Phonon mode resolved anharmonic heat capacity of solids

We develop and validate a lattice dynamics framework to include anharmonic effects in the calculation of mode-level phonon heat capacities. To capture anharmonicity, the phonons are renormalized using a temperature-dependent effective potential and a proposed approach based on instantaneous normal modes. Ground-truth total heat capacities are obtained from molecular dynamics simulations. For Lennard-Jones argon (Stillinger-Weber silicon), the deviation of the potential energy contribution to the total heat capacity from the harmonic Dulong-Petit law is $\ensuremath{-}12%$ ($+16%$) at the highest studied temperature of 80 K (1300 K). The mode heat capacities from the lattice dynamics calculations are summed and compared with the ground-truth total heat capacity. For all temperatures considered, the instantaneous normal mode approach gives the best prediction for Lennard-Jones argon (within 1.1%), while for Stillinger-Weber silicon the temperature-dependent effective potential is best (within 0.7%). The Lennard-Jones argon mode heat capacities decrease with increasing frequency and are impacted by the effect of anharmonicity on the mode's self energy and its interactions with other modes. In Stillinger-Weber silicon, the acoustic mode heat capacities increase by up to 30% relative to the Dulong-Petit law, with these deviations driven by the interactions between modes. The proposed calculation framework will improve high-temperature thermal conductivity calculations, where the heat capacity is generally assumed to take on the harmonic value from the Dulong-Petit law.