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We present a framework for quantifying the uncertainty that results from thechoice of exchange-correlation (XC) functional in predictions of phononproperties and thermal conductivity that use density functional theory (DFT) tocalculate the atomic force constants. The energy ensemble capabilities of theBEEF-vdW XC functional are first applied to determine an ensemble ofinteratomic force constants, which are then used as inputs to lattice dynamicscalculations and a solution of the Boltzmann transport equation. The frameworkis applied to isotopically-pure silicon. We find that the uncertainty estimatesbound property predictions (e.g., phonon dispersions, specific heat, thermalconductivity) from other XC functionals and experiments. We distinguish betweenproperties that are correlated with the predicted thermal conductivity [e.g.,the transverse acoustic branch sound speed ($R^2=0.89$) and average Gr\"uneisenparameter ($R^2=0.85$)] and those that are not [e.g., longitudinal acousticbranch sound speed ($R^2=0.23$) and specific heat ($R^2=0.00$)]. We find thatdifferences in ensemble predictions of thermal conductivity are correlated withthe behavior of phonons with mean free paths between $100$ and $300$ nm. Theframework systematically accounts for XC uncertainty in phonon calculations andshould be used whenever it is suspected that the choice of XC functional isinfluencing physical interpretations.

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