An accurate description of light-matter interactions is a must to understand numerous phenomena of interest in Chemistry, Biology, Engineering and Physics [1,2]. Charge transfer processes, redox reactivity, photosynthesis, protein folding, and electron transport efficiency in photovoltaic materials are just a few examples of fundamental processes initiated by light [3,4]. Current laser technologies now enable the acquisition of time-resolved images of nuclear dynamics and rearrangements in chemical reactions [5], occurring on the scale of tens of femtoseconds (1 fs = 10^-15 seconds) to picoseconds (1 ps = 10^-12 seconds). Even attosecond resolution (1 as = 10^-18 seconds) has become accessible in the last two decades [6], allowing the observation of electron dynamics triggered at the very early stages of light-matter interaction. Coherent laser sources capable of extracting information with high spatial (atomic) and temporal (down to attoseconds) resolution are available in many laboratories worldwide, including table-top setups and large free-electron laser facilities [4,7]. These sources produce laser pulses across a wide range of frequencies, and an increasing number of experiments and applications are been developed to drive excitation and ionization processes in molecules [1,2,7-9]. A profound theoretical understanding of the mechanisms underlying these light-induced dynamic interactions at their natural time scales is essential to predict and design novel strategies to manipulate chemical properties and reactivity, as demonstrated by the prolific field of Femtochemistry (see Nobel Prize Lecture from A. Zewail in 1999) [5] and the emerging field of Attochemistry (see Nobel Prize Lecture from P. Agostini, F. Krausz and A. L'Huillier in 2023) [6]. In traditional photochemistry studies, excitation typically targets a specific electronic state. However, the use of ultrashort pulses (a few femtoseconds or even attoseconds) [6] can initiate an electronic response characterized not by a stationary state but by a molecular wave packet involving multiple electronic states. Consequently, stationary-state models based on lowest-order perturbation theory are often inapplicable, necessitating the solution of the time-dependent Schrödinger equation. The first step is thus to accurately describe these light-induced electronic dynamics, which requires a proper characterization of both light and matter. Few methodologies implemented in standardized software packages accurately describe the initial wave packet created by interaction with ultrashort pulses during excitation and/or ionization. Moreover, laser parameters such as frequency, pulse duration, and intensity are critically important to the observed dynamics.

This course aims to provide a comprehensive foundation in the theoretical principles underlying the interaction of coherent light pulses with molecules. Through a series of in-depth tutorials, students will explore ultrafast electron and nuclear dynamics in various scenarios, ranging from traditional weak-field approaches to strong-field light-induced phenomena. The Key components of the course include (both via tutorials and practical sessions): i) Pulse Characterization Techniques [10] and Signal Analysis: Introduction to methods employed in High-Order Harmonic Generation (HHG) [11] laboratories and Free Electron Laser (FEL) facilities. ii) Theoretical Background and detailed exploration of weak-field and strong-field light-induced phenomena. iii) Discussion on applications and hands-on experience with open-source codes for describing light in time and frequency domains, and its interaction with molecules using various laser parameters. iv) DFT and TDDFT Approaches: Extensive tutorials and practical sessions on using OCTOPUS software [12,13] to describe light-induced phenomena in large molecules and biomolecules. The course is organized into blocks of tutorials and practical sessions, enabling students to engage with the latest applications of ultrashort laser pulses in Chemistry.

This course is designed for Master's level students and early-stage PhD students in Chemistry and Physics. It is particularly suited for theoretical quantum chemists, and both experimental and theoretical physicists working with light sources or in related fields of atomic and molecular physics and chemistry, and optics. The skills and knowledge gained from this course will provide a solid foundation for research and professional practice in these areas. This course is an important component of the Erasmus Mundus Master in Theoretical Chemistry and Computational Modeling. It includes hands-on tutorials conducted in the computer lab, where students will take their first steps in exploring photo-induced ultrafast phenomena. By the end of the course, students will be well-versed in both the theoretical and practical aspects of light-matter interaction, equipped with the tools and knowledge to advance their research and professional careers in this cutting-edge field.