How we deal with cluster dynamics

The understanding of the complicated dynamical scenarios such as the ones described previously requires dedicated theoretical modelling. Cluster physics and even more so cluster dynamics lays at the interface of several fields of science, especially chemistry and physics. The theory of cluster dynamics has thus borrowed inspiration from these various domains to develop its own and original methods.

Not surprisingly, a direct transposition of methods well developed in a given field only provides guidelines and a starter for further developments. Still, it also allows to benchmark new developments on well established test cases. Cluster dynamics has thus benefited a lot from experience gained in chemistry, especially at the side of moderate excitation, and in physics for more violent scenarios, especially from solid state and nuclear physics. The description of cluster dynamics is made difficult by two basic problems: The fact that one would like to deal with large (although finite) systems and the fact that electrons and ions move at awfully different time scales (typically a factor 100). This implies huge simulation times to be able to resolve simultaneously electronic and ionic dynamics. One thus needs both robust and simple approaches to overcome these two difficulties of time scales and system size.

Fig.1: Irradiation of Na9+ by a laser pulse.

In the case of violent excitation, the most robust and simple approaches rely on Density Functional Theory, a theory developed since the mid 60's for electronic systems and which has met impressive successes, in bulk materials as well as in finite molecules.

???In density functional theory, the complicated many-body electronic problem is simplified as it can be shown that the one body electronic density constitutes a key ingredient, espcially for computing the energy of the system. The extension of this theory to truly time-dependent processes is more recent and still in development and cluster dynamics offers here a fascinating domain of applications and testing.???

In order to illustrate the capabilities of such methods we present here two examples of cluster response to violent external excitation. Figure 1 shows the irradiation of Na₉⁺ by a laser pulse, while Figure 2 displays a collision of Na₉⁺ with Ar⁸⁺ considered as an energetic projectile. The actual dynamical scenarios can be visualized through the two movies below (click on the image to download the corresponding movie). Various characteristics of the dynamics, especially in terms of time scales, are presented in both figures. These cartoons demonstrate strong interactions between electrons and ions and a complex non-adiabatic dynamics.

Fig.2: Collision of Na9+ with Ar8+