Density sensitive analysis for evaluating density functional theory approximations to exchange-correlation energies

We developed a density sensitivity difference measure using theory from density-corrected Density Functional Theory that provides a physically-motivated comparison of exchange-correlation functional approximations. Analyzing the comparative density sensitivities with machine-learning reveals striking trends among standard functionals. Comparative differences between approximate functionals are more easily quantified than absolute errors, and are indifferent to the intent or construction of the functional. Evaluating individual molecules with this approach indicates clear molecular groupings, highlighting the similarities or differences of various external potentials. Our analysis provides a new method for evaluating DFT functionals, and enables a new data driven approach for dataset generation.