Error decomposition in dissociation processes: a density functional ensemble perspective

Density Functional Theory (DFT) is a widely used electronic structure method, offering accurate results at low computational cost. However, DFT struggles with bond dissociation, even in simple systems like H₂⁺ and H₂. The failure of H₂⁺ stems from self-interaction and delocalization errors, while that of H₂ arises from static correlation error. Density-corrected DFT (DC-DFT), which employs the Hartree–Fock (HF) density instead of the self-consistent one, has been proposed to mitigate such issues. Yet, for H₂⁺ and H₂, little improvement has been reported. Here, we assess DC-DFT performance for NaCl, H₂⁺, He₂⁺, and H₂, focusing on charge and spin ensembles during dissociation. In all cases, errors in dissociation energies correlate with deviations from ideal fractional charge or spin behavior, even when using non-self-consistent densities. DC-DFT improves over standard DFT when HF correctly describes charge localization, but offers little benefit when HF yields incorrectly charged fragments. For strongly correlated systems like dissociating H₂, DC-DFT can worsen results, as deviations from the correct spin ensemble increase when using non-SCF densities, indicating dominance of functional-driven errors.