Uncertainty quantification of DFT-predicted finite temperature thermodynamic properties within the Debye model

Abstract

Density functional theory (DFT) calculations are routinely used to screen for functional materials for a variety of applications. This screening is often carried out with a few descriptors, which uses ground-state properties that typically ignores finite temperature effects. 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 (BEEF-vdw). 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 1 arXiv:1910.07891v1 [cond-mat.mtrl-sci] 4 Oct 2019NiO, 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. Given the computational efficiency of the approach, we believe that uncertainty quantification should be routinely incorporated into finite-temperature predictions. In order to facilitate this, we have open-sourced the code base, under the name, Depye.

Uncertainty Quantification of First Principles Computational Phase Diagram Predictions of Li-Si System Via Bayesian Sampling

“…Using the fitted properties of the equation of state, a Debye-Grunessen theory analysis 38 was used to incorporate vibrational properties and predict the Gibbs free energy as a function of temperature as the Debye model is a reasonable approximation that yields finite temperature thermodynamics of sufficient accuracy 16 . This process was repeated for the ensemble of 2000 non-self consistent exchange-correlation functionals within the BEEF-vdW model space framework, but not every functional can lead to successful result (see computational details of Supplimentary Information).…”

“…To estimate the vibrational properties of the Gibbs energy relating to the zero-point energy and entropy, a Debye-Grunessen theory analysis 38 was performed using the DePye software 16 which enables the efficient processing and vibrational predictions of the ensemble of functionals.…”

“…3,[10][11][12] Bayesian error estimation capabilities of the BEEF-vdW exchange correlation function has been used to quantify uncertainty associated with a variety of DFT-predicted material properties. [13][14][15][16] In this work, we implement model-parameter selection through the use of Bayesian Information Criterion (BIC) applied to specific phases and specific temperature range to find the optimal number of parameters and parameter types in the CALPHAD models. An implementation of Bayesian Error Estimation with van der Waals correction, the BEEF-vdW 3 was trained on a set of benchmark data spanning solid-state properties, covalent organic systems, noncovalent and van der Waals interactions, and chemisorption on solid metallic surfaces.…”

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

“…While the BEEF-vdW XC functional ensemble was generated to recreate differences between experimental and DFT data, there is no guarantee of its suitability for predicting properties not considered in the original training data set. The results of subsequent studies, 36,37,[39][40][41][42][43][44][45][46] however, demonstrated that the ensemble can reliably describe the XC uncertainty in self-consistent DFT predictions of a wide range of systems and material properties. In other words, the ensemble is transferable, in the sense that the variation in most self-consistent predictions is bounded in an interval of a few ensemble standard deviations.…”

“…BEEF-vdW has been applied to quantify XC uncertainty in predictions of molecular vibrational frequencies, 36 magnetic ground states, 37 , intercalation energies, 38 heterogeneous catalysis, [39][40][41] electrocatalysis, [42][43][44] mechanical properties of solid electrolytes, 45 and thermodynamic properties. 46 Such uncertainty estimates are useful in machine learning-based materials design applications. For example, knowing the uncertainty associated with a DFT calculation can improve the robustness of workflows that rely on ab initio calculations to screen materials.…”