Visualization of orbital free models of Kinetic Energy density in solids

The metaGGA functional for describing the exchange-correlation (XC) energy in density functional theory (DFT) is conventionally constructed as a functional dependent on the density, density gradient, and kinetic energy density (KED). The addition of the KED makes metaGGA’s a more accurate functional than ones that use the density and its gradient alone but also more computationally expensive for some applications such as ab initio molecular dynamics simulations. The calculation of the XC energy in meta-GGAs can be made less expensive by replacing the explicit orbital dependence in the KED with expressions involving only the particle density and its gradient and Laplacian. We test the validity of recent deorbitalization strategies in the literature by visualizing their predictions for the KED and related quantities, and comparing these to exact calculations. For an effective test, we perform these calculations on ionic, semiconductor, simple metal, and transition metal solids to see how well the KED for these different binding topologies can be represented by a single metaGGA model in terms of the scaled gradient and Laplacian of the density. The calculations of exact KED and electron density are done with the ABINIT DFT plane-wave pseudopotential code.