Quantifying Uncertainty in First-Principles Predictions of Molecular Vibrational Frequencies, Phonon Properties, and Thermal Conductivity*

We present a robust method for quantifying the uncertainty in molecular vibrational frequencies, phonon properties, and thermal conductivities predicted from density functional theory calculations using the BEEF-vdW exchange-correlation (XC) functional. The procedure starts by displacing atoms in an equilibrium structure. 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. The energy ensembles of the perturbed structures are used with finite difference formulas 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 vibrational frequencies of a molecule or the phonon frequencies, group velocities, lifetimes, heat capacity, and thermal conductivity of a crystal, whose spreads can be used to quantify uncertainty. Results for molecules, molecular complexes from the S22 dataset, and silicon are presented and compared to predictions from XC functionals at the local density approximation and generalized gradient approximation levels.