Quantifying Uncertainty 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 (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. To validate our BEEF-vdW results, we also perform calculations using the LDA, PBE, PBEsol, and optPBE-vdW XC functionals.

We find that the uncertainty estimates bound property predictions (e.g., phonon dispersions, specific heat, thermal conductivity, Gruneisen parameter) from other XC functionals and experiments. Using BEEF-vdW yields a thermal conductivity prediction of 171 W/(m K), while LDA yields the lowest value of 122 W/(m K). BEEF-vdW also predicts weak anharmonicity, with an average Gruneisen parameter of 0.92, and strong harmonic properties, such as the highest LA sound speed of the XC functionals tested (8564 m/s). LDA predicts strong anharmonicity (1.16 average Gruneisen parameter) and weak harmonic properties (8388 m/s LA sound speed). The combined effects of harmonic and anharmonic properties leads to a high thermal conductivity using BEEF-vdW and a low thermal conductivity using LDA.

Using correlation analysis, we distinguish between properties that are correlated with the predicted thermal conductivity [e.g., the transverse acoustic branch sound speed (R2=0.89) and average Grüneisen parameter (R2=0.85)]. The correlation analysis specifically allows us to determine properties that are important physically but that do not vary between XC functionals, such as the longitudinal acoustic branch sound speed (R2=0.23) and specific heat (R2=0.00).

We also 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, which is observed from the thermal conductivity accumulation function. We find through a further investigation of the thermal accumulation function of only the TA phonons that the disagreement of these 100-300 nm mean free path phonons is due to variation in the predictions of the TA phonons.

The framework systematically accounts for XC uncertainty in phonon calculations. We have demonstrated the power of the framework here with silicon, but the conclusions could vary between systems due to the non-linear nature of the lattice dynamics and BTE calculations. We recommend that it be used whenever it is suspected that the choice of XC functional is influencing physical interpretations.