  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 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 density-driven
error, utilizing the restricted HF Hubbard dimer as an illustrative example.
