Study of Some Simple Approximations to the Non-Interacting Kinetic Energy Functional

TL;DR

This paper investigates simple approximation methods for the non-interacting kinetic energy functional in density functional theory, demonstrating their accuracy in atomic shell structure and exploring potential extensions to molecules and clusters.

Contribution

It introduces and evaluates simple series expansion approximations to the kinetic energy functional, showing they accurately reproduce atomic shell features.

Findings

Enhancement factors match exact atomic shell peaks

Series expansions provide simple yet accurate functional forms

Potential applicability to molecules and clusters suggested

Abstract

Within the framework of density functional theory, we present a study of approximations to the enhancement factor of the non-interacting kinetic energy functional $T_s[\rho]$. For this purpose, we employ the model of Liu and Parr [S. Liu and R.G. Parr, Phys. Rev. A {\bf 55}, 1792 (1997)] based on a series expansion of $T_s[\rho]$ involving powers of the density. Applications to 34 atoms, at the Hartree-Fock level showed that the enhancement factors present peaks that are in excellent agreement with those of the exact ones and give an accurate description of the shell structure of these atoms. The application of Z-dependent expansions to represent some of the terms of these approximation for neutral atoms and for positive and negative ions, which allows $T_s[\rho]$ to be cast in a very simple form, is also explored. Indications are given as to how these functionals may be applied to molecules and clusters