(544dl) Robust Uncertainty Quantification Framework in Computational Electrochemical Functional Materials Design

While DFT, with regard to computationally-driven material discovery, has been successful in eliminating bad candidate materials, often times, good candidates are lost due to uncertainty. Therefore, a robust quantification of uncertainty is important to increase the success of descriptor-based screening and its incorporation may better machine learning models in materials science[1]. Using built-in Bayesian error estimation capabilities within the BEEF-vdW exchange correlation functional, we propose a robust and computationally efficient method for quantifying confidence in predicted mechanical properties, magnetic ground states, catalytic activity, active reaction mechanism, potential determining step, and electrode surface speciation (surface pourbaix diagram).

To quantify uncertainty in mechanical properties, which depend on the derivatives of the energy, we calculate energies around the equilibrium cell volume at different strains and an energy-strain relationship. At each strain, we use an ensemble of energies to obtain an ensemble of fits and thereby, an ensemble of mechanical properties, whose spread can be used to quantify its uncertainty[2]. The importance of this method will be discussed in the context of designing solid-electrolytes with the desired mechanical properties for Li metal anodes. Uncertainty in magnetic ground states is predicted by calculating the energy of a single material for various magnetic configurations. Each magnetic configuration has an ensemble of calculated energies with each energy corresponding to a specific exchange-correlation functional. We then compare the relative ordering of the energies of all possible magnetic states functional by functional to determine the consistency of the prediction. We define the c-value[3] as the proportion of functionals that agree with the best fit prediction and will discuss how this metric can be used to aid in high throughput material discovery.

Estimating uncertainty in the activity of catalysts is done by first determining the precise catalyst surface speciation. It is therefore important to quantify uncertainty in the surface pourbaix diagram and we develop a probabilistic pourbaix diagram using the uncertainty in free energies of adsorbed species. Secondly, using this probabilistic surface speciation diagram, we can determine the adsorption free energy of reaction intermediates under relevant reaction conditions. We use this framework to successfully demonstrate uncertainty in activity for oxygen reduction reaction[4], oxygen evolution reaction, hydrogen evolution reaction, chlorine evolution reaction[5]. We extend this framework and use c-value as a confidence quantifying tool for robustly identifying the reaction mechanism that is operative on a catalyst, which is particularly of significance for multi-electron reactions with competing pathways[6]. We utilize the uncertainty in scaling relations to quantify confidence in predictions of the potential determining step by constructing a probability density function for each intermediate in the free energy diagram. We specifically demonstrate the approach for the cases of oxygen reduction, hydrogen evolution and oxygen evolution.

We believe uncertainty quantification will emerge as a crucial enabler as computational methods move from providing robust qualitative insigh

[1] J. Ling, M. Hutchinson, E. Antono, S. Paradiso, B. Meredig, arXiv:1704.07423.

[2] Z. Ahmad and V. Viswanathan, Phys. Rev. B, 94, 064105 (2016).

[3] G. Houchins and V. Viswanathan, Phys. Rev. B, 96, 134426 (2017).

[4] S. Deshpande, J. R. Kitchin, and V. Viswanathan, ACS Catal. 6, 5251 (2016).

[5] D. Krishnamurthy, V. Sumaria, V. Viswanathan, J. Phys. Chem. Lett., 9, 588-595 (2017).

[6] V. Sumaria , D. Krishnamurthy, V. Viswanathan, arXiv:1804.02766 [cond-mat.matr.sci].