Visualizing and testing orbital free models of the kinetic energy density in semiconductors

Meta-generalized gradient approximations (mGGAs) for describing the exchange-correlation (XC) energy in density functional theory (DFT) conventionally are dependent on the density, density gradient, and kinetic energy density (KED). The addition of the KED makes mGGAs more accurate than GGAs but also more computationally expensive for some applications such as ab initio molecular dynamics. Deorbitalized mGGAs replace the KED with the density Laplacian. We explore, through visualization, how well the exact KED can be represented by a single mGGA model in terms of the scaled density gradient, density Laplacian, and scaled 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 find a near-universal linear correlation with the density Laplacian and density gradient for regions outside the atomic bond. We report how this and other models perform compared to exact results for lattice constants and bulk moduli of common materials using non-self-consistent calculations.