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Machine learning potentials (MLPs) for atomistic simulations have an enormous prospective impact on materials modeling, offering orders of magnitude speedup over density functional theory (DFT) calculations without appreciably sacrificing accuracy in the prediction of material properties. However, the generation of large datasets needed for training MLPs is daunting. Herein, we show that MLP-based material property predictions converge faster with respect to precision for Brillouin zone integrations than DFT-based property predictions. We demonstrate that this phenomenon is robust across material properties for different metallic systems. Further, we provide statistical error metrics to accurately determine a priori the precision level required of DFT training datasets for MLPs to ensure accelerated convergence of material property predictions, thus significantly reducing the computational expense of MLP development. 

Understanding how to control the nucleation and growth rates is crucial for designing nanoparticles with specific sizes and shapes. In this study, we show that the nucleation and growth rates are correlated with the thermodynamics of metal–ligand/solvent binding for the pre-reduction complex and the surface of the nanoparticle, respectively. To obtain these correlations, we measured the nucleation and growth rates by in situ small angle X-ray scattering during the synthesis of colloidal Pd nanoparticles in the presence of trioctylphosphine in solvents of varying coordinating ability. The results show that the nucleation rate decreased, while the growth rate increased in the following order, toluene, piperidine, 3,4-lutidine and pyridine, leading to a large increase in the final nanoparticle size (from 1.4 nm in toluene to 5.0 nm in pyridine). Using density functional theory (DFT), complemented by 31 P nuclear magnetic resonance and X-ray absorption spectroscopy, we calculated the reduction Gibbs free energies of the solvent-dependent dominant pre-reduction complex and the solvent-nanoparticle binding energy. The results indicate that lower nucleation rates originate from solvent coordination which stabilizes the pre-reduction complex and increases its reduction free energy. At the same time, DFT calculations suggest that the solvent coordination affects the effective capping of the surface where stronger binding solvents slow the nanoparticle growth by lowering the number of active sites (not already bound by trioctylphosphine). The findings represent a promising advancement towards understanding the microscopic connection between the metal–ligand thermodynamic interactions and the kinetics of nucleation and growth to control the size of colloidal metal nanoparticles.