Clusters in strong external perturbations

Many experiments are done for clusters in contact with a substrate. The strong interface interaction modifies the cluster and theoretical simulations become more involved. However, some features can only be explored in connection with a substrate. E.g., the symmetry breaking through a surface gives access to second-harmonic generation (SHG).

The figure beneath shows the results from a TDLDA simulation of SHG for Na₈ attached to a NaCl surface [248]. The spectra resulting from irradiation with a 1.4 eV pulse shows nicely the peaks at multiple frequencies. The SHG signal can be enhanced by increasing the laser intensity. This, however, breaks down at some point where the signals are substantially broadened. This is caused by a large ionization which spoils the otherwise clean dipole response of metal clusters.

TDLDA coupled with molecular dynamics (MD) for ionic motion is a very powerfull tool to describe cluster dynamics. One application is cluster deposition which is illustrated in the figure on the left. It shows Na₆ impinging on an Ar surface (see [328] for further details). The substrate consists of six layers of Ar taken from an appropriate cut of the Ar fcc structure. The Na₆ cluster consist in a ring of 5 ions topped by one ion on the symmetry axix. The Na₆ approaches the surface with the symmetry axis in z direction (=perpendicular) and the top ion facing away from the surface.

The upper panel shows the evolution of the z coordinates, Na ions in red and Ar atoms in green. The cluster is immediately stopped by the surface. A large fraction of impact momentum is transferred at once to the substrate and propagates with velocity of light through the layers. The large dissipation through energy transfer and intrinsic cluster excitation leads to catching of the cluster by the subtrate. The kinetic energies in the lower panel confirm the dramatic and very fast energy exchange at the moment of first impact. Another fraction of energy, not shown in the figure, is turned into the large shape changes.

Clusters in the strong fields of extremely intense lasers show a much different dynamics. Core electrons can be released and contribute strongly to the process. The detailed description at the fully quantum mechanical level of TDLDA becomes untractable. However, the excitations involved validate classical approaches.

The figure to the right shows the result of a molecular dynamics simulation of electronic and ionic dynamics of Na₄₁⁺ under the influence of strong laser fields [332]. Ionization is drawn as function of laser intensity. One sees a sharp kink at a critical intensity of I = 10¹⁶ W/cm². This threshold value is explained by the fact that the Coulomb force from the laser field at the threshold just equals the binding forces of the core electrons. The increase is due to the core electrons which now start to participate in the dynamics. This view is illustrated by separating the contributions from valence (green line) and core electrons (red line). There is indeed zero emission from core electrons up to I = 10¹⁶ W/cm² and the strong increase above that critical intensity is exclusively due to the contribution from core electrons.