A new density functional method for electronic structure calculation of atoms and molecules

TL;DR

This paper introduces a novel Cartesian coordinate grid-based variational DFT method for accurate electronic structure calculations of atoms and molecules, demonstrating its feasibility and advantages over traditional atom-centered grid approaches.

Contribution

The paper presents a new CCG-based DFT methodology that directly builds basis sets and potentials on a 3D Cartesian grid, offering an alternative to atom-centered grids with demonstrated accuracy.

Findings

Successfully applied to various chemical systems with different XC functionals.

Achieved accurate calculations of energies, ionization energies, and potential energy curves.

Demonstrated clear advantages and potential of the CCG approach in quantum chemistry.

Abstract

This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies are discussed at some length. Within the realm of non relativistic Hohenberg-Kohn-Sham (HKS) DFT and making use of the familiar LCAO-MO principle, relevant KS eigenvalue problem is solved numerically. Unlike the commonly used atom-centered grid (ACG), here we employ a 3D cartesian coordinate grid (CCG) to build atom-centered localized basis set, electron density, as well as all the two-body potentials directly on grid. The Hartree potential is computed through a Fourier convolution technique via a decomposition in terms of short- and long-range interactions. Feasibility and viability of our proposed scheme is demonstrated for a series of chemical systems; first with homogeneous, local-density-approximated XC functionals followed by non-local, gradient- and Laplacian-dependent functionals. A detailed, systematic analysis on obtained results relevant to quantum chemistry, are made, \emph{for the first time}, using CCG, which clearly illustrates the significance of this alternative method in the present context. Quantities such as component energies, total energies, ionization energies, potential energy curve, atomization energies, etc., are addressed for pseudopotential calculations, along with a thorough comparison with literature data, wherever possible. Finally, some words on the future and prospect of this method are mentioned. In summary, we have presented a new CCG-based \emph{variational} DFT method for accurate, dependable calculation of atoms and molecules.