Understanding AuPd Alloy Nanoparticle Structure under Vacuum Using DFT and Monte Carlo Methods

AuPd is a miscible metal alloy that is often used in catalysis. Supported AuPd catalysts, at high Au/Pd ratios, form single-atom alloys (SAAs) that have been shown to enhance rates and/or selectivities for many catalytic reactions, including (de)hydrogenations, hydrogenolysis, and C–C and C–O coupling reactions. While many computational studies have examined the stability of AuPd structures (the arrangement of atoms within the miscible alloy), most focused on generic alloys rather than SAAs and those that have closely investigated SAAs focused on single crystal surfaces. In this work, we use density functional theory (DFT) to calculate exchange energies (swapping an Au atom with a Pd atom) in a 201-atom truncated octahedral nanoparticle model with a focus on particles with high Au/Pd ratios. We calculate these exchange energies as a function of Pd location within the nanoparticle, the number of Pd atoms neighboring and near those exchange sites, and the total Pd content in the nanoparticle. These DFT-calculated exchange energies are also used to inform simple physics-based models (in contrast to cluster expansion or neural network models) that show good agreement with DFT-calculated values with relatively few regressed parameters. These models are then implemented into Monte Carlo (MC) simulations to predict the nanoparticle structure as a function of composition and temperature. The results show that Pd prefers to be in the subsurface of nanoparticles and that Pd prefers to be isolated from itself within Au. Both observations agree well with prior experimental and computational studies of single-crystal systems. We also show that the overall composition of the nanoparticle influences exchange energies by changing the electronic properties (e.g., Fermi level) of the system, which is relevant as Pd has one fewer valence electron than Au. MC simulations show that, in a vacuum, Pd begins to populate the surface of these ∼2 nm nanoparticles at around 20 mol % Pd (at 298 K) and that the number of Pd surface monomers, desired for SAA applications, goes through a maximum near 40 mol % Pd. As the temperature increases, Pd is more prevalent at the surface, but the influence of temperature is relatively muted. While AuPd structures are known to change in the presence of reactive gases (e.g., CO or O2), these studies characterize the baseline thermodynamic arrangements that can be used to understand surface restructuring during catalyst characterization and reaction studies.AuPd是一种可互溶金属合金，广泛应用于催化研究。负载型AuPd催化剂在高Au/Pd配比条件下会形成单原子合金（single-atom alloys, SAAs），这类合金已被证实可提升诸多催化反应的反应速率与/或选择性，涵盖（脱）加氢、氢解以及C–C与C–O偶联反应等领域。目前已有众多计算研究围绕AuPd结构（即可互溶合金内部的原子排布）的稳定性展开，但多数研究聚焦于通用合金而非单原子合金；即便针对单原子合金的相关研究，也多集中于单晶表面体系。本研究采用密度泛函理论（density functional theory, DFT），针对201原子截断八面体形纳米颗粒模型计算交换能（即Au原子与Pd原子的置换能），重点关注高Au/Pd配比的纳米颗粒体系。我们将交换能作为以下变量的函数进行计算：Pd在纳米颗粒内的位置、交换位点附近的相邻Pd原子数目，以及纳米颗粒中的总Pd含量。本研究通过DFT计算得到的交换能，还被用于构建基于物理原理的简单模型（区别于团簇展开或神经网络模型），该模型仅需少量回归参数即可与DFT计算结果实现良好吻合。随后我们将这些模型应用于蒙特卡洛（Monte Carlo, MC）模拟，以预测纳米颗粒结构随组分与温度的变化规律。结果表明，Pd更倾向于分布在纳米颗粒的次表层，且更倾向于在Au基体中彼此孤立存在。这两项观测结果均与此前针对单晶体系的实验及计算研究吻合良好。我们还发现，纳米颗粒的整体组分可通过改变体系的电子性质（例如费米能级）来影响交换能，这一点具有重要参考价值，因为Pd的价电子数比Au少1个。蒙特卡洛模拟结果显示，在真空环境下，当Pd摩尔占比约为20%（298 K时），Pd开始在这类~2 nm纳米颗粒的表面富集；而适用于单原子合金应用的Pd表面单原子位点数量，在Pd摩尔占比接近40%时达到峰值。随着温度升高，Pd在表面的占比会有所提升，但温度的影响相对较弱。尽管已知AuPd结构在反应性气体（例如CO或O₂）存在时会发生变化，但本研究表征的是基础热力学排布，可用于理解催化剂表征与反应研究过程中的表面重构行为。