Visualizing orbital free models of the kinetic energy density in semiconductors

The meta-GGA class of functionals for the exchange-correlation (XC) energy in density functional theory (DFT) is conventionally constructed as a function of the density, its gradient, and the kinetic energy density (KED). Inclusion of the KED betters meta-GGAs accuracy but raises computational cost for some applications such as ab initio molecular dynamics simulations. That cost can be reduced by replacing the explicit orbital dependence in the KED with expressions using the Laplacian of the density. We calculate the exact KED and electron density of semiconductor solids with varying ionicity and atomic number using the ABINIT DFT plane-wave pseudopotential code. We visualize how well the exact KED can be represented by a single meta-GGA model in terms of the scaled density gradient and scaled Laplacian. We test the validity of recent deorbitalization strategies by comparing their predictions to the exact calculations. We find a near-universal linear correlation with the Laplacian and gradient of the density for regions outside of the atomic bond, which can be fit to a simple gradient expansion.