Significance of energy conservation in coupled-trajectory approaches to non-adiabatic dynamics

Through approximating electron-nuclear correlation terms in the exact factorization approach, trajectory-based methods have been derived and successfully applied to the dynamics of a variety of light-induced molecular processes, capturing quantum (de)coherence effects rigorously. These terms account for the coupling among the trajectories, recovering the non-local nature of quantum nuclear dynamics which is completely overlooked in traditional independent-trajectory algorithms. Nevertheless, some of the approximations introduced in the derivation of some of these methods do not conserve the total energy. We analyze energy conservation in the coupled- trajectory mixed quantum-classical (CTMQC) algorithm and explore the performance of a modified algorithm, CTMQC-E where some of the terms are redefined to restore energy conservation. A set of molecular models is used as test, namely 2-cis-penta-2,4-dienimium cation, bis(methylene) adamantyl radical cation, butatriene cation, uracil radical cation, and neutral pyrazine.