The Role of the Reduced Laplacian Renormalization in the Kinetic Energy Functional Development

Abstract

The Laplacian of the electronic density diverges at the nuclear cusp, which complicates the development of Laplacian-level meta-GGA (LLMGGA) kinetic energy functionals for all-electron calculations. Here, we investigate some Laplacian renormalization methods, which avoid this divergence. We developed two different LLMGGA functionals, which improve the kinetic energy or the kinetic potential. We test these KE functionals in the context of Frozen-Density-Embedding (FDE), for a large palette of non-covalently interacting molecular systems. These functionals improve over the present state-of-the-art LLMGGA functionals for the FDE calculations.

Unveiling the Physics Behind Hybrid Functionals

“…In this sense, the here developed v c GGA–OEPx may open such a path, but more accurate potential models can be built considering exact conditions on correlation potentials (including derivative discontinuity problem , ), and right semilocal ingredients, such as the Laplacian of the density (∇ 2 ρ), which is crucial for describing various quantum oscillations and to impose exact properties in the bond and core regions. , …”

Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms

“…The differences mostly occur in the core (due to Laplacian of the density , term in GGA potentials) and asymptotic regions (due to the differences in the asymptotic behavior between OEPx (−1/ r ) and semilocal DFAs). The oscillation in both regions are significantly diminished for LRC-ωPBE-DH potentials, which are quite similar to those obtained with OEP2-SOS or interaction-strength interpolation methods .…”

Plasmon Couplings from Subsystem Time-Dependent Density Functional Theory

“…The ∼ superscript symbol in eq indicates that the KE functional T s is (necessarily) approximated. In fact, the kinetic energy as a functional of the electronic density is not known and different approximations can be used. − ,,,, On the other hand, the XC functional is, in the case of a semilocal functional, already expressed as a functional of the density, so eq can be computed exactly (within the semilocal approximation). Additional approximations are instead required in the case of more advanced XC functionals. − …”

“…The FDE method can reproduce the exact Kohn–Sham (KS) ground-state density of the whole (supermolecular) system, considering only calculations of the subsystems, thanks to the inclusion of an embedding potential. , The accuracy of the embedding potential, however, depends on the accuracy of the kinetic energy (KE) functional as a function of the density, which is unknown and must be approximated. Current approximations for the KE functional are very accurate only for weakly interacting systems. − For subsystems connected by chemical bonds, either reconstructed potentials by the inversion technique − or external orthogonality methods − have been employed.…”