Exact-factorization-based methods for coupled electrons, ions, and photons.

The description of excited state phenomena requires both an adequate description of the electronic structure and electron-nuclear correlation, while calling for computationally efficient methods to deal with the size and complexity of the systems of interest. This talk focusses on the electron-nuclear correlation problem within the exact factorization (XF) framework, which provides exact potentials that drive different coupled quantum subsystems, and, more practically, provides a rigorous starting point for approximate methods. We show that XF-derived modifications to the surface-hopping equations contain terms that correctly lead to population transfer and decoherence, while retaining a computationally-efficient independent trajectory picture, with particularly improved predictions of non-adiabatic dynamics when several electronic states become coupled. We further discuss the extensions of these methods to polaritonic systems where strong light-matter coupling through confinement modifies the chemical and physical properties of matter. Finally, the exact potential driving the photons is used to analyze the accuracy of Ehrenfest methods adapted to account for many photon modes.