# Density functional analysis: The theory of density-corrected DFT

## TL;DR

This paper develops a formal framework for density-corrected DFT, generalizing it to compare any two functionals, and analyzes its applicability and effects on strong correlation problems.

## Contribution

It introduces a generalized theoretical framework for DC-DFT, allowing comparison of arbitrary functionals and providing criteria for its application.

## Key findings

- Generalized DC-DFT to compare any two functionals
- Defined density-space basins for analysis applicability
- Analyzed strong correlation effects on density-driven error

## Abstract

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.