Long range behavior of high-rank topological multipole moments

The construction of a high-rank multipolar force field (for peptides) is a complex task, leading to several intermediate questions in need of a clear answer. Here we focus on the convergence of the (electrostatic) multipolar expansion at medium and long range. Using molecular electron densities, quantum chemical topology (QCT) defines the atoms as finite volumes, each endowed with multipole moments. The terms in the multipole expansion are grouped according to powers of the internuclear distance, R(-L). Given two atom types at a given distance, we determine which rank (L) is necessary for the electrostatic energy to converge to the exact interaction energy within a certain error. With this information, the rank of the expansion for each interaction can be adapted to the required accuracy and the available computing power.