A focus on delocalization error poisoning the density-functional many-body expansion

Broderick and Herbert's article (D. R. Broderick and J. M. Herbert, Chem. Sci., 2024, 15, 19893-19906, https://doi.org/10.1039/D4SC05955G) explores an open concern about using energies from density-functional approximations when developing force fields and machine learning potentials for large-scale simulations. The authors explicitly decomposed self-interaction errors (SIEs) from density-functional approximations (DFAs) and found how they behave in many-body expansions (MBEs) that are leveraged in large-scale simulations. For DFAs to be deemed reliable for developing many-body potentials, they would ideally provide stable energetics within the MBE terms that are most often used by force fields and machine learning potentials (MLPs), i.e., within their three- and four-body terms. It was instead found that many widely used DFAs produce wild oscillations in these MBE terms, whereby three-body terms can become problematically enormous. This raises concerns that any force field and/or MLP that appears well-fitted to DFA data on small systems might be poorly conditioned for large-scale simulations due to intrinsic SIEs. This commentary provides more context of Broderick and Herbert's work and its consequences for members of the multiscale modeling community.