Grid-based density functional calculation of many-electron systems

TL;DR

This paper presents a grid-based density functional approach for calculating electronic properties of many-electron systems, demonstrating accurate results without auxiliary basis sets using Fourier convolution techniques.

Contribution

It introduces a novel 3D Cartesian grid method combined with Fourier convolution for efficient and accurate density functional calculations without auxiliary basis sets.

Findings

Excellent agreement with reference values for molecules and atoms

Accurate calculation of total energies and ionization energies

Efficient classical Coulomb potential computation

Abstract

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set, electronic density and the two-body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange-correlation potential, while Hay-Wadt-type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom-centered grid as well as the grid-free calculation. Results for 3 atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many-electron systems.