Comparison of van der Waals coefficient C$_{6}$ of sodium clusters obtained via spherical jellium background model and all-electron ab-initio method

TL;DR

This study compares the van der Waals coefficient C6 of sodium clusters calculated using all-electron ab initio methods and the spherical jellium background model within time-dependent density functional theory, assessing accuracy and structural effects.

Contribution

It provides a direct comparison between ab initio and jellium model calculations of C6 for sodium clusters, highlighting the impact of ionic structure on dispersion coefficients.

Findings

Jellium model results closely match ab initio calculations for small clusters.

Ionic structure significantly influences the van der Waals coefficient.

The study validates the use of simplified models for certain cluster sizes.

Abstract

In this paper we employ two distinct approaches - all-electron \textit{ab initio} method and the spherical jellium background model- within time dependent density functional theory to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) $C_{6}$ of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation. All the calculations are carried out with local density approximation for exchange-correlation energy functional. These two sets of results are compared to assess the accuracy of jellium based results and to ascertain the effect of detail ionic structure of the clusters on the van der Waals coefficient.