Untangling Sources of Error in the Density-Functional Many-Body Expansion

The
many-body expansion provides a framework for data-driven applications
of electronic structure theory, including parametrization of classical
force fields and machine learning. However, we demonstrate that its
use significantly amplifies quadrature grid errors when modern density-functional
approximations are employed. Standard grids that work well in conventional
density-functional calculations result in runaway error accumulation
when used with the many-body expansion. At the same time, delocalization
error is also exacerbated, leading to exaggerated estimates of nonadditive n-body interactions. This is illustrated for anion–water
clusters using the SCAN, r2SCAN, ωB97X-V and ωB97M-V
functionals. By employing dense quadrature grids, the inherent self-interaction
error is exposed, which can then be mitigated using a variety of other
strategies.