The advent of attoseconds light pulses (1 attosecond = 10^-18 seconds), produced either in tabletop set ups or in kilometer-long X-ray free electron facilities, has opened the way to image and control electronic motion in atoms, molecules and solids at its natural time scale [1]. These tools are currently being used to follow in real time light-induced electron and charge transfer processes as those occurring in some of the most fundamental processes in nature, e.g., photooxidation, electronic transport and radiation damage. For this reason, attosecond light pulses are expected to have an important impact in chemistry, as illustrated by the recently born field of Attosecond Chemistry (see, e.g, recent reviews by one of the applicants [2,3]). The importance of the generation of attosecond pulses was recently recognized by the 2023 Nobel Prize in Physics awarded to Anne L’Huillier, Ferenc Krausz and Pierre Agostini, who, in their Nobel lecture, recognized the crucial role played by theoretical and computational investigations in their discovery and experimental characterization. Regarding applications of this new technology, the huge potential of Attosecond Chemistry has been recognized by the European Research Council and the COST Action association, with the awarded Synergy Grant TOMATTO (“The ultimate time scale in organic molecular opto-electronics, the attosecond”) with € 11,7 million (GA nº 951224) and the AttoChem network (https://www.cost.eu/actions/CA18222/#tabs|Name:parties), respectively, both coordinated by one of the applicants, and the newly born COST Action NEXT (https://www.cost.eu/actions/CA22148/). This field of research is also being further boosted by worldwide constructions of new experimental facilities to generate such pulses, namely high-harmonic generation sources (ELI-ALPS and LaserLab laboratories, all of them international user facilities located in Europe) and X-ray free electron lasers (European XFEL, SwissFEL, FERMI-Italy, LCSL-USA, XFEL-SACLA-Japan). 

As mentioned above, the inherent complexity of experiments performed in these facilities inevitably requires theoretical support able to describe the interaction of attosecond pulses with atoms, molecules, and solids, as well as to design new experimental approaches. This goes beyond the capabilities of commercially available quantum-chemistry packages, especially when ionization processes come into play, as it is the case when XUV and X-ray pulses or intense IR pulses are employed. For this reason, new theoretical methods and computational tools, not yet commercially available, have been developed during the last decade (see, e.g., [2,3] and the special issue in Attosecond Chemistry software published in 2024 in Computer Physics Communications https://www.sciencedirect.com/special-issue/1066VSNVMGQ). The goal of the school is to provide a solid theoretical basis and give access to the newly developed computational tools to describe electron and nuclear dynamics following ionization by attosecond pulses or strong IR fields, and high harmonic generation. The lectures of the school are structured to introduce these methods in increasing order of complexity: state-of-the-art ab-initio and hybrid time-dependent approaches, as well as more advanced methods that can cope with the electronic continuum of molecules, with emphasis on strong-field and weak-field ionization and on methods that properly account for electron correlation in the ionization continuum (see recent applications of the methods introduced in the school in references [4-8]). The school is directed to advanced PhD students and young post-doctoral researchers in atomic and molecular physics, theoretical chemistry and applied mathematics, with an interest in using and developing new software for coherent control of electronic dynamics in systems of chemical interest. 

From our experience in past editions of the school, the ideal format is 5 days, each one devoted to a specific topic, with a morning theoretical session and an afternoon hands-on training session for each topic. The topics will cover high-harmonic generation, strong field ionization, ionization induced by attosecond pulses, attosecond pump-probe spectroscopy and electronic structure calculations in the ionization continuum.  The theoretical sessions will provide an overview of the field, followed by a comprehensive introduction to the formalism, mathematical expressions and a tutorials of the theoretical tools that will be used in the practical sessions held in the afternoons. Both simple and complex systems will be considered: from diatomic molecules to large organic molecules and biomolecules.  It is important to emphasize that the lectures and the training sessions will be imparted by the main actors/developers in the field of Attosecond Chemistry (see the key references below), which is in itself a point of attraction for students.