Density Functional Analysis: The Theory of Density-Corrected DFT

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. arXiv:1908.05721v1 [physics.chem-ph]

Range-separation and the multiple radii functional approximation inspired by the strongly interacting limit of density functional theory

“…For this reason, the correlation component w MRF c,1 (r) becomes unphysically positive in this region (see the insets of Figures 4 and 5). This feature has also been observed in inter-shell regions of real atoms 13 .…”

“…However, one can in principle define the λdependent σ λ i (r) and by integration of the corresponding w λ MRF [n] from 0 to 1, one can recover T c . Such a concept was recently discussed by Vuckovic 13 . Nevertheless, for simplicity we restrict here to the analysis of the λ = 1 case.…”

“…However, as discussed in Ref. 13 x; u) is scaled by n(x), we also show the density (between the panels -teal) for reference.…”

“…We next observe that in all cases in Figure 7, the lr MRF xc energy densities (the less accurate of the two range-separation resolved components) again become accurate at large |x|, due to the fact that MRF xc energy densities display the correct asymptotic behavior. 13 . We remark that by virtue of our U sr and U lr definitions, w lr 1 (x) behaves asymptotically as w 1 (x): − 1 2|x| (|x| → ∞), whereas w sr 1 (x) decays much faster.…”

“…2,3,[8][9][10] Despite that, we still do not have a DFA able to correctly describe the physics of strong electronic correlations without compromising the accuracy of standard DFAs for weakly and moderately correlated systems. 2,3,7,11 In attempt to address the long-standing strong correlation problem, Vuckovic and Gori-Giorgi recently proposed a new way for the construction of DFAs, 12,13 inspired by the features of the exact xc functional from the strongly-interacting limit (SIL) of DFT. [14][15][16][17][18] More specifically, they simplified and rescaled the xc functional from the SIL, and thus they made it suitable for the treatment of physical systems at a reasonable computational cost.…”