Evaluation of Force Fields for Molecular Dynamics Simulations of Platinum in Bulk and Nanoparticle Forms

Machine learning-enabled exploration of the electrochemical stability of real-scale metallic nanoparticles

Surface Pourbaix diagrams are critical to understanding the stability of nanomaterials in electrochemical environments. Their construction based on density functional theory is, however, prohibitively expensive for real-scale systems, such as several nanometer-size nanoparticles (NPs). Herein, with the aim of accelerating the accurate prediction of adsorption energies, we developed a bond-type embedded crystal graph convolutional neural network (BE-CGCNN) model in which four bonding types were treated differently. Owing to the enhanced accuracy of the bond-type embedding approach, we demonstrate the construction of reliable Pourbaix diagrams for very large-size NPs involving up to 6525 atoms (approximately 4.8 nm in diameter), which enables the exploration of electrochemical stability over various NP sizes and shapes. BE-CGCNN-based Pourbaix diagrams well reproduce the experimental observations with increasing NP size. This work suggests a method for accelerated Pourbaix diagram construction for real-scale and arbitrarily shaped NPs, which would significantly open up an avenue for electrochemical stability studies.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

Atomistic Simulations of the Elastic Compression of Platinum Nanoparticles

The elastic behavior of nanoparticles depends strongly on particle shape, size, and crystallographic orientation. Many prior investigations have characterized the elastic modulus of nanoscale particles using experiments or simulations; however their reported values vary widely depending on the methods for measurement and calculation. To understand these discrepancies, we used classical molecular dynamics simulation to model the compression of platinum nanoparticles with two different polyhedral shapes and a range of sizes from 4 to 20 nm, loaded in two different crystal orientations. Multiple standard methods were used to calculate the elastic modulus from stress-vs-strain data for each nanoparticle. The magnitudes and particle-size dependence of the resulting moduli varied with calculation method and, even for larger nanoparticles where bulk-like behavior may be expected, the effective elastic modulus depended strongly on shape and orientation. Analysis of per-atom stress distributions indicated that the shape- and orientation-dependence arise due to stress triaxiality and inhomogeneity across the particle. When the effective elastic modulus was recalculated using a representative volume element in the center of a large nanoparticle, the elastic modulus had the expected value for each orientation and was shape independent. It is only for single-digit nanoparticles that meaningful differences emerged, where even the very center of the particle had a lower modulus due to the effect of the surface. These findings provide better understanding of the elastic properties of nanoparticles and disentangle geometric contributions (such as stress triaxiality and spatial inhomogeneity) from true changes in elastic properties of the nanoscale material.

Size-dependent shape distributions of platinum nanoparticles

While it is well established that nanoparticle shape can depend on equilibrium thermodynamics or growth kinetics, recent computational work has suggested the importance of thermal energy in controlling the distribution of shapes in populations of nanoparticles. Here, we used transmission electron microscopy to characterize the shapes of bare platinum nanoparticles and observed a strong dependence of shape distribution on particle size. Specifically, the smallest nanoparticles (<2.5 nm) had a truncated octahedral shape, bound by 〈111〉 and 〈100〉 facets, as predicted by lowest-energy thermodynamics. However, as particle size increased, the higher-energy 〈110〉 facets became increasingly common, leading to a large population of non-equilibrium truncated cuboctahedra. The observed trends were explained by combining atomistic simulations (both molecular dynamics and an empirical square-root bond-cutting model) with Boltzmann statistics. Overall, this study demonstrates experimentally how thermal energy leads to shape variation in populations of metal nanoparticles, and reveals the dependence of shape distributions on particle size. The prevalence of non-equilibrium facets has implications for metal nanoparticles applications from catalysis to solar energy.

Atomistic origin of nano-silver paracrystalline structure: molecular dynamics and x-ray diffraction studies

Classical molecular dynamics (MD) and x-ray diffraction (XRD) have been used to establish the origin of the paracrystalline structure of silver nanoparticles at the atomic scale. Models based on the face-centred cubic structure have been computer generated and their atomic arrangements have been optimized by the MD with the embedded-atom model (EAM) potential and its modified version (MEAM). The simulation results are compared with the experimental XRD data in reciprocal and real spaces, i.e. the structure factor and the pair distribution function. The applied approach returns the structural models, defined by the Cartesian coordinates of the constituent atoms. It has been found that most of the structural features of Ag nanoparticles are better reproduced by the MEAM. The presence of vacancy defects in the structure of the Ag nanoparticles has been considered and the average concentration of vacancies is estimated to be 3 at.%. The average nearest-neighbour Ag-Ag distances and the coordination numbers are determined and compared with the values predicted for the bulk Ag, demonstrating a different degree of structural disorder on the surface and in the core, compared to the bulk crystalline counterpart. It has been shown that the paracrystalline structure of the Ag nanoparticles has origin in the surface disorder and the disorder generated by the presence of the vacancy defects. Both sources lead to network distortion that propagates proportionally to the square root of the interatomic distances.