Discrete variable representation method calculation of the electronic structure of noble gas atoms

TL;DR

This paper introduces a novel computational approach using the discrete variable representation method to calculate the electronic structure of noble gas atoms by solving a transformed Schrödinger equation.

Contribution

It applies the DVR method with Coulomb wave functions to efficiently compute atomic charge densities and energies, offering an alternative to finite difference techniques.

Findings

Accurate ground state charge densities obtained

Energies of noble gas atoms calculated successfully

Method implemented in Mathematica 7.0

Abstract

We have been calculated the ground state charge densities and energies of noble gas atoms through a single time dependent quantum fluid Schr$\ddot{o}$dinger equation. By using imaginary - time, the Schr$\ddot{o}$dinger equation has been transformed into diffusion equation. This equation numerically solved through discrete variable representation (DVR) method. Instead of the usual finite difference method the radial coordinate is discretized using the discrete variable representation constructed from Coulomb wave functions. Our calculations were performed using the Mathematica 7.0 programm.