Assessment of the Performance of Long-Range-Corrected Density Functionals for Calculating the Absorption Spectra of Silver Clusters

We assess the accuracy of several long-range-corrected (LC-) density functionals for the prediction of absorption spectra of silver clusters by time-dependent density functional theory. Several types of LC-functionals, with the exact Hartree-Fock exchange at long-range, are used: those applying the long-range correction to a standard GGA-type functional (LC-BP86, LC-ωPBE) or to a local meta-GGA functional (LC-M06L) and two global hybrid functionals (CAM-B3LYP and ωB97x). The spectra calculated with those density functionals are in good agreement with the recent accurate experimental measurements. We show that CAM-B3LYP and ωB97x are some of the most accurate functionals for evaluating the electronic excitation energies, while LC-M06L is more effective in reducing the occurrence of spurious states. The long-range correction appears to be essential in describing the absorption spectra of large clusters. The description of the plasmon-like band with LC functionals as transitions associated with excitations from s orbitals to s + p orbitals is in fairly good agreement with the classical interpretation as a collective excitation of valence s electrons.