Delocalization error poisons the density-functional many-body expansion

The many-body expansion is a fragment-based approach to large-scale quantum chemistry that partitions a single monolithic calculation into numerous, manageable subsystems. This technique is increasingly being used as a basis for fitting classical force fields to electronic structure calculations, especially for water and aqueous ions, and for machine learning. Here, we show that the many-body expansion based on semilocal density functional theory affords wild oscillations and runaway error accumulation for ion-water interactions, which is attributable to self-interaction or delocalization error in the approximate density functional. The effect is minor or negligible in small water clusters, explaining why it has not been noticed previously, but grows to catastrophic proportion in clusters that are only moderately larger. This behavior can be counteracted using hybrid functionals but only if the fraction of exact exchange is >= 50%. Other mitigation strategies including meta-generalized gradient approximations, density correction (via exchange-correlation functionals evaluated atop Hartree-Fock densities), and dielectric continuum boundary conditions do little to curtail the problematic oscillations. In contrast, energy-based screening to cull unimportant subsystems can successfully forestall divergent behavior. These results suggest that extreme caution is required when the many-body expansion is combined with density functional theory.