Density functional theory (DFT) is by far the most-employed computational method due to its excellent accuracy/cost ratio. The construction of density functionals approximations (DFAs) has turned towards the disproportionate use of empirical parameters fitted to accurate computations or experimental data, gradually leading to very specific DFAs that are very accurate for particular problems but lack universality and produce less accurate densities.1 New theoretical models and calibration tools are needed to aid the design of new functionals. In this work, we use a model system that displays different correlation regimes where dynamic and static correlation are tunable.2-4 The model is realistic as far as the electron correlation is concerned and it thus represents a suitable playground for DFAs. Quasi-exact energies and densities of a large family of functionals are tested at different correlation regimes, showing that none of the tested functionals if both accurate for strongly and weakly correlated systems. The importance of choosing various indicators to compare the approximate and the reference density is stressed. Namely, the density and its gradient are checked using the Euclidean distance, the quantum similarity indices, and the Kullback-Leibler divergence. Analytical results at the strong-correlated limit reveal the incorrect asymptotic behavior of the correlation and exchange parts of many DFA. These results suggest new means to improve DFAs, leading to less specific functionals.5

DFT functional calibration from highly-accurate energies and densities at different correlation regimes

255th National Meeting (2018)

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