Many-Overlapping-Body (MOB) Expansion: A Generalized Many Body Expansion for Nondisjoint Monomers in Molecular Fragmentation Calculations of Covalent Molecules

A common approach to approximating the full electronic energy of a molecular system is to first divide the system into nonoverlapping (disjoint) fragments and then compute the two-body or three body fragment-fragment interactions using a many-body expansion. In this paper, we demonstrate that, by using a set of fragments which overlap with each other, a many-body expansion converges much faster than using nonoverlapping fragments. A new hierarchical fragmentation scheme is therefore proposed which generalizes the many body expansion expressions and describes a simple procedure for generating the set of overlapping monomers. This method is referred to as the many-overlapping-body (MOB) expansion and is evaluated with two example systems: four dendritic isomers of C29H60 and 10 conformational isomers of a polypeptide molecule. In both examples, the MOB methodology significantly improves the two-body corrected energies.