Simulating passage through a cascade of conical intersections with collapse-to-a-block molecular dynamics

The Ehrenfest with collapse-to-a-block (TAB) molecular dynamics approach was recently introduced to allow accurate simulation of nonadiabatic dynamics on many electronic states. Previous benchmarking work has demonstrated it to be highly accurate for modelling dynamics in one-dimensional analytical models, but nonadiabatic dynamics often involves conical intersections, which are inherently two-dimensional. In this report, we assess the performance of TAB on two-dimensional models of cascades of conical intersections in dense manifolds of states. Several variants of TAB are considered, including TAB-w, which is based on the assumption of a Gaussian rather than exponential decay of the coherence, and TAB-DMS, which incorporates an efficient collapse procedure based on approximate eigenstates. Upon comparison to numerically exact quantum dynamics simulations, it is found that all TAB variants provide a suitable description of the dynamical passage through a cascade of conical intersections. The TAB-w approach is found to provide a somewhat more accurate description of population dynamics than the original TAB method, with final absolute population errors $ \leq 0.013 $ <= 0.013 in all cases. Even when only four approximate eigenstates are computed, the use of approximate eigenstates was found to introduce minimal additional error (absolute population error $ \leq 0.018 $ <= 0.018 in all models).