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Uncertainty Quantification of DFT-predicted Finite Temperature Thermodynamic Properties within the Debye Model

Finite-temperature effects can be included by calculating the vibrations properties and this can greatly improve the fidelity of computational screening. An important challenge for DFT-based screening is the sensitivity of the predictions to the choice of the exchange correlation function. In this work, we rigorously explore the sensitivity of finite temperature thermodynamic properties to the choice of the exchange correlation functional using the built-in error estimation capabilities within the Bayesian Error Estimation Functional. The vibrational properties are estimated using the Debye model and we quantify the uncertainty associated with finite-temperature properties for a diverse collection of materials. We find good agreement with experiment and small spread in predictions over different exchange correlation functionals for Mg, Al$_2$O$_3$, Al, Ca, and GaAs. In the case of Li, Li$_2$O, and NiO, however, we find a large spread in predictions as well as disagreement between experiment and functionals due to complex bonding environments. While the energetics generated by BEEF-vdW ensemble is typically normal, the complex mapping through the Debye model leads to the derived finite temperature properties having non-Gaussian behavior. We test a wide variety of probability distributions that best represent the finite temperature distribution and find that properties such as specific heat, Gibbs free energy, entropy, and the thermal expansion coefficient are well described by normal or transformed normal distributions, while the prediction spread of volume at a given temperature does not appear to be drawn from a single distribution.