Analyzing density-driven errors: Principles and pitfalls

The theory of density-corrected density functional theory (DC-DFT) separates the error in any approximate DFT calculation into a functional-driven contribution and a density-driven error. Practical DC-DFT calculations often use the Hartree–Fock (HF) density instead of a self-consistent DFT density—a method known as HF-DFT—and reduce energetic errors in several classes of chemical problems. Using principles of DC-DFT, we illustrate several pitfalls when analyzing HF-DFT errors, including an interpolator for density-driven errors that is chronically inaccurate, using proxies instead of accurate densities, and conflating common measures of density errors with those of DC-DFT. We report ideal density-driven errors for one- and two-electron systems, where we can calculate most properties exactly, illustrating these problems. A simple analysis of benchmarking data shows that proxy benchmark densities proposed in recent literature are too inaccurate to be useful in DC-DFT. We argue that the success of HF-DFT for barrier heights need not rely on error cancellation. While HF-DFT errors can indeed be smaller than functional errors, the reason for the remarkable consistency of this improvement remains an open question.