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

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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.