Convergent sum of gradient expansion of the kinetic-energy density functional up to the sixth order term using Pade approximant

TL;DR

This paper improves the convergence of the gradient expansion of the kinetic-energy density functional up to sixth order by using Pade approximants, reducing divergence issues in atomic and model systems.

Contribution

It introduces a Pade approximant approach to replace the divergent sixth order gradient expansion in kinetic-energy functionals for finite systems.

Findings

Pade approximants improve accuracy over partial sums

Reduction of divergence in kinetic-energy calculations

Effective for atoms and Hooke's law models

Abstract

The gradient expansion of the kinetic energy functional, when applied for atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the integral by replacing the asymptotic series including the sixth order term in the integrand by a rational function. Pade approximants show moderate improvements in accuracy in comparison with partial sums of the series. The results are discussed for atoms and Hooke law model for two electron atoms.