Laplacian-Level Kinetic Energy Approximations Based on the Fourth-Order Gradient Expansion: Global Assessment and Application to the Subsystem Formulation of Density Functional Theory

Abstract

We tested Laplacian-level meta-generalized gradient approximation (meta-GGA) noninteracting kinetic energy functionals based on the fourth-order gradient expansion (GE4). We considered several well-known Laplacian-level meta-GGAs from the literature (bare GE4, modified GE4, and the MGGA functional of Perdew and Constantin (Phys. Rev. B 2007,75, 155109)), as well as two newly designed Laplacian-level kinetic energy functionals (L0.4 and L0.6). First, a general assessment of the different functionals is performed to test them for model systems (one-electron densities, Hooke's atom, and different jellium systems) and atomic and molecular kinetic energies as well as for their behavior with respect to density-scaling transformations. Finally, we assessed, for the first time, the performance of the different functionals for subsystem density functional theory (DFT) calculations on noncovalently interacting systems. We found that the different Laplacian-level meta-GGA kinetic functionals may improve the description of different properties of electronic systems, but no clear overall advantage is found over the best GGA functionals. Concerning the subsystem DFT calculations, the here-proposed L0.4 and L0.6 kinetic energy functionals are competitive with state-of-the-art GGAs, whereas all other Laplacian-level functionals fail badly. The performance of the Laplacian-level functionals is rationalized thanks to a two-dimensional reduced-gradient and reduced-Laplacian decomposition of the nonadditive kinetic energy density.

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

“…[113] Another important quantity to describe the density behavior is the Laplacian of the density r 2 qðrÞ. This quantity appears in the fourthorder gradient expansions (GE4) of both the exchange [107] and kinetic [114][115][116] energies via the dimensionless reduced Laplacian…”

“…Another important quantity to describe the density behavior is the Laplacian of the density r 2 qðrÞ. This quantity appears in the fourthorder gradient expansions (GE4) of both the exchange [107] and kinetic [114][115][116] energies via the dimensionless reduced LaplacianThe reduced Laplacian, which is by construction invariant under the uniform density scaling (see Appendix B), is therefore a natural meta-GGA input ingredient. It contains more information than the reduced gradients, being able to distinguish the nuclear region (q !…”

Kinetic and Exchange Energy Densities near the Nucleus

“…Similar shortcomings as for the XE density near the nucleus affect also many KE functionals at the GGA level [51][52][53][54][55] or at the Laplacian level [56]; for a recent review of semilocal functionals, see [57]. The KE density is usually defined in terms of the KE enhancement factor:…”

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals

“…This is due to its promise of achieving potentially exact results at a reduced computational cost, as well as to the high insight into the nature of interacting systems provided by the associated embedding potentials. Thus, numerous applications related to non-covalent [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] as well as covalent bonded systems [28][29][30][31] have been considered. In addition, the frozen density embedding (FDE) method [3,32,33] has emerged as a practical tool for efficient simulations of different properties [18,[33][34][35][36][37][38].…”