Isomeric Forms, Polarizabilities, and Optical Absorption Spectra of Ag$_{11}$

First principles based computational results on the atomic structures, static polarizabilities, and optical absorption spectra of eight low-energy isomers of Ag$_{11}$ are presented and discussed. The computations were performed using the static and time-dependent formalisms of the density functional theory. Comparison of the computed spectra with those measured for Ag$_{11}$ embedded in Ar and Ne matrices\footnote{F. Conus, V. Rodrigues, S. Lecoultre, A. Rydio, and C. Felix, J. Chem. Phys. {\bf 125}, 024511 (2006).} shows that it is the spectrum of the lowest energy isomer that exhibits the best overall agreement with the experiment. The theoretical analysis indicates that the $d$ electrons play a more important role in optical transitions in Ag$_{11}$ than in smaller Ag$_n$,$n\le 8$, clusters.\footnote{J. C. Idrobo, S. Ogut, and J. Jellinek, Phys. Rev. B {\bf 72}, 085445 (2005).}