# DFT calculations of atoms and molecules in Cartesian grids

## TL;DR

This paper develops a Cartesian grid-based variational DFT method for atoms and molecules, offering accurate results and a practical alternative to traditional atom-centered grid approaches, with initial steps towards non-uniform grids to reduce computational costs.

## Contribution

The paper introduces a Cartesian grid-based variational DFT approach for atoms and molecules, including a Fourier convolution method for Coulomb potentials and initial non-uniform grid implementation.

## Key findings

- Accurate calculation of energies and properties using Cartesian grids.
- Effective Coulomb potential computation via Fourier convolution and Ewald decomposition.
- Potential reduction in computational overhead with non-uniform grids.

## Abstract

Density functional theory (DFT) has emerged as one of the most versatile and lucrative approaches in electronic structure calculations of many-electron systems in past four decades. Here we give an account of the development of a variational DFT method for atoms and molecules \emph{completely} in a Cartesian grid. The non-relativistic Kohn-Sham equation is solved by using an LCAO-MO ansatz. Atom-centered localized basis set, electron density, molecular orbitals, two-body potentials are directly constructed on the grid. We adopt a Fourier convolution method for classical Coulomb potentials by making an Ewald-type decomposition technique in terms of short- and long-range interactions. It produces quite accurate and competitive results for various properties of interest, such as component energy, total energy, ionization energy, potential energy curve, atomization energy, etc. Both local and non-local functionals are employed for pseudopotential as well as full calculations. While most results are offered in a \emph{uniform} grid, initial exploratory attempts are made in a \emph{non-uniform} grid, which can significantly reduce the computational overhead. This offers a practical, viable alternative to atom-centered grid-based implementations, currently exploited by the majority of programs available world-wide.