Quantification of uncertainty in first-principles predicted mechanical properties of solids: Application to solid ion conductors

Abstract

Computationally-guided material discovery is being increasingly employed using a descriptor-based screening through the calculation of a few properties of interest. A precise understanding of the uncertainty associated with first principles density functional theory calculated property values is important for the success of descriptor-based screening. Bayesian error estimation approach has been built-in to several recently developed exchange-correlation functionals, which allows an estimate of the uncertainty associated with properties related to the ground state energy, for e.g. adsorption energies. Here, we propose a robust and computationally efficient method for quantifying uncertainty in mechanical properties, which depends on the derivatives of the energy. The procedure involves calculating the energy around the equilibrium cell volume with different strains and fitting the obtained energies to the corresponding energy-strain relationship. At each strain, we use instead of a single energy, an ensemble of energies, giving us an ensemble of fits and thereby, an ensemble of mechanical properties associated with each fit, whose spread can be used to quantify its uncertainty. The generation of ensemble of energies is only a post-processing step involving a perturbation of parameters of the exchange-correlation functional and solving for the energy non-self consistently. The proposed method is computationally efficient and provides a more robust uncertainty estimate compared to the approach of self-consistent calculations employing several different exchange-correlation functionals. We demonstrate the method by calculating the uncertainty bounds for Si using the developed method. We show that the calculated uncertainty bounds the property values obtained using three different GGA functionals: PBE, PBEsol and RPBE.