Dispersion interactions in machine learning potentials for large-scale atomistic simulations

Dispersion interactions are intermolecular interactions that are present in all materials. Due to their cumulative and long-range nature, and the fact that these interactions originate from electron correlation, they are not properly captured by most exchange-correlation functionals used in density-functional theory (DFT). Instead, some kind of dispersion correction is often added to these calculations to account for the missing dispersion interactions. In many systems, accurate modeling of dispersion interactions requires many-body dispersion (MBD) to be taken into account, but these interactions significantly increase the computational resources required for simulations compared to the often used pairwise additive models, making them intractable for large-scale atomistic simulations. With the recent advent of machine learning (ML) in materials science, the problem with the computational cost of the DFT calculations can be mitigated by training ML potentials for various materials using DFT data as the reference database. These potentials are able to interpolate new results on the potential energy surfaces of the systems without further DFT calculations. However, because these potentials are trained on the DFT data based on descriptors of local atomic environments, they also lack proper dispersion interactions. The non-local nature of these interactions and the locality requirement of the ML potentials pose a challenge to the inclusion of these interactions in ML frameworks. In this thesis, we show how dispersion interactions can be included in ML potentials using local parametrization of the atomic environment. We first modify a pairwise-additive dispersion model for the ML framework such that it produces atom-centered contributions to the dispersion energies from local parameters. Next, the method is generalized to MBD by deriving the atom-centered dispersion from the global MBD energy such that the computational scaling of the final model is linear with respect to the number of atoms. Since the MBD implementation inevitably incurs a significant additional computational cost to the computationally efficient ML potentials, we also design a method to reparametrize the pairwise-additive model with periodic corrections from the MBD model on the fly during molecular dynamics simulations. With this method we achieve a significant speed-up for the simulations with an acceptable error in the results. As linear-scaling and readily parallelizable by design, our methodology allows one to run extremely large-scale molecular dynamics in a fraction of the computational time required for the corresponding DFT calculations, while producing quantum-mechanically accurate results that include MBD interactions.