We applied the recently developed Generalized Langevin equation (GLE) approach for dielectric response of liquids and glasses to link the vibrational density of states (VDOS) to the dielectric response of a model orientational glass. The dielectric functions calculated based on the GLE, with VDOS obtained in experiments and simulations as input, are compared with experimental data for the paradigmatic case of 2-adamantanone at various temperatures. The memory function is related to the integral of the VDOS times a spectral coupling function $\gamma \left({\omega }_p\right)$, which tells the degree of dynamical coupling between molecular degrees of freedom at different eigenfrequencies. With respect to previous empirical fittings, the GLE-based fitting reveals a broader temperature range over which the secondary relaxation is active. Furthermore, the theoretical analysis provides clear evidence of secondary relaxation being localized within the THz ($0.5-1$ THz) range of eigenfrequencies, and thus not too far from the low-energy modes involved in $\alpha$ relaxation. In the same THz region, the same material displays a crowding of low-energy optical modes that may be related to the secondary relaxation.

• Received 1 October 2019
• Revised 3 February 2020
• Accepted 3 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.104202