Since 1927, starting with the seminal works of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting Kinetic Energy, $T_{s}[\rho]$, the subject of this work. The typical paradigm is to first approximate the energy functional, and then take its functional derivative, $\frac{\delta T_{s}[\rho]}{\delta \rho(r)}$, yielding a potential that can be used in orbital-free DFT, or subsystem DFT simulations. In this work, we challenge the commonly adopted paradigm and set out to construct the potential from the second-functional derivative by functional integration. Following this guiding principle, we prescribe two new nonlocal functionals for $T_{s}[\rho]$: one has a density independent kernel and the other has a density dependent kernel. These functionals are constructed to satisfy three exact conditions: (1) the existence of a “kinetic electron” arising from the existence of the exchange hole; (2) for homogeneous densities, the second functional derivative is the inverse Lindhard function; (3) potential and energy are derived by functional integration of the second derivative involving a line integral. In our pilot calculations, these new functionals are capable of reproducing Kohn–Sham DFT equilibrium volumes, bulk moduli, phase energy ordering and electron densities for CD, FCC, and BT Silicon as well as FCC Aluminum. Although more benchmark work is needed to fully assess, the current results are very encouraging and warrant further investigation of these functionals.

Nonlocal kinetic energy functionals by functional integration

255th National Meeting (2018)

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