An exact-factorization perspective on quantum-classical approaches to excited-state dynamics

Trajectory-based quantum-classical schemes to excited-state dynamics are the most promising approaches to study photochemical and photophysical phenomena occurring in complex molecular systems. Theoretical developments in this field are mainly directed towards proposing generally-applicable approximations to the full quantum-mechanical problem, able to capture the key features of the mechanisms of interest. The task is indeed hard. Therefore, comparisons among approximate methods, and comparisons with exact results for typical model examples provide guidelines for theoreticians who decide to embark on this path. In this work, Ehrenfest dynamics and surface hopping will be analyzed adopting the exact-factorization perspective. A theoretical investigation will be supported by numerical results on a two-electronic-state one-dimensional model system. Numerical results based on the quantum-classical algorithm derived from the exact factorization will be presented as well, allowing to point out strengths and deficiencies of Ehrenfest dynamics and surface hopping. The combined analysis of the potential that drives classical trajectories and of quantum decoherence is essential to highlight similarities or differences among these quantum-classical approaches.