Terahertz spectroscopy and solid-state density functional theory calculation of anthracene: effect of dispersion force on the vibrational modes

The phonon modes of molecular crystals in the terahertz frequency region often feature delicately coupled inter- and intra-molecular vibrations. Recent advances in density functional theory such as DFT-D(*) have enabled accurate frequency calculation. However, the nature of normal modes has not been quantitatively discussed against experimental criteria such as isotope shift (IS) and correlation field splitting (CFS). Here, we report an analytical mode-decoupling method that allows for the decomposition of a normal mode of interest into intermolecular translation, libration, and intramolecular vibrational motions. We show an application of this method using the crystalline anthracene system as an example. The relationship between the experimentally obtained IS and the IS obtained by PBE-D(*) simulation indicates that two distinctive regions exist. Region I is associated with a pure intermolecular translation, whereas region II features coupled intramolecular vibrations that are further coupled by a weak intermolecular translation. We find that the PBE-D(*) data show excellent agreement with the experimental data in terms of IS and CFS in region II; however, PBE-D(*) produces significant deviations in IS in region I where strong coupling between inter- and intra-molecular vibrations contributes to normal modes. The result of this analysis is expected to facilitate future improvement of DFT-D(*).