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 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 densities proposed in recent literature are too inaccurate to be useful in DC-DFT. Despite recent claims to the contrary, we show that the success of DC-DFT for barrier heights does not rely on a cancellation of errors, and it is to be expected that HF-DFT errors can be smaller than functional errors, but we fall short of explaining why the improvement is so quantitatively systematic.