Determination of the lowest-energy structure of ${\mathrm{Ag}}_8$ from first-principles calculations

The ground-state electronic and structural properties and the electronic excitations of the lowest-energy isomers of the ${\mathrm{Ag}}_8$ cluster are calculated using density functional theory (DFT) and time-dependent DFT (TDDFT) in real-time and real-space schemes, respectively. The optical spectra provided by TDDFT predict that the $D_{2d}$ dodecahedron isomer is the structural minimum of the ${\mathrm{Ag}}_8$ cluster. Indeed, it is borne out by the experimental findings.

Figure 1

(Color online) Energy levels, partial and total densities of states, and shapes of the delocalized molecular orbitals for the higher-lying occupied and lower-lying unoccupied levels of ${\mathrm{Ag}}_8$ isomers: (a) $T_d$-TT and (b) $D_{2d}$-DD. The orbitals below the Fermi level are double occupied; for these levels only one molecular orbital is presented. The solid vertical line represents the Fermi level.

Figure 2

Comparison between two experimental recorded spectra and the calculated spectra for both (solid line) $D_{2d}$-DD and (dashed line) $T_d$-TT isomers at a temperature of $10\mathrm{K}$. Open circles correspond to the resonant two-photon-ionization (R2PI) spectroscopy on ${\mathrm{Ag}}_8$ clusters in He droplets [21] while the solid triangles are for the excitation spectrum of ${\mathrm{Ag}}_8$ excited with monochromatic Xe light in an Ar matrix [22]. The $D_{2d}$-DD isomer spectrum is in excellent agreement with the experiment whereas the $T_d$-TT isomer spectrum is around $0.31\mathrm{eV}$ blueshifted compared to the R2PI spectrum.