Machine learning-accelerated density functional theory optimization of PtPd-based high-entropy alloys for hydrogen evolution catalysis

Abstract

High-entropy alloys (HEAs) have emerged as promising catalysts for the hydrogen evolution reaction (HER) due to their compositional diversity and synergistic effects. In this study, machine learning-accelerated density functional theory (DFT) calculations were employed to assess the catalytic performance of PtPd-based HEAs with the formula PtPdXYZ (X, Y, Z = Fe, Co, Ni, Cu, Ru, Rh, Ag, Au; X ≠ Y ≠ Z). Among 56 screened HEA(111) surfaces, PtPdRuCoNi(111) was identified as the most promising, with adsorption energies (Eads) between −0.50 and −0.60 eV and high d-band center of −1.85 eV, indicating enhanced activity. This surface showed the hydrogen adsorption free energy (ΔGH*) of −0.03 eV for hydrogen adsorption, outperforming Pt(111) by achieving a better balance between adsorption and desorption. Machine learning models, particularly extreme gradient boosting regression (XGBR), significantly reduced computational costs while maintaining high accuracy (root-mean-square error, RMSE = 0.128 eV). These results demonstrate the potential of HEAs for efficient and sustainable hydrogen production.

1. Introduction

Hydrogen energy is a promising alternative to fossil fuels, contributing to the transition toward sustainable and renewable energy systems. It can be stored, transported, and utilized in various applications, which refers to using hydrogen gas (H2) as a fuel and energy carrier [1–3]. To produce hydrogen gas, the hydrogen evolution reaction (HER) is the key method for generating hydrogen through the electrochemical process from water, which usually occurs at an electrode during electrolysis [1,4–5]. The HER occurs at the cathode, where protons from the solution combine with electrons at the electrode surface, leading to the potential production of hydrogen gas [2,6–7]. The HER with the initial step involves the adsorption of protons (H+) at the electrode surface (Volmer reaction), followed by either recombination of adsorbed hydrogen atoms (Tafel reaction) or reaction with additional protons (Heyrovsky reaction) to produce hydrogen gas [2,8–9]. Despite water electrolysis being a promising hydrogen production method, it is thermodynamically unfavorable and requires highly efficient electrode materials to minimize overpotentials [6–7]. However, their high cost and scarcity limit widespread application. Therefore, there is a critical need for efficient, low-cost, and earth-abundant catalysts for HER to enable sustainable hydrogen production with minimal resource consumption [6–7]. For this reason, developing catalysts for HER involves several challenges that need to be addressed to enhance efficiency, reduce costs, and ensure sustainability.

The catalysts used for the HER typically consist of noble metals such as Pt [10–13], Pd [14], and Au [9] due to their highly efficient catalytic properties. Pt has been demonstrated as the suitable catalyst that provided high catalytic activity and established standard benchmarks for catalytic activity in HER [10–13]. However, noble metals’ scarcity and high-cost limit their widespread application, necessitating the search for cost-effective alternatives, availability, and durability [10–11,13,15]. Ongoing research and development aim to discover new materials that can match or exceed the catalytic performance of noble metals while being more sustainable and cost-effective. Alternatively, addressing their cost and abundance concerns is crucial for advancing hydrogen production technologies for practical applications. High-entropy alloys (HEAs) have five or more principal elements.