Not so loosely bound: temperature dependent vibrational fingerprints of Au$_N$Kr$_M$ clusters

In order to interpret the vibrational spectra of \textit{neutral} Au$_N$Kr$_M$ clusters, as measured in a Multiple Photon Dissociation Far-IR experiment (P. Gruene \emph{et al.}, Science \textbf{321}, 674 (2008)), we calculated their finite temperature vibrational spectra, by means of all electron density functional theory, including the Tkatchenko-Scheffler van der Waals correction. We surprisingly find that Kr forms weak chemical bonds (binding energy around 0.2 eV per Kr atom) with 1- to 3-fold coordinated Au atoms belonging to small Au$_N$ clusters ($N \leq 4$). Such Au$_N$Kr$_M$ clusters have a vibrational spectrum which is different from the related Au$_N$ clusters. For bigger Au$_N$ clusters, Kr physisorbs to the clusters, forming a complex whose vibrational spectrum is practically identical to the spectrum of the bare cluster. Anharmonicities affect the spectrum by changing (with respect to the harmonic spectrum) the relative intensity of the peaks and by showing new peaks, due to interactions among eigenmodes.