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 test Laplacian-level meta-generalized gradient approximation (meta-GGA) non-interacting kinetic energy functionals based on the fourth-order gradient expansion (GE4). We consider several well known Laplacian-level meta-GGAs from literature (bare GE4, modified GE4, and the MGGA functional of Perdew and Constantin [Phys. Rev. B \textbf{75},155109 (2007)]), as well as two newly designed Laplacian-level kinetic energy functionals (named L0.4 and L0.6). First, a general assessment of the different functionals is performed, testing them for model systems (one-electron densities, Hooke's atom and different jellium systems), atomic and molecular kinetic energies as well as for their behavior with respect to density-scaling transformations. Finally, we assess, for the first time, the performance of the different functionals for Subsystem Density Functional Theory (DFT) calculations on non-covalently interacting systems. We find 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 Subsystem DFT calculations, the here proposed L0.4 kinetic energy functional is 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 non-additive kinetic energy density.

19 pages, 6 figures

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• Laplacian-dependent models of the kinetic energy density: Applications in subsystem density functional theory with meta-generalized gradient approximation functionals
• Data-driven kinetic energy density fitting for orbital-free DFT: linear vs Gaussian process regression
• Jellium-with-gap model applied to semilocal kinetic functionals
• Subsystem density functional theory with meta generalized gradient approximation exchange-correlation functionals
• FDE-vdW: A van der Waals Inclusive Subsystem Density-Functional Theory
• Methods to generate the reference total and Pauli kinetic potentials