  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 modeling 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 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 in all models).
