Density Functional Analysis: The Theory of Density-Corrected DFT.

Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for the analysis of any functional minimization with an approximate functional. We generalize DC-DFT to allow the comparison of any two functionals, not just comparison with the exact functional. We introduce a linear interpolation between any two approximations and use the results to analyze global hybrid density functionals. We define the basins of density space in which this analysis should apply and give quantitative criteria for when DC-DFT should apply. We also discuss the effects of strong correlation on the density-driven error, utilizing the restricted HF Hubbard dimer as an example.