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

Abstract

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.

Subsystem density‐functional theory (update)

“…Recently, they proposed an expansion of the Yukawa kernel in Equation 16in terms of Gaussian functions in order to facilitate an implementation in quantum-chemical program packages using Gaussian-type orbitals as basis functions. 63…”

“…They showed that such functionals are able to accurately model the linear response of the electron gas and obtained promising results for rare‐gas atoms as well as jellium clusters. Recently, they proposed an expansion of the Yukawa kernel in Equation in terms of Gaussian functions in order to facilitate an implementation in quantum‐chemical program packages using Gaussian‐type orbitals as basis functions 63 …”

Subsystem Density-Functional Theory (Update)

“…Recently, they proposed an expansion of the Yukawa kernel in Eq. 16 in terms of Gaussian functions in order to facilitate an implementation in quantum-chemical program packages using Gaussian-type orbitals as basis functions [63].…”

Subsystem Density-Functional Theory (Update)

“…Recently, they proposed an expansion of the Yukawa kernel in Eq. 15 in terms of Gaussian functions in order to facilitate an implementation in quantum-chemical program packages using Gaussian-type orbitals as basis functions [63].…”