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Determining the energetically most favorable structure of nanoparticles is a fundamentally important task towards understanding their stability. In the case of bimetallic nanoclusters, their vast configurational space makes it especially challenging to find the global energy optimum via experimental or computational screening. To that end, this work proposes a two-step optimization-based design framework to address this hard combinatorial problem. Given a nanocluster of fixed shape, a rigorous mixed-integer linear programming model is formulated based on a bond-centric cohesive energy function to identify the most cohesive bimetallic configuration for a given composition. This capability is coupled with a metaheuristic strategy that searches over the space of nanocluster shapes to obtain optimal structures. We apply our proposed methodology on AgCu, AuAg and CuAu systems, quantifying how the size and composition of a nanocluster influences its overall cohesion. Furthermore, we observe various synergistic effects between Cu and Au in promoting cohesive energy, while multiple segregation patterns are identified in all three studied binary systems. Our methodology serves as an efficient computational tool for investigating bimetallic nanoclusters stability properties as well as provides model nanoclusters for further investigations. 

Small nanoparticles, a.k.a. nanoclusters, of transition metals have been studied extensively for a wide range of applications due to their highly tunable properties dependent on size, structure, and composition. For these small particles, there has been considerable effort towards theoretically predicting what is the most energetically favorable arrangement of atoms when forming a nanocluster. In this work, we develop a computational framework that couples density-functional theory calculations with mathematical optimization modeling to identify highly stable, mono-metallic transition metal nanoclusters of various sizes. This is accomplished by devising and solving a rigorous mathematical optimization model that maximizes a general cohesive energy function to obtain nanocluster structures of provably maximal cohesiveness. We then utilize density-functional theory calculations and error term regression to identify model corrections that are necessary to account with better accuracy for different transition metals. This allows us to encode metal-specific, analytical functions for cohesive energy into a mathematical optimization-based framework that can accurately predict which nanocluster geometries will be most cohesive according to density-functional theory calculations. We employ our framework in the context of Ag, Au, Cu, Pd and Pt, and we present sequences of highly cohesive nanoclusters for sizes up to 100 atoms, yielding insights into structures that might be experimentally accessible and/or structures that could be used as model nanoclusters for further study.