Bayesian Optimization of High‐Entropy Alloy Compositions for Electrocatalytic Oxygen Reduction**

Abstract

Active,s elective and stable catalysts are imperative for sustainable energy conversion, and engineering materials with such properties are highly desired. High-entropya lloys (HEAs) offer av ast compositional space for tuning such properties.T oo vast, however,t ot raverse without the proper tools.H ere,w er eport the use of Bayesiano ptimization on am odel based on density functional theory (DFT) to predict the most active compositions for the electrochemical oxygen reduction reaction (ORR) with the least possible number of sampled compositions for the two HEAs Ag-Ir-Pd-Pt-Ru and Ir-Pd-Pt-Rh-Ru. The discoveredo ptima are then scrutinized with DFT and subjected to experimental validation where optimal catalytic activities are verified for Ag-Pd, Ir-Pt, and Pd-Ru binary alloys.This study offers insight into the number of experiments needed for optimizing the vast compositional space of multimetallic alloys whichhas been determined to be on the order of 50 for ORR on these HEAs.

A Mean-Field Model for Oxygen Reduction Electrocatalytic Activity on High-Entropy Alloys

“…The composition space remains highly unexplored, both in terms of the constituent elements but also in the relative concentrations of the elements. Some attempts to obtain trends within fixedelement composition spaces have been investigated both experimentally [8,9,10,11] and theoretically [5,12,13] .…”

“…The aim of an optimization is finding the elements that make a certain desired adsorption energy most likely by perturbing the ensemble adsorption energy for a given composition while ensuring as many of the optimal sites as possible. As of yet, all models of HEA catalytic activity have used a vast dataset of simulated adsorption energies derived from DFT [5,11,12,13,14,17] . These simulations have then been used in conjunction with a regression model to predict the adsorption energy on an arbitrary surface site, taking into consideration the neighboring atoms.…”

“…These simulations have then been used in conjunction with a regression model to predict the adsorption energy on an arbitrary surface site, taking into consideration the neighboring atoms. The regression model can be arbitrarily chosen, popular choices are neural network [12,17] , Gaussian process [14] , and linear regression models [5,11,13] . For models producing the same prediction accuracy, the least parameterized model is often the preferred, since it is less computationally intensive to train and employ, and is easier to comprehend and extract knowledge from.…”

“…Initially, a dataset of DFT calculated *OH and O* adsorption energies on AgIrPdPtRu (Figure 3a) was used to train three different regressors (Figure 3b-d) for prediction of the adsorption energy: a graph convolutional neural network model (GCNNM), a linear model (LM), and a normal distribution model (NDM) (the mean-field model). The structure of the GCNNM is described in the supporting information (SI), and the linear model has been described in detail previously [13] .…”

“…The brute-force implementation of this adsorbate interaction was applied in a number of our previous studies [9,11,13] , requiring the specification of an explicit surface typically measuring 100×100×3 atoms. A probabilistic implementation of the same interaction has been developed and investigated in the current study.…”