Significance of Energy Conservation in Coupled-Trajectory Approaches to Nonadiabatic 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 nonlocal nature of quantum nuclear dynamics that 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 a test, namely, 2-cis-penta-2,4-dienimium cation, bis-(methylene) adamantyl radical cation, butatriene cation, uracil radical cation, and neutral pyrazine.