Quantum Anharmonic Phonon Thermodynamics from the Free Energy Cumulant Expansion
Abstract
Abstract We present a computationally efficient workflow based on the free energy cumulant expansion to calculate vibrational thermodynamic properties with quantum effects and up to quartic anharmonicity. Helmholtz free energy, internal energy, entropy, and heat capacity are computed using renormalized self-consistent phonons, exact first- and second-order cumulants, and a rapidly convergent estimator for the reference potential energy. For classical Lennard-Jones (LJ) argon and Stillinger-Weber silicon, the free energies are within 0.25 meV/atom of thermodynamic integration (TI) at all temperatures with a comparable cost but simpler workflow. For quantum LJ neon, the cumulant expansion workflow is one-to-two orders of magnitude faster than TI because it does not require path-integral simulations. The predicted lattice constants and internal energies for LJ neon are within 0.004~\r{A} and 0.05 meV/atom of the reference. The speed and accuracy of the cumulant expansion workflow make it ideal for high-throughput quantum anharmonic thermodynamics.
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