Quantifying Uncertainty in First-Principles Predictions of Phonon Properties and Thermal Conductivity

We present a robust method for quantifying the uncertainty in phonon properties and thermal conductivity predicted from density functional theory calculations using the BEEF-vdW exchange-correlation (XC) functional. The procedure starts by displacing atoms in an equilibrium structure and using the energies of the perturbed structures to determine harmonic and anharmonic force constants. BEEF-vdW generates an ensemble of energies for each perturbed structure as a computationally efficient post-processing step by perturbing the XC functional and solving for the energy non-self consistently. Thus, each perturbed structure yields an ensemble of energies. This energy ensemble is then used to determine an ensemble of force constants, which is then used as input to lattice dynamics calculations and a solution of the Boltzmann transport equation. This procedure results in ensembles for the phonon frequencies, group velocities, and lifetimes, and overall heat capacity and thermal conductivity, whose spreads can be used to quantify uncertainty. Results for silicon, graphene, and graphite are presented and compared to predictions from the PBE, RPBE, and PBEsol XC functionals.