The core of our activities concerns the theoretical analysis of the dynamics of molecules and clusters. The method of choice for most of our studies is time-dependent density functional theory. One can sort our activities along three major directions of research: intrinsic dynamical system properties investigated with moderate external excitations (perturbative regime), response to strong external fields analyzed with a bunch of different observables taking care particularly of information from electron emission, and development of the necessary numerical as well as theoretical tools. The majority of applications deals with free molecules and clusters. One branch of studies deals also with clusters in contact with polarizable media (raregas matrices, insulating surfaces).

Theoretical developments

Understanding of cluster dynamics requires elaborate theoretical tools. Time-Dependent Density Functional Theory (TDDFT) represents here a robust starting point which allows to address a great variety of situations. We use TDDFT at various levels of sophistication. Basis is the most efficient, Time-Dependent Local-Density Approximation (TDLDA). It is augmented by a Self-Interaction Correction (SIC) for a proper description of electron emission and associated observables. Ionic motion is propagated simultaneously by classical Molecular Dynamics (MD) amounting together to TDLDA-MD. Very energetic processes allow semi-classical approximations for which we use mostly the Vlasov-LDA approximation. The latter allows a relatively simple extension by dynamical correlations with a collision term which accounts properly for the Pauli principle leading to the Vlasov-Uehling-Uhlenbeck (VUU) equation.
Recent developments focus on the implementation of such dynamical correlations in the fully quantum mechanical framework of TDLDA. A robust, phenomenological route is followed with the Relaxation-Time Approximation (RTA) known from bulk matter and implemented now for finite Fermion systems. An exact evaluation of the quantum-mechanical collision is prohibitively expensive. With Stochastic TDLDA (STDLDA), we render the case manageable by a stochastic evaluation of the collisions. Full STDLDA can cope even with large fluctuations of the mean field as they are typical for violent dynamical processes. Further savings are possible in the regime of small statistical fluctuations which allows to use one average mean field delivering Average STDLDA (ASTDLDA). In any case, the dynamical correlations thus implemented allow a pertinent description of dissipation in electron dynamics which becomes an important ingredient at longer times (in metal clusters typically > 50 fs).
Numerically, we solve TDLDA and related approaches in coordinate-space grid representations, fully three-dimensional if necessary and in the much faster cylindrically symmetric 2D grid if the case allows. All grids are surrounded bands generating absorbing boundary conditions to allow a correct description and analysis of electron emission.

Intrinsic dynamical properties of molecules and clusters

At moderate perturbations, the system response dominantly reflects its own (structure and dynamical) properties. The most prominent feature is the optical response which characterizes the coupling of photons to the electrons of the system. We obtain it from TDLDA driven in the regime of weak perturbations [Cal97]. As optical response is the doorway to almost all further dynamical processes, it is regularly scanned before starting with more involved scenarios (see below).
The ionic dynamics of molecules and clusters is explored by pump and probe scenarios, again driven in the regime of moderate excitations to explore the system as such without too much perturbation.

Free clusters in strong external fields

When applying stronger external fields, a world of dynamical scenarios is opened as, e.g., multi-photon ionization, higher harmonic generation, multi-fragmentation, or Coulomb explosion [Fen10].
A large part of our activities is concerned with dynamical information which can be obtained from electron emission. The simplest and most widely used observable is the net ionization, often in connection with time resolved measurements. The trends of ionization with systematically varied laser parameters (frequency, intensity, pulse length, delay times) contain already a lot of valuable information. More can be obtained by looking at the emitted electrons in detail collecting the distributions of kinetic energies, called Photo-Electron Spectra (PES), or angular directions, in the ideal case even both together as Angular Resolved PES (ARPES). Our numerical tools (coordinate-space representation with absorbing boundary conditions) to solve TDLDA allow a rather convenient computation of all these detailed distributions, if needed even in time resolved manner. We apply them to simulate measurements in raregas atom, metal clusters, and C₆₀ [Wop15].
The detailed distributions ARPES indicate indicate limitations of a mere mean-field description as in TDLDA. They overestimate, e.g., the forward/backward emission along the laser polarization axis. This calls for dissipation in electron dynamics as it is given by dynamical correlations. This is the main line of present development and applications.

Molecules and clusters in contact with a polarizable environment

Clusters can be more easily handled experimentally when they are produced in contact with an environment (deposited on a surface or embedded in a matrix). Thus a large amount experimental data was produced under these conditions. We have thus developed a simplified description of the environment in terms of classical Molecular Mechanics (MM) taking care to include a proper modeling of its dynamical polarizability. This is coupled to the standard Quantum-Mechanical (QM) handling of the electron cloud in the active molecule or cluster, yielding together QM/MM method. This hierarchical approach allows us to explore various dynamical scenarios, as optical response of deposited clusters, deposition processes, irradiation of embedded clusters by an intense laser field, etc with sufficiently large samples for the environment [Din09].