The development of accurate and efficient interatomic potentials is crucial for simulating nanomaterial growth processes, which often involve complex atomic interactions over extended time and length scales. Traditional molecular dynamics (MD) simulations rely on empirical potentials that sacrifice accuracy for computational efficiency, while density functional theory (DFT) provides high accuracy but is limited to small systems and short timescales. Machine learning interatomic potentials (MLIPs) bridge this gap by combining the precision of quantum mechanical calculations with the scalability of classical MD, enabling realistic simulations of nanomaterial synthesis and growth.
MLIPs leverage neural networks or Gaussian processes to learn the relationship between atomic configurations and their corresponding energies and forces, as derived from ab initio calculations. The training process begins with generating a diverse dataset of atomic structures, typically using DFT or other quantum chemistry methods. These structures must encompass a wide range of bonding environments, defects, and transition states relevant to the growth process. Active learning strategies are often employed to iteratively improve the potential by identifying and incorporating configurations where the model exhibits high uncertainty. Uncertainty quantification is critical, as it ensures the reliability of predictions and prevents extrapolation into unphysical regions of the potential energy surface.
Several MLIP frameworks have been developed, each with distinct architectures and training methodologies. The ANI (ANAKIN-ME) potential uses a neural network ensemble trained on a large dataset of organic molecules, achieving near-DFT accuracy for molecular systems. The Gaussian Approximation Potential (GAP) employs kernel-based methods, offering interpretability and robustness for materials like silicon and carbon-based nanostructures. NequIP (Equivariant Neural Network Potentials) incorporates equivariance to rotations and translations, improving data efficiency and accuracy for complex systems. These frameworks differ in their computational cost, scalability, and suitability for specific material classes.
MLIPs have demonstrated significant success in simulating nanomaterial growth processes. For metal nanoparticle sintering, MLIPs accurately capture the diffusion dynamics and coalescence mechanisms that govern particle stability and morphology. Simulations reveal how surface energy anisotropy and defect migration influence sintering rates, providing insights for controlling nanoparticle assemblies. In chemical vapor deposition (CVD) of 2D materials like graphene or transition metal dichalcogenides, MLIPs model the precursor decomposition, adsorption, and surface diffusion processes that determine film quality. These simulations help optimize growth conditions by predicting the effects of temperature, pressure, and substrate interactions. Colloidal nanocrystal growth is another area where MLIPs excel, enabling the study of ligand-surface binding, solvent effects, and facet-selective growth kinetics at atomic resolution.
Despite their advantages, MLIPs face challenges in rare-event sampling, where infrequent but critical processes like nucleation or phase transitions occur on timescales beyond conventional MD. Enhanced sampling techniques, such as metadynamics or umbrella sampling, can be combined with MLIPs to accelerate these events, but the accuracy depends on the choice of collective variables. Additionally, MLIPs require careful validation against experimental data or higher-level theory to ensure transferability across different growth conditions. The computational cost of training and inference, though lower than DFT, remains non-negligible for large-scale simulations.
Active learning strategies address some of these limitations by dynamically expanding the training dataset to cover underrepresented configurations. For example, during a simulation, if the model detects high uncertainty in predicting forces for a particular atomic arrangement, it can trigger a new DFT calculation to refine the potential. This approach minimizes the need for exhaustive upfront data generation and improves the model's robustness. Bayesian optimization techniques further enhance efficiency by prioritizing the most informative configurations for training.
Success stories highlight the transformative potential of MLIPs. In one study, a GAP model accurately predicted the melting behavior of aluminum nanoparticles, matching experimental observations without empirical adjustments. Another application demonstrated how an MLIP enabled the simulation of defect dynamics in silicon carbide growth, revealing mechanisms that control polytype formation. For colloidal quantum dots, MLIPs have elucidated the role of ligand coverage in shape evolution, guiding synthetic efforts to achieve monodisperse particles.
Current research focuses on improving the generality and scalability of MLIPs. Efforts include developing unified potentials that span multiple elements and phases, incorporating long-range interactions, and integrating MLIPs with continuum models for multiscale simulations. The ultimate goal is to create a predictive framework that accelerates the discovery and optimization of nanomaterials by connecting atomic-scale processes to macroscopic properties. As MLIP methodologies mature, they will play an increasingly central role in computational nanoscience, offering unprecedented insights into nanomaterial growth mechanisms and enabling the rational design of next-generation materials.