Density functional calculation of many-electron systems in cartesian coordinate grid

TL;DR

This paper presents a density functional method using Cartesian grids and Fourier convolution for accurate calculations of atoms and molecules, demonstrating good agreement with existing results and offering a promising approach for many-electron systems.

Contribution

The paper introduces a novel density functional approach on Cartesian grids with Fourier convolution, enabling efficient and accurate calculations of atomic and molecular properties.

Findings

Accurate total and ionization energies for selected atoms and molecules.

Good agreement with literature for pseudopotential and all-electron calculations.

Demonstrates the method's potential for reliable many-electron system computations.

Abstract

A recently developed density functional method, within Hohenberg-Kohn-Sham framework, is used for faithful description of atoms, molecules in Cartesian coordinate grid, by using an LCAO-MO ansatz. Classical Coulomb potential is obtained by means of a Fourier convolution technique. All two-body potentials (including exchange-correlation (XC)) are constructed directly on real grid, while their corresponding matrix elements are computed from numerical integration. Detailed systematic investigation is made for a representative set of atoms/molecules through a number of properties like total energies, component energies, ionization energies, orbital energies, etc. Two nonlocal XC functionals (FT97 and PBE) are considered for pseudopotential calculation of 35 species while preliminary all-electron results are reported for 6 atoms using the LDA XC density functional. Comparison with literature results, wherever possible, exhibits near-complete agreement. This offers a simple efficient route towards accurate reliable calculation of many-electron systems in the Cartesian grid. Future prospect of this method is also discussed.