Visualizing Orbital-Free Models of the Kinetic Energy Density in Solids*

Meta-generalized gradient approximations (mGGAs) for the exchange-correlation (XC) energy in density functional theory (DFT) conventionally depend upon the Kohn-Sham kinetic energy density (KED). Use of the KED makes mGGAs more accurate than generalized gradient approximations (GGAs) but also more computationally expensive for applications such as ab initio molecular dynamics. Deorbitalizated mGGAs replace the KED with a pure density functional. 

Through visualization we explore how well the exact KED can be represented by a single KE mGGA functional dependent upon the scaled density, scaled density gradient and density Laplacian. We calculate the KE and electron density of representative solids with varying ionicity and atomic number using the ABINIT DFT plane-wave pseudopotential code.

For semiconductors we find a near-universal linear correlation with the density Laplacian and density gradient for regions outside the atomic bond, consistent with a modification of the second-order gradient expansion and devise a KE functional to fit these results. We finally explore how well this model extends to other classes of systems, including simple metals, where the gradient expansion should be reasonable, and transition metals.