Nonlocal Kinetic Energy Functionals By Functional Integration

Starting with the seminal works of Thomas and Fermi, the Density-Functional Theory (DFT) community has been searching for accurate electron density functionals. The typical paradigm is to first approximate the energy functional, and then take its functional derivative yielding a potential that can be used in DFT simulations. In this work, we take a different route and construct the potential from the second-functional derivative by functional integration. Following this principle, we prescribe two nonlocal noninteracting Kinetic Energy functionals, $T_{s}[\rho]$, having density dependent and independent kernels, respectively. The functionals 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 derive by functional integration of the second derivative involving a line integral. In pilot calculations the 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, the results are very encouraging.