Transmission electron microscopy revealed size-dependent shape distributions in platinum nanoparticles, which were consistent with trends observed by applying Boltzmann statistics to the energy computed with atomistic models.

Conspectus Multimetallic nanoparticles (NPs) have highly tunable properties due to the synergy between the different metals and the wide variety of NP structural parameters such as size, shape, composition, and chemical ordering. The major problem with studying multimetallic NPs is that as the number of different metals increases, the number of possible chemical orderings (placements of different metals) for a NP of fixed size explodes. Thus, it becomes infeasible to explore NP energetic differences with highly accurate computational methods, such as density functional theory (DFT), which has a high computational cost and is typically applied to up to a couple of hundred metal atoms. Here, we demonstrate a methodology advancing NP simulations by effectively exploring the vast materials space of multimetallic NPs and accurately identifying the ones with the most thermodynamically preferred chemical orderings. With accuracies reaching that of DFT, our methodology is applicable to practically any NP size, shape, and metal composition. We achieve this by significantly advancing the bond-centric (BC) model, a physics-based model that has been previously shown to rapidly predict bimetallic NP cohesive energies (CEs). Specifically, the BC model is trained in a way to understand how the bimetallic bond strength changes under different coordination environments present on a NP and how the metal composition of every site affects the detailed coordination environment using fractional coordination numbers. This newly modified BC model leads to an improvement from 0.331 (original model) to 0.089 eV/atom in CE predictions when compared to DFT values on a robust data set of 90 different NPs consisting of PtPd, AuPt, and AuPd NPs with varying compositions and chemical orderings. By incorporating the modified BC model into an in-house-developed genetic algorithm (GA) we can effectively and accurately predict the most stable chemical orderings of large, realistic bimetallic NPs consisting of thousands of metal atoms. This is demonstrated on AuPd bimetallic NPs, a challenging system due to the similarity in the cohesion of the two metals. By training our BC model using a unique DFT calculation on a bimetallic NP (one calculation for two metals combining together), we expand to explore the chemical ordering of multimetallic NPs. We first demonstrate the application of our methodology on a AuPdPt NP and validate our stability predictions with literature data. Then, we effectively explore the vast materials space of multimetallic NPs consisting of combinations of Au, Pt, and Pd as a function of metal composition. Our thermodynamic stability trends are presented in a ternary diagram revealing detailed, and yet, unexpected chemical ordering trends. Our computational framework can aid both experimental and computational researchers toward effectively screening multimetallic NP stability. Moreover, we provide an outlook of how this framework can be applied to catalyst discovery, high-entropy alloys, and single-atom alloys.

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