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.

Through visualization we explore how well the exact KED can be represented by a simpler functional dependent upon the scaled density, scaled density gradient and density Laplacian and thus reduce computation time. We perform calculations using the pseudopotential plane wave code Abinit, with non-core-corrected pseudopotentials and focus on simple metals Al and Li and the transition metal Cu.

Although it could be presumed that the kinetic energy density for simple metals should correlate well to models derived from the slowly-varying electron gas, we find that not to be the case. Further, the Kohn-Sham KED in Cu is nowhere close to the uniform gas limit. We also examine simple behavior described in the Xia and Carter paper [Phys. Rev. B 91 045124 (2015)] and show that some of the behaviors described are based on pseudopotential affected data. This raises questions as to how to better describe the KED of metals.