When are Many-Body Effects Significant?

Many-body effects are required for an accurate description of both structure and dynamics of large chemical systems. However, there are numerous such interactions to consider, and it is not obvious which ones are significant. We provide a general and fast method for establishing which small set of three- and four-body interactions are important. This is achieved by estimating the maximum many-body effects, epsilon(max), that can arise in a given arrangement of bodies. Through careful analysis of epsilon(max), we find two overall causes for significant many-body interactions. First, many-body induction propagates in nonbranching paths, that is, in a chain-like manner. Second, linear arrangements of bodies promote the alignment of the dipoles to reinforce the many-body interaction. Consequently, compact and extended linear arrangements are favored. The latter result is not intuitive as these linear arrangements can lead to significant many-body effects extending, over large distances. For the first time, this study provides a rigorous explanation as to how cooperative effects provide enhanced stability in helices making them one of the most common structures in biomolecules. Not only do these helices promote linear dipole alignment, but their chain-like structure is consistent with the way many-body induction propagates. Finally, using ems to screen for significant many-body interactions, we are able to reproduce the total three- and four-body interaction energies using a small number of individual many-body interactions.