# Laplacian-dependent models of the kinetic energy density: Applications in subsystem density functional theory with meta-generalized gradient approximation functionals

## TL;DR

This paper explores Laplacian-dependent models for kinetic energy density in density functional theory, demonstrating their effectiveness in subsystem DFT with meta-GGA functionals and highlighting the importance of Laplacian contributions.

## Contribution

It introduces and evaluates simple Laplacian-dependent kinetic energy density models for use in subsystem DFT with meta-GGA functionals, improving local feature modeling.

## Key findings

- Laplacian contribution is crucial for accurate KED modeling.
- A simple Thomas-Fermi plus Laplacian model performs best.
- Models show good accuracy in non-bonded systems.

## Abstract

The development of semilocal models for the kinetic energy density (KED) is an important topic in density functional theory (DFT). This is especially true for subsystem DFT, where these models are necessary to construct the required non-additive embedding contributions. In particular, these models can also be efficiently employed to replace the exact KED in meta-Generalized Gradient Approximation (meta-GGA) exchange-correlation functionals allowing to extend the subsystem DFT applicability to the meta-GGA level of theory. Here, we present a two-dimensional scan of semilocal KED models as linear functionals of the reduced gradient and of the reduced Laplacian, for atoms and weakly-bound molecular systems. We find that several models can perform well but in any case the Laplacian contribution is extremely important to model the local features of the KED. Indeed a simple model constructed as the sum of Thomas-Fermi KED and 1/6 of the Laplacian of the density yields the best accuracy for atoms and weakly-bound molecular systems. These KED models are tested within subsystem DFT with various meta-GGA exchange-correlation functionals for non-bonded systems, showing a good accuracy of the method.