Static polarizabilities and optical absorption spectra of gold clusters (Aun,n=2–14and 20) from first principles

Abstract

Static polarizabilities and optical absorption spectra for the ground state structures of gold clusters (${\mathrm{Au}}_{n}$, $n=2--14$ and 20) are investigated from first principles within static and time-dependent density functional theory. The static polarizabilities of clusters with less than 14 atoms generally increase as a function of size modulated by even-odd oscillations. The polarizabilities of ${\mathrm{Au}}_{14}$ and ${\mathrm{Au}}_{20}$ are noticeably lower due to the shape transition from two-dimensional to three-dimensional structures at $n=14$. The analyses of the optical absorption spectra calculated within the time-dependent local density approximation indicate that the $d$ electrons in ${\mathrm{Au}}_{n}$ clusters are significantly more involved in low-energy transitions and give rise to more quenched oscillator strengths (by screening the $s$ electrons) than in ${\mathrm{Ag}}_{n}$ clusters. These stronger effects of the $d$ electrons in the optical properties of ${\mathrm{Au}}_{n}$ are due to the larger degree of proximity of the $s$ and $d$ levels in the Au atom as compared to the Ag atom, which gives rise to stronger $s\text{\ensuremath{-}}(p)\text{\ensuremath{-}}d$ hybridization in the molecular orbitals of ${\mathrm{Au}}_{n}$. The calculated spectra are found to be in good agreement with experimental data and results from earlier studies for the available sizes.