Effective Wang-Teter kernels for improved orbital-free density functional theory simulations

We propose computationally cheap and accurate approximants to the noninteracting kinetic energy density functional $T_s\left[n\right]$ by leveraging the simplicity and computational efficiency of the Wang-Teter functional [L.-W. Wang and M. Teter, Phys. Rev. B 45, 13196 (1992)]. It depends on a single parameter, the average electron density ${\rho }_0$. We address limitations of the Wang-Teter functional, which include variational instabilities and inability to treat materials with finite band gaps. We introduce three physically motivated methods for determining ${\rho }_0$: DEN, minimizing the integrated difference of the self-consistent Wang-Teter electron density from the one from conventional Kohn-Sham density functional theory (DFT); KIN, minimizing the deviation between the Wang-Teter $T_s\left[n\right]$ and the exact value from conventional Kohn-Sham DFT; and finally ENE, minimizing the difference between the Wang-Teter and conventional Kohn-Sham DFT total energies. The crucial result of this work is that our approaches effectively mitigate the drawbacks of the Wang-Teter functional. We provide a thorough analysis of our methods and discuss their potential for large-scale simulations and as templates for density-dependent nonlocal functionals.