Accurate and Efficient Phonon Calculations in Molecular Crystals via Minimal Molecular Displacements

Vibrational dynamics governs the fundamental properties of molecular crystals, shaping their thermodynamics, mechanics, spectroscopy, and transport phenomena. However desirable, the first-principles calculation of solid-state vibrations, i.e.\ phonons, stands as a major computational challenge in molecular crystals characterized by many atoms in the unit cell and by weak intermolecular interactions. Here we propose a formulation of the harmonic lattice dynamics based on a natural basis of molecular coordinates consisting of rigid-body displacements and intramolecular vibrations. This enables a sensible \emph{minimal molecular displacement} approximation for the calculation of the dynamical matrix, combining isolated molecule calculations with only a small number of expensive crystal supercell calculations, ultimately reducing the computational cost by up to a factor 10. The comparison with reference calculations demonstrates the quantitative accuracy of our method, especially for the challenging and dispersive low-frequency region it is designed for. Our method provides an excellent description of the thermodynamic properties and offers a privileged molecular-level insight into the complex phonons band structure of molecular materials.