Cutoff-Based Modeling of Coulomb Interactions for Atomistic-to-Continuum Multiscale Methods

Atomic interactions in a large class of functional materials, essentially—all dielectrics, polarizable solids and ionic solids, involve long-range Coulomb interactions. Yet atomistic-to-continuum multiscale methods, such as the quasicontinuum method, are currently applicable only in cases where the atomic interactions are short-ranged. This restriction on the nature of atomic-level interactions for multiscale methods excludes numerous materials that are central to various scientific and industrial applications. A number of studies have pointed out unphysical artifacts in molecular simulations upon using the direct cutoff-based truncated sum to evaluate Coulomb interactions in ionic solids. However, recently it is understood that the artifacts of the direct cutoff-based truncated sum can be significantly minimized if a suitable correction term is added. In this work we examine whether or not the Wolf summation method, one of the prominent cutoff-based methods, is suitable to carry out the accumulation of the Coulomb interactions within the context of atomistic-to-continuum multiscale methods. In this regard, we choose the quasicontinuum method from the existing collection of multiscale methods for demonstration. It is found that the Wolf summation method can be applied if the atomistic system has charge ordering; otherwise, the error in the accumulation of the Coulomb interactions could be large.