Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters

TL;DR

This study uses all-electron time-dependent density functional theory to accurately calculate van der Waals coefficients and static polarizabilities of sodium clusters, revealing a strong correlation between cluster volume and dispersion interactions.

Contribution

It introduces a detailed ab-initio approach with two exchange-correlation potentials to compute dispersion coefficients and polarizabilities of sodium clusters, validating the accuracy against experimental data.

Findings

SAOP results closely match experimental data

C6 scales quadratically with cluster volume

Calculated interactions for cluster-Ar and cluster-N2 are provided

Abstract

In this paper we employ all-electron \textit{ab-initio} time-dependent density functional theory based method 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. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical average of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C_{6} and static polarizability are quite accurate and very close to the experimental results. We examine the relationship between volume of the cluster and van der Waals coefficient and find that to a very high degree of correlation C_{6} scales as square of the volume. We also present the results for van der Waals coefficient corresponding to cluster-Ar atom and cluster-N_{2} molecule interactions.