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

Development of meta-generalized gradient approximations (meta-GGAs) has generally led to more accurate density-functional approximations, albeit ones that have more stringent requirements for the quadrature grids that are used to evaluate the exchange-correlation energy. Here, we demonstrate that grid-induced errors are amplified when meta-GGAs are used in conjunction with a many-body expansion, which is a popular means to parameterize classical force fields using electronic structure calculations. At the same time, delocalization errors are exacerbated by the many-body expansion, leading to exaggerated estimates of nonadditive n-body interactions, as illustrated here for anion–water clusters using the meta-GGA functionals SCAN and wB97X-V. Standard grids that are typically accurate for noncovalent interactions with meta-GGA functionals result in runaway error accumulation when used with the many-body expansion. Denser grids eliminate this problem and expose the inherent self-interaction error, which must be mitigated using other strategies that are discussed herein.