Time dependent density functional theory calculation of van der Waals coefficient C$_{6}$ of alkali-metal atoms Li, Na, K, alkali dimers Li$_{2}$, Na$_{2}$, K$_{2}$ and sodium clusters Na$_{n}$

TL;DR

This study uses all-electron TDDFT to accurately compute van der Waals coefficients for alkali-metal atoms, dimers, and sodium clusters, providing insights into their long-range dispersion interactions.

Contribution

It introduces a comprehensive TDDFT-based approach to calculate $C_6$ coefficients for alkali metals, dimers, and clusters, extending previous methods to larger sodium clusters.

Findings

Calculated $C_6$ coefficients for Li, Na, K atoms and their dimers.

Determined $C_6$ for sodium clusters with 2 to 20 atoms.

Validated TDDFT results with Casimir-Polder relation.

Abstract

In this paper we employ all-electron time dependent density functional theory (TDDFT) to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) $C_{6}$ of alkali-metal atoms Li, Na, K, alkali-metal atom dimers Li$_{2}$, Na$_{2}$, K$_{2}$ and sodium clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder expression which relates it to the frequency dependent linear polarizabilty at imaginary frequencies. The frequency dependent polarizabilities are calculated by employing TDDFT--based complete sum-over-states expressions for the atoms, and direct TDDFT linear response theory for the closed shell dimers and clusters.