Random Batch Sum-of-Gaussians Method for Molecular Dynamics of Born-Mayer-Huggins Systems

The Born-Mayer-Huggins (BMH) potential, which combines Coulomb interactions with dispersion and short-range exponential repulsion, is widely used for ionic materials such as molten salts. However, large-scale molecular dynamics simulations of BMH systems are often limited by computation, communication, and memory costs. We recently proposed the random batch sum-of-Gaussians (RBSOG) method, which accelerates Coulomb calculations by using a sum-of-Gaussians (SOG) decomposition to split the potential into short- and long-range parts and by applying importance sampling in Fourier space for the long-range part. In this work, we extend the RBSOG to BMH systems and incorporate a random batch list (RBL) scheme to further accelerate the short-range part, yielding a unified framework for efficient simulations with the BMH potential. The combination of the SOG decomposition and the RBL enables an efficient and scalable treatment of both long- and short-range interactions in BMH system, particularly the RBL well handles the medium-range exponential repulsion and dispersion by the random batch neighbor list. Error estimate is provided to show the theoretical convergence of the RBL force. We evaluate the framework on molten NaCl and mixed alkali halide with up to $5\times10^6$ atoms on $2048$ CPU cores. Compared to the Ewald-based particle-particle particle-mesh method and the RBSOG-only method, our method achieves approximately $4\sim10\times$ and $2\times$ speedups while using $1000$ cores, respectively, under the same level of structural and thermodynamic accuracy and with a reduced memory usage. These results demonstrate the attractive performance of our method in accuracy and scalability for MD simulations with long-range interactions.