Gaussian expansion of Yukawa non-local kinetic energy functionals: Application to metal clusters

The development of kinetic energy (KE) functionals is one of the current challenges in density functional theory (DFT). The Yukawa non-local KE functionals [Phys. Rev. B 103, 155127 (2021)] have been shown to describe accurately the Lindhard response of the homogeneous electron gas (HEG) directly in the real space, without any step in the reciprocal space. However, the Yukawa kernel employs an exponential function which cannot be efficiently represented in conventional Gaussian-based quantum chemistry codes. Here, we present an expansion of the Yukawa kernel in Gaussian functions. We show that for the HEG this expansion is independent of the electronic density, and that for general finite systems the accuracy can be easily tuned. Finally, we present results for atomistic sodium clusters of different sizes, showing that simple Yukawa functionals can give superior accuracy as compared to semilocal functionals.