Light provides one of the most detailed windows into molecules and matter. Modern light sources allow the probing of equilibrium and non-equilibrium phenomena with Å‐level spatial resolution and femto‐ to attosecond temporal precision. Advances in ultrafast laser technology, together with the rise of X-ray free‐electron lasers and next-generation synchrotron sources, have repeatedly pushed the boundaries of spectroscopic methods from low‐frequency collective modes in biomolecules to electronic and core‐level dynamics. An extensive toolbox of linear and multidimensional spectroscopic techniques now spans the entire electromagnetic spectrum. Terahertz (THz) pulses can coherently drive intermolecular and lattice vibrations in solids and soft matter [1], Mid‐IR and Raman methods map vibrational energy (re)distribution in liquids and vibrational signatures of individual modes in complex molecules [2]. Visible spectroscopy tracks ultrafast charge dynamics in chromophores [3] and photochemical molecular pathways [4], while X-ray sources from free-electron lasers and high-harmonic generation setups enabled time-resolved X-ray diffraction of gas‐phase [5] and condensed systems [6].

Despite sharing common scientific goals, the respective communities have traditionally operated in relative disconnection from each other, relying on different approximations, targeting different observables, and employing distinct numerical implementations. This disconnection manifests, among other symptoms, in the fact that schools, conferences, and workshops are often dedicated to a specific frequency window (e.g. IR spectroscopy) or to simulation methods targeting a class of specific processes (e.g. vibrational dynamics). Opportunities for dialogue and the building of a shared language are lacking. In fact, while preparing this proposal,  it became evident that even foundational terms like ab initio or quantum dynamics carry different meanings across communities.

To address this fragmentation, the proposed CECAM school brings together researchers from diverse backgrounds to foster mutual understanding and build lasting conceptual bridges. Over five days, participants will engage with both the theoretical foundations and practical implementations of spectroscopies across different communities. We will highlight the fact that despite their apparent differences, all spectroscopic methods can be traced back to a common starting point: a light–matter Hamiltonian that includes the quantum description of electronic, nuclear, and photonic degrees of freedom. From this unified framework, we will explore how different approximations—introduced at various stages—lead to the distinct theoretical approaches adopted in each field. 

The first part of the school will focus on approaches that solve the exact quantum molecular dynamics in reduced dimensionality. Within this framework, molecules are treated fully quantum-mechanically, while light is treated classically as an external perturbation within the dipole approximation. From the matter perspective, this means that the full electron + nuclear wavefunction is accessible, offering a great level of detail and information, and the accurate treatment of non-Born-Oppenheimer dynamics. From the light perspective, this means that spectroscopic signals are conveniently calculated via the response function approach (RFA) [7], which is however only valid in the weak field limit. Recently, the RFA has been used to design and simulate several spectroscopic signals of femtosecond molecular photochemistry using novel X-ray pulse sources [8], including stimulated X-ray Raman [9], transient X-ray absorption and transmission [10], and many others [11].

In the second part, we will shift the focus to longer time scales with more degrees of freedom and study larger molecules in explicit environments (solvent, substrate, etc). In these cases, it is common practice to apply the Born-Oppenheimer approximation and take the classical limit for the nuclei, while keeping the electrons quantum, leading to (finite temperature) molecular dynamics (MD) approaches. To make these simulations computationally tractable, while retaining an explicit description of the electrons, electron–electron interactions are typically simplified using ground-state density functional theory (DFT). This approach, commonly referred to as ab initio molecular dynamics (AIMD), enables the simulation of vibrational spectroscopies such as infrared (IR) and Raman [12,13], as well as surface-specific techniques like sum-frequency generation (SFG) [14,15]. To access larger system sizes and longer simulation timescales, forces can be derived from classical interatomic potentials, facilitating the convergence of multidimensional spectroscopic observables such as THz-Raman spectra [16]. Alternatively, forces can be learned directly from first-principles data using machine-learning (ML) models, enabling ML-driven molecular dynamics and spectroscopy [17-21].  Through path integral techniques, the quantum nature of the nuclei can be recovered, which is particularly important for systems containing light atoms, such as hydrogen [22-24].

The third part of the school will explore what happens when the primary interest shifts from vibrational to electronic dynamics. In this context, the electron dynamics at the DFT level can be incorporated by considering its time-dependent version (TDDFT), where the exchange-correlation functionals are usually adiabatic. With this method, UV-visible absorption [25], circular dichroism [26], inelastic X-ray scattering, and electron energy loss [27], and other spectroscopies can be computed. Finally, there are situations in which strong light-matter coupling demands an explicit treatment of the photons [28]. These can be reintroduced either by dressing the Kohn-Sham Hamiltonian with electron-photon exchange-correlation potentials (known as quantum-electrodynamics DFT, or QEDFT) [29] or by a semiclassical treatment of the photons solving Maxwell’s equations (the Maxwell-TDDFT method)[30]. These methods enable the calculation of spectra in cavities or arbitrary electromagnetic environments [31], and can account for polaritonic phenomena, radiative lifetimes, superradiance, and many more.

This school brings together leading experts from exact quantum dynamics, ab initio MD, ML‐enabled simulations, and Maxwell–TDDFT to forge a common language and cross‐fertilize ideas. Lectures will cover both the fundamental principles and the latest advances in each area, highlighting current applications and open challenges. Complementing the lectures, hands-on tutorials will reinforce foundational concepts and provide important hands-on experience on several popular computational approaches (see hands-on section below).

By spanning the electromagnetic spectrum and the hierarchy of theoretical methods, this school will equip PhD students and postdocs with a unified, multi‐scale, and inter-community perspective on quantum dynamics and spectroscopy. Participants will leave with both a solid grounding in foundational techniques and direct experience of the latest computational frontiers, ready to tackle open challenges in molecular and materials science.