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

TL;DR

This paper introduces a framework to quantify the uncertainty in phonon property and thermal conductivity predictions caused by the choice of exchange-correlation functional in density functional theory, demonstrated on silicon.

Contribution

The authors develop a systematic method to incorporate XC functional uncertainty into phonon and thermal conductivity calculations using DFT, enhancing reliability of predictions.

Findings

Uncertainty estimates encompass other XC functionals and experimental data.

Properties like sound speed and Grüneisen parameter are strongly correlated with thermal conductivity.

Differences in thermal conductivity predictions relate to phonons with mean free paths of 100-300 nm.

Abstract

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 (DFT) to calculate the atomic force constants. The energy ensemble capabilities of the BEEF-vdW 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 that are correlated with the predicted thermal conductivity [e.g., the transverse acoustic branch sound speed ($R^2=0.89$) 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 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.