Electrons as probes of dynamics in molecules and clusters: A contribution from Time Dependent Density Functional Theory

Abstract

There are various ways to analyze the dynamical response of clusters and molecules to electromagnetic perturbations. Particularly rich information can be obtained from measuring the properties of electrons emitted in the course of the excitation dynamics. Such an analysis of electron signals covers observables such as total ionization, Photo-Electron Spectra (PES), Photoelectron Angular Distributions (PAD), and ideally combined PES/PAD. It has a long history in molecular physics and was increasingly used in cluster physics as well. Recent progress in the design of new light sources (high intensity, high frequency, ultra short pulses) opens new possibilities for measurements and thus has renewed the interest on these observables, especially for the analysis of various dynamical scenarios, well beyond a simple access to electronic density of states. This, in turn, has motivated many theoretical investigations of the dynamics of electronic emission for molecules and clusters up to such a complex and interesting system as C60. A theoretical tool of choice is here Time-Dependent Density Functional Theory (TDDFT) propagated in real time and on a spatial grid, and augmented by a Self-Interaction Correction (SIC). This provides a pertinent, robust, and efficient description of electronic emission including the detailed pattern of PES and PAD. A direct comparison between experiments and well founded elaborate microscopic theories is thus readily possible, at variance with more demanding observables such as for example fragmentation or dissociation cross sections.The purpose of this paper is to describe the theoretical tools developed on the basis of real-time and real-space TDDFT and to address in a realistic manner the analysis of electronic emission following irradiation of clusters and molecules by various laser pulses. After a general introduction, we shall present in a second part the available experimental results motivating such studies, starting from the simplest total ionization signals to the more elaborate PES and PAD, possibly combining them and/or resolving them in time. This experimental discussion will be complemented in a third part by a presentation of available theoretical tools focusing on TDDFT and detailing the methods used to address ionization observables. We shall also discuss the shortcomings of standard versions of TDDFT, especially what concerns the SIC problem, and show how to improve formally and practically the theory on that aspect. A long fourth part will be devoted to representative results. We shall illustrate the use of total ionization in pump and probe scenarios with fs lasers for tracking ionic dynamics in clusters. More challenging from the experimental point of view is pump and probe setups using attosecond pulses. The effort there is more on the capability to define proper signals to be measured/computed at such a short time scale. TDDFT analysis provides here a valuable tool in the search for the most efficient observables. PES and PAD will allow one to address more directly electronic dynamics itself by means of fs or ns laser pulses. We shall in particular discuss the impact of the dynamical regime in PES and PAD. We shall end this fourth part by addressing the role of temperature in PES and PAD. When possible, the results will be directly compared to experiments. The fifth part of the paper will be devoted to future directions of investigations. From the rich choice of developments, we shall in particular address two aspects. We shall start to discuss the information content of energy/angular spectra of emitted electrons in case of excitation by swift and highly charged ions rather than lasers. The second issue concerns the account of dissipative effects in TDDFT to be able to consider longer laser pulses where the competition between direct electron emission and thermalization is known to play a role as, e.g., in experiments with C60. Although such questions have been superficially addressed in the simple case of alkaline clusters by means of semi-classical methods, no satisfying quantum formulation, compulsory for most realistic systems, is yet available. First encouraging results will be presented on that occasion. We shall finally give a short conclusion.