft Matter 14, 8475 (2018).
 M. Baggioli and A. Zaccone, Phys. Rev. Lett. 122, 145501 (2019).
 M. Baggioli and A. Zaccone, arXiv:1812.07245 .