Uncertainty quantification in first-principles predictions of phonon properties and lattice thermal conductivity

We present a framework for quantifying the uncertainty that results from the choice of exchange-correlation (XC) functional in predictions of phonon properties and thermal conductivity that use density functional theory to calculate the atomic force constants. The energy ensemble capabilities of the Bayesian error estimation functional with van der Waals correlation XC functional are first applied to determine an ensemble of interatomic force constants, which are then used as inputs to lattice dynamics calculations and a solution of the Boltzmann transport equation. The framework is applied to isotopically pure silicon. We find that the uncertainty estimates bound property predictions (e.g., phonon dispersions, specific heat, thermal conductivity) from other XC functionals and experiments. We distinguish between properties in silicon that are correlated with the predicted thermal conductivity [e.g., the transverse-acoustic branch sound speed (squared Pearson correlation coefficient, ${R}^{2}$, of 0.89) and average Gr\"uneisen parameter (${R}^{2}=0.85$)] and those that are not [e.g., longitudinal-acoustic branch sound speed (${R}^{2}=0.23$) and specific heat (${R}^{2}=0.00$)]. We find that differences in ensemble predictions of thermal conductivity are correlated with the behavior of transverse-acoustic phonons with mean free paths between 100 and 300 nm. The framework systematically accounts for XC uncertainty in phonon calculations and should be used whenever it is suspected that the choice of XC functional is influencing physical interpretations.