Nonlocal kinetic energy functionals in real space using a Yukawa-potential kernel: Properties, linear response, and model functionals

Abstract

In the quest for accurate approximations of the noninteracting kinetic energy functional as a functional of the electronic density, two different paths are usually employed: semilocal functionals based on the derivatives of the electronic density (mainly the gradient and the Laplacian) or nonlocal functionals based on the linear response of the homogeneous electron gas, i.e., the Lindhard function. While the former are defined in real space but fail to reproduce the Lindhard function, the latter cannot be expressed exactly in real space (being defined only in the reciprocal space), so applications to finite systems are complicated. In this paper we introduce a nonlocal ingredient (${y}_{\ensuremath{\alpha}}$) based on the Yukawa potential, i.e., the screened Hartree potential, which can be combined with other semilocal ingredients to obtain a more accurate description of the Lindhard function for both small and large wave vectors. We show and analyze the different properties of ${y}_{\ensuremath{\alpha}}$ and introduce a class of density functionals, the Yukawa-generalized gradient approximation (yGGA). We show that both the total energy and the first functional derivative (the kinetic potential) of yGGA functionals can be easily computed in real space. We present model yGGA functionals which well approximate the Lindhard function for both small and large wave vectors and can accurately describe jellium clusters and their perturbations.