Exploring High Entropy Alloys as Nanoparticle Catalysts by Combining Monte Carlo Sampling with Machine Learning

High-entropy alloys (HEAs), primarily considered for use as structural materials, are now emerging as promising catalytic materials due to synergistic effects among different elements leading to high catalytic activity [1]. Materials with high functionality are expected to exist in the vast compositional space of multi-element systems, thus efficient composition optimization methods are needed. Previous studies have tackled this challenge using methodologies combining first-principles calculation, machine learning, and optimization algorithms. However, optimization using the reaction activity as the objective function led to the discovery of binary systems rather than HEAs. Moreover, the assumption of complete mixing led to discrepancies between experimental value and predicted value in the compositions that actually cause phase separation [2].<br/>To address these shortcomings, we have worked on the development of a more practical composition optimization method for HEAs. In this work, thermodynamic stability and activity for hydrogen evolution reaction (HER) were used as the objective functions for optimization.<br/>First, the total energies and the hydrogen adsorption energies of octahedral cluster models were computed by density functional theory (DFT) calculations. Since actual catalysts are often used as nanoparticles, octahedrons containing edges and terraces were used as the structural models instead of slabs. Nine transition metals were used as candidate elements for composition optimization. Then, based on the DFT data, a machine learning (ML) model was constructed to predict the total energies of clusters with arbitrary atomic arrangements. Using this model, a program which performs Monte Carlo sampling was created to search for stable atomic configurations and predict the physical properties, taking into account elemental segregation. Composition optimization was then performed using free energy calculated by thermodynamic integration as the objective function. Another ML model was then constructed to predict the hydrogen adsorption energy on the nanoclusters. Multiple explanatory variables and regression methods were compared. Finally, composition optimization was conducted for HER activity calculated by the ML model.<br/>For the cluster energy prediction, it was found that the bond centric model, proposed for alloy nanoparticles [3], had higher flexibility than the neural network potential. For the free energy optimization using this model, the covariance matrix adaptation evolution strategy (CMA-ES) was found to be efficient, and an optimal composition containing seven elements was identified. Unlike previous studies, by using the distributions of adsorption energies for evaluation, four-element systems were found to have a higher HER activity than two-element ones. Furthermore, multi-objective Bayesian optimization for stability and reaction activity was performed to narrow down promising compositions.<br/>Our newly developed methodology is robust and enables exploration of high-entropy alloys towards high-performance nanoparticle catalysts.<br/><br/>This research was supported by JST e-ASIA Joint Research Program JPMJSC21E2.<br/><br/>[1] T. Fujita, <i>Mater. Trans.,</i> <b>64</b>, 2386 (2023).<br/>[2] J. K. Pedersen et al., <i>Angew. Chem. Int. Ed., </i><b>60</b>, 24144 (2021).<br/>[3] Z. Yan et al., <i>Nano Lett</i>., <b>18</b>, 2696 (2018).