Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives

Abstract

We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals.

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

“…Thus, both classes of functionals have positive and negative features. Recently, we have introduced a new class of KE functionals, named Yukawa‐Generalized Gradient Approximation (yGGA), with the following general form [61,62]: where [with and being the Fermi wave vector and the electron density, respectively] is the Thomas‐Fermi (TF) kinetic energy density (KED), is the enhancement factor, is the reduced gradient, is the reduced Laplacian, and …”

“…A key point of the reduced Yukawa potential is that it yields a non‐linear contribution to the linear response function of the HEG, so that the Lindhard function can be well reproduced [61,62]. This is a fundamental improvement with respect to conventional KE functionals based only on semilocal ingredients (such as and ), which yield an incorrect polynomial linear response function [36,61,62].…”

“…Thus, both classes of functionals have positive and negative features. Recently, we have introduced a new class of KE functionals, named Yukawa-Generalized Gradient Approximation (yGGA), with the following general form [61,62]:…”

Kinetic energy density for open-shell systems: Analysis and development of a novel technique

“…This quantity has long been associated with proper electronic shell structure [15,30,31]. Recently, shell-structure-based functionals are also showing promises [32,33].…”

Dedication: Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of His 80th Birthday

“…We can notice the large panel of scientific topics covered by Karlheinz's knowledge. We deeply acknowledge the following contributions related to spectroscopy by Manuel Yañez et al [12], Juan-Carlos Sancho-García and Emilio San-Fabián [13]; excited states by Ágnes Nagy [14], Kalidas Sen et al [15] and Fabrizia Negri et al [16]; DFT developments by Fabio Della Sala et al [17], Mathias Rapacioli and Nathalie Tarrat [18], Emmanuel Fromager et al [19], José Manuel García de la Vega et al [20] and Harry Ramanantoanina [21]; results analysis by Andreas Savin et al [22] and Manuel Richter et al [23]; and, of course, the solid state and surfaces by Leila Kalantari and Fabien Tran et al [24], Denis Salahub et al [25], Peter Blaha et al [26], Samuel B. Trickey [27], William Lafargue-Dit-Hauret and Xavier Rocquefelte [28], Tzonka Mineva and Hazar Guesmi et al [29]. (H.C.)…”