Error Decomposition in Dissociation Processes within Density-Corrected DFT: An Ensemble Perspective

Density functional theory (DFT) is widely used for electronic structure calculations but can fail to describe bond dissociation correctly, even for simple systems such as H2+ and H2. These failures are commonly attributed to delocalization error in H2+ and static correlation in H2. More generally, dissociation errors are closely linked to deviations from ideal fractional charge and fractional spin ensemble behavior. Here, we investigate bond dissociation within density-corrected DFT (DC-DFT) for NaCl, H2+, He2+, and H2, using Hartree-Fock (HF) and alternative localized densities. We seek to understand why DC-DFT improves the dissociation behavior of some systems, such as NaCl, while providing little benefit in others, such as H2+. We show that for H2+, a localized density can yield substantially more accurate dissociation energetics than the exact HF density when it is used within DC-DFT. Although formally less accurate, the localized density compensates for the functional's delocalization error and recovers the correct asymptotic behavior. This result demonstrates that an approximate density can sometimes yield a more accurate energy than an exact density when used with an approximate functional. In both NaCl and H2+, localization compensates for the energetic consequences of the convex fractional-charge behavior of the functional by effectively driving the system toward an ensemble end point corresponding to an integer charge. We further show that the connection between dissociation errors and ensemble behavior is preserved within DC-DFT and that HF densities worsen the dissociation of strongly correlated systems such as H2.